Recorded data and provenance for the associated calculation.
| experiment_key | interval-positive-count-pair-contact-bound |
|---|---|
| created_utc | 2026-10-12T11:44:31.782115+00:00 |
| interval_decimal_precision | 80 |
| evaluations | 1362 |
View complete data
{
"experiment_key": "interval-positive-count-pair-contact-bound",
"created_utc": "2026-10-12T11:44:31.782115+00:00",
"interval_decimal_precision": 80,
"sources": {
"experiments/positive-count-contact-bound.py": "096c1aa015ceec88f98b83b8cd525243064b513b19f9866b339f1e2813b097c8",
"experiments/positive-count-contact.py": "ace032e592c4e37fd921faacee4376b0181965e9cfc29db3ad9d8b00808f10f6",
"experiments/positive-count-wave.py": "80cb47fd98590a2a54a8287f8fa24fcbe0b2a9edb48869402aa98a5166e487dc",
"experiments/convex-count-envelope.py": "6650f29a11b56cf16794e50c809fb92cf6a25829453698095912b357307ad8d0",
"experiments/forward-count-action.py": "5f1dd9a03cf8e6b07a56d507791fed8ff859f10abf22bb755c60c3bd1ed6d909",
"experiments/inverse-current-radial.py": "52d9f1c981635192e06d96b11f0b1e4e5e2d1bf3d5ed420b59411fd45ef7be80",
"experiments/excited-shell-orientation-current.py": "508484d445dbb86da9f88a31642268b5a1dba8264588e6f48ebb6cc00cf9c264"
},
"evaluations": 1362,
"cases": [
{
"depth": 2,
"shell_levels": [
75,
80
],
"other_unsmoothed_chart_minimum_source_cost_lower_bound": "0.00118886451983703988674766566485251392854995062323744927335233525363175216764394045735950825297041807",
"common_smoothing_width_interval": "[0.00003970760187135478964154730942511701397745508053711967522862079237823054779163585056431, 0.00003970760187135478964154730942511701397745508053711967522862079237823054792301403910759]",
"smoothing_bands": [
{
"lower_level": 79,
"upper_level": 80,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.00226698769395558781615541758053181529948781876959492507039469921497872897212746884891861414640546673",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.003118313282530072171219514984056283233035340261527955416848419041446037224923517262004, 0.003118313282530072171219514984056283233035340261527955416848419041446037226333367833535]",
"[0.0031693447302471709930655903616562592530492810285701714398169991987194773740702315017, 0.003169344730247170993065590361656259253049281028570171439816999198719477375649258740092]",
"[0.003220376177964269814911665739256235273063221795612387462785579355992917523216945741397, 0.003220376177964269814911665739256235273063221795612387462785579355992917524965149646649]",
"[0.003161922719217543017634388059124017254525425267244846522082867343903342524893722310046, 0.003161922719217543017634388059124017254525425267244846522082867343903342526869098461564]",
"[0.002942298169771657284148205230190310091910754938717923207116234969311502337742358613771, 0.002942298169771657284148205230190310091910754938717923207116234969311502340125727861371]",
"[0.002559826635666475270857932864636947653046296802097264141261652782759904898409782169012, 0.002559826635666475270857932864636947653046296802097264141261652782759904901603162616306]",
"[0.002266987693955587816155417580531815299487818769594925070394699214978728972127468848919, 0.002266987693955587816155417580531815299487818769594925070394699214978728976912161201382]",
"[0.002343910362074231769456571730410304920698070323896370985217869895554112136194211905857, 0.00234391036207423176945657173041030492069807032389637098521786989555411214405873384325]",
"[0.002785182763733509989727992773783595904555423969955473833909925908987751103309580557895, 0.002785182763733509989727992773783595904555423969955473833909925908987751117342765847008]",
"[0.003301701568432187505937201500957562250498102663477986172108296496964941027633351830368, 0.003301701568432187505937201500957562250498102663477986172108296496964941055186990043349]",
"[0.0036360222132117263575038645078773087043853504763358671728870771937433961916942640665, 0.003636022213211726357503864507877308704385350476335867172887077193743396252034645810966]",
"[0.003789146380373930702778218681170882871997881132702574248967626108001348368141755643512, 0.003789146380373930702778218681170882871997881132702574248967626108001348512809613708613]",
"[0.00381863945886588939499286889823114053964280689285406341923254006551238040082347743393, 0.00381863945886588939499286889823114053964280689285406341923254006551238076352647400311]",
"[0.003848132537357848087207519115291398207287732653005552589497454023023412268984792351605, 0.003848132537357848087207519115291398207287732653005552589497454023023413178763779855275]"
]
},
{
"lower_level": 78,
"upper_level": 79,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.006630453641630148511713614511768567738478041734141367542139883153661830400313595213325386180840372297",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.007428762815660417322201056961718104361810944336491557334275317507809462460077698877845, 0.007428762815660417322201056961718104361810944336491557334275317507809462461095960560994]",
"[0.007458255894152376014415707178778362029455870096643046504540231465320494601719656549472, 0.007458255894152376014415707178778362029455870096643046504540231465320494602852569263937]",
"[0.007487748972644334706630357395838619697100795856794535674805145422831526743361614221098, 0.007487748972644334706630357395838619697100795856794535674805145422831526744609177958644]",
"[0.007424141904669774794190804074607790977461733835711038621811254764977950166558395344449, 0.007424141904669774794190804074607790977461733835711038621811254764977950167976198834804]",
"[0.007222428895018659572357187121949443644639996101940015972726512732617213431014402605088, 0.007222428895018659572357187121949443644639996101940015972726512732617213432774359759744]",
"[0.006879979818635743158569348939581441459451453716053317666583451076217352173386038070655, 0.006879979818635743158569348939581441459451453716053317666583451076217352175868465293997]",
"[0.006630453641630148511713614511768567738478041734141367542139883153661830400313595213325, 0.006630453641630148511713614511768567738478041734141367542139883153661830404256160041872]",
"[0.006731789701709230955699694963954649414896450121191239053429338153962147292811116078082, 0.006731789701709230955699694963954649414896450121191239053429338153962147299622387605079]",
"[0.007172452570408702631389454683180921974262972863447619470463605146346091267902064029663, 0.007172452570408702631389454683180921974262972863447619470463605146346091280525655980993]",
"[0.007674480715813171186117484197848404333362181105436673436201531397587932733549673155043, 0.007674480715813171186117484197848404333362181105436673436201531397587932759052596127798]",
"[0.007991851035811724601323543590633374012259515440878748750089045625419069220902289625592, 0.007991851035811724601323543590633374012259515440878748750089045625419069277919436851899]",
"[0.008125280929816240192687123451517640153790719589230639321222554923955510933745858689812, 0.008125280929816240192687123451517640153790719589230639321222554923955511072280609280099]",
"[0.008133023951208877267657330625188312376809007851264688527292702666603004342971253149975, 0.008133023951208877267657330625188312376809007851264688527292702666603004692881623651247]",
"[0.008140766972601514342627537798858984599827296113298737733362850409250497592392294745703, 0.008140766972601514342627537798858984599827296113298737733362850409250498473287029118768]"
]
},
{
"lower_level": 77,
"upper_level": 78,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.008238766921348600640422870677613921929818861790201661209345809646222094059383406310949486394512868791",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.009067019745648904260292805536260406118387917624158709078463597884603925230452016564866, 0.009067019745648904260292805536260406118387917624158709078463597884603925231269292389045]",
"[0.009074762767041541335263012709931078341406205886192758284533745627251418745319424181923, 0.009074762767041541335263012709931078341406205886192758284533745627251418746228249210761]",
"[0.00908250578843417841023321988360175056442449414822680749060389336989891226018683179898, 0.009082505788434178410233219883601750564424494148226807490603893369898912261187206016006]",
"[0.009006565734246868130536829826491622916568430213959839682910774246224445121360616245368, 0.009006565734246868130536829826491622916568430213959839682910774246224445122505058887599]",
"[0.00880583157121685043905438520916514095366665357528672709378417623109976827118300261275, 0.00880583157121685043905438520916514095366665357528672709378417623109976827263529459894]",
"[0.008477185399299473576751638452722284369506552111628104813008518538723202945667074761774, 0.008477185399299473576751638452722284369506552111628104813008518538723202947791787204804]",
"[0.008238766921348600640422870677613921929818861790201661209345809646222094059383406310949, 0.008238766921348600640422870677613921929818861790201661209345809646222094062890545140045]",
"[0.00833101977134863760729796139491241573913523730009074867767776948590614333223714589034, 0.008331019771348637607297961394912415739135237300090748677677769485906143338484000328872]",
"[0.00874072493140121549872529095824229275694506534609197273694976551493204430874009141387, 0.008740724931401215498725290958242292756945065346091972736949765514932044320556942557093]",
"[0.009204360934568652578336518721370449179670248880845187449120070393080353592839328166811, 0.009204360934568652578336518721370449179670248880845187449120070393080353616997173792388]",
"[0.009489353366220926548365946680564664078040545605728611372529173343695306492459207939035, 0.009489353366220926548365946680564664078040545605728611372529173343695306546770965841905]",
"[0.009596557050690891397952829585200226453920613131339387358580319891637003708485117131162, 0.009596557050690891397952829585200226453920613131339387358580319891637003840718257320937]",
"[0.009582371133482114400678729461290426982886264553717774485783314048190956214251446307492, 0.009582371133482114400678729461290426982886264553717774485783314048190956548504191161014]",
"[0.009568185216273337403404629337380627511851915976096161612986308204744908567181786897096, 0.009568185216273337403404629337380627511851915976096161612986308204744909409126123882932]"
]
},
{
"lower_level": 76,
"upper_level": 77,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.006962373324712855654319816610408160300607261354102393579108117714817394883083834623403085179874973153",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.007896416247600139051057839161406141709302747044640622739619847650504773311318285066637, 0.007896416247600139051057839161406141709302747044640622739619847650504773312148957042936]",
"[0.007882230330391362053783739037496342238268398467019009866822841807058725918045373364038, 0.007882230330391362053783739037496342238268398467019009866822841807058725918974144939689]",
"[0.007868044413182585056509638913586542767234049889397396994025835963612678524772461677911, 0.007868044413182585056509638913586542767234049889397396994025835963612678525799332819969]",
"[0.007773212176062963473591527860820733625310102156734760142124254947070625773161592574649, 0.007773212176062963473591527860820733625310102156734760142124254947070625774336353186266]",
"[0.007557966719446378203819730364322827084247881845973908474167707836929236857030401839649, 0.007557966719446378203819730364322827084247881845973908474167707836929236858509136730343]",
"[0.007219129719003468221823230438534820637282713607587467790949130070047005108378372696652, 0.00721912971900346822182323043853482063728271360758746779094913007004700511050984585946]",
"[0.006962373324712855654319816610408160300607261354102393579108117714817394883083834623403, 0.006962373324712855654319816610408160300607261354102393579108117714817394886549075455199]",
"[0.007014972288038442151375209466219437915431737362257715093967556453979278428955854271997, 0.00701497228803844215137520946621943791543173736225771509396755645397927843505855847622]",
"[0.00736607820425695584373916415809787130074309444458590768860373880587040901395506188033, 0.007366078204256955843739164158097871300743094444585907688603738805870409025413805958173]",
"[0.007769580722762409370715515614526919519947729165293474153401906610063335394429924248807, 0.00776958072276240937071551561452691951994772916529347415340190661006333541774413359722]",
"[0.00800816806501441919807634264564962548972633204115316553842078183382972935933679933028, 0.008008168065014419198076342645649625489726332041153165538420781833829729411597738811162]",
"[0.008083216140663545993739735104283291907270633708856176103256427546264956410963085849571, 0.008083216140663545993739735104283291907270633708856176103256427546264956538005956817272]",
"[0.008046955029695707402492309547770786351946283307536380770433425301519959002012782613606, 0.008046955029695707402492309547770786351946283307536380770433425301519959322958283104769]",
"[0.008010693918727868811244883991258280796621932906216585437610423056774961446289730581873, 0.008010693918727868811244883991258280796621932906216585437610423056774962254683376570992]"
]
},
{
"lower_level": 75,
"upper_level": 76,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.002678138972320189965808261452789063201663998318002943942871415563418588618604578449851551257210524704",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.003801709226773297915160077440810142599041046968476075884181951205041610132432516182001, 0.003801709226773297915160077440810142599041046968476075884181951205041610133529162191275]",
"[0.003765448115805459323912651884297637043716696567156280551358948960296612820367139011002, 0.003765448115805459323912651884297637043716696567156280551358948960296612821596551262136]",
"[0.003729187004837620732665226327785131488392346165836485218535946715551615508301761840003, 0.003729187004837620732665226327785131488392346165836485218535946715551615509663940332998]",
"[0.003609505249665188701388019002860872378767921507269282672978590011559875255736121381766, 0.003609505249665188701388019002860872378767921507269282672978590011559875257278667583022]",
"[0.003365657200088731890165114240717202583069704587012960134476861620110326693654206170624, 0.003365657200088731890165114240717202583069704587012960134476861620110326695526514221963]",
"[0.002994793562829691530645068722249970481791440789358191672097429656625601304578693968273, 0.002994793562829691530645068722249970481791440789358191672097429656625601307114829666804]",
"[0.002692928576543966134440594094261828527853436714970247552671473060576662911182214130991, 0.002692928576543966134440594094261828527853436714970247552671473060576662915034988127606]",
"[0.002678138972320189965808261452789063201663998318002943942871415563418588618604578449852, 0.002678138972320189965808261452789063201663998318002943942871415563418588625025069637987]",
"[0.002945627368230553045891981182601861241583658070884576461420406147276841416644095792568, 0.00294562736823055304589198118260186124158365807088457646142040614727684142824547863768]",
"[0.003269348711550504239672681633759689797601580307931369599222178588449060735183264626266, 0.003269348711550504239672681633759689797601580307931369599222178588449060758223486104626]",
"[0.003448861322747236224494933757799587491716973766105860303215807160349911048899510881875, 0.003448861322747236224494933757799587491716973766105860303215807160349911099853237761494]",
"[0.003486408993240146394142934457729309128731110872063676564880418121341464883461396658948, 0.003486408993240146394142934457729309128731110872063676564880418121341465006533802348254]",
"[0.003427958888695226480936055782339346752742800775205833318450986911447657756990797952512, 0.003427958888695226480936055782339346752742800775205833318450986911447658067087998764642]",
"[0.003369508784150306567729177106949384376754490678347990072021555701553850488936142724291, 0.003369508784150306567729177106949384376754490678347990072021555701553851269226265119408]"
]
}
],
"pointwise_nonnegative_pair_energy_certified": true,
"second_is_unassigned_mathematical_control": false
},
{
"depth": 2,
"shell_levels": [
75,
94
],
"other_unsmoothed_chart_minimum_source_cost_lower_bound": "0.00118886451983703988674766566485251392854995062323744927335233525363175216764394045735950825297041807",
"common_smoothing_width_interval": "[0.00003970760187135478964154730942511701397745508053711967522862079237823054779163585056431, 0.00003970760187135478964154730942511701397745508053711967522862079237823054792301403910759]",
"smoothing_bands": [
{
"lower_level": 93,
"upper_level": 94,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.01621487304643030979491831309249746158355827483483034968290877651825238423896223415586416227393187832",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.01691470979093712838519935927371058058307556987261128522533362319396137886379018031779, 0.01691470979093712838519935927371058058307556987261128522533362319396137886943246675161]",
"[0.01714369650481675681718991642212830315168844397532715481486564613403503325501120815124, 0.0171436965048167568171899164221283031516884439753271548148656461340350332614112313038]",
"[0.0173726832186963852491804735705460257203013180780430244043976690741086876462322359847, 0.017372683218696385249180473570546025720301318078043024404397669074108687653389995856]",
"[0.01739800444446673505886052237267604941610725848491032929137144874554122683200736415352, 0.01739800444446673505886052237267604941610725848491032929137144874554122683999949659263]",
"[0.01712626542804442602520407320326196193370664125490990210010011786398257416528588958771, 0.01712626542804442602520407320326196193370664125490990210010011786398257417435332022115]",
"[0.01655752016850380482570464942601382344187521177678729261612731958019325767325930818757, 0.01655752016850380482570464942601382344187521177678729261612731958019325768394118771683]",
"[0.01621487304643030979491831309249746158355827483483034968290877651825238423896223415586, 0.01621487304643030979491831309249746158355827483483034968290877651825238425229715320443]",
"[0.01667092211720783166756306117332689688687990276576888683884138119888731682456295056568, 0.01667092211720783166756306117332689688687990276576888683884138119888731684242363700322]",
"[0.01789271216181461430553930240666039050064648868941236257042577058858657873981992929385, 0.01789271216181461430553930240666039050064648868941236257042577058858657876560099052587]",
"[0.01924948327513900929404368486803482761288725053734282979017859910769416350881713865083, 0.01924948327513900929404368486803482761288725053734282979017859910769416354913047884452]",
"[0.02018089389529696007300157150589379894899370282755390518706125232978960610865427926883, 0.02018089389529696007300157150589379894899370282755390518706125232978960617777071509653]",
"[0.0206809192297470162723938719888731358561014854491936391848570619117549157846811668663, 0.02068091922974701627239387198887313585610148544919363918485706191175491591587806498721]",
"[0.02088157474566193907851748797073641683591622447206739651781534584538499491846834156351, 0.02088157474566193907851748797073641683591622447206739651781534584538499519134175502135]",
"[0.0210822302615768618846411039525996978157309634949411538507736297790150739585810772041, 0.0210822302615768618846411039525996978157309634949411538507736297790150745604798540998]"
]
},
{
"lower_level": 92,
"upper_level": 93,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.05055049894308396119087460596281455889494693499609826874050335264905911047806102848714947125611290584",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.05055049894308396119087460596281455889494693499609826874050335264905911047806102848715, 0.05055049894308396119087460596281455889494693499609826874050335264905911048311413259526]",
"[0.05075115445899888399699822194467783987476167401897202607346163658268918968235008138918, 0.05075115445899888399699822194467783987476167401897202607346163658268918968807600701887]",
"[0.05095180997491380680312183792654112085457641304184578340641992051631926888663913429122, 0.0509518099749138068031218379265411208545764130418457834064199205163192688930378813766]",
"[0.05104659124515371467576210341946157435071073706607922512745557014572728436410272259848, 0.05104659124515371467576210341946157435071073706607922512745557014572728437125111892251]",
"[0.05098135941021058628848516123993602153344496588245996081825117373135640599516040575436, 0.05098135941021058628848516123993602153344496588245996081825117373135640600329949333602]",
"[0.05074979826304759393096350222582381523766761794982624670414179267620603989571161767266, 0.05074979826304759393096350222582381523766761794982624670414179267620603990538020001274]",
"[0.05081471968523160949817750092178986937364218033918006654846233291924828787542114691251, 0.05081471968523160949817750092178986937364218033918006654846233291924828788765629481194]",
"[0.05166876626443707213257439636094291159100593900610619611339768444624337955875584622577, 0.05166876626443707213257439636094291159100593900610619611339768444624337957542521784416]",
"[0.05322212441984645862159759083016910897406450183671319279712762282496997755774048942924, 0.0532221244198464586215975908301691089740645018367131927971276228249699775822207402915]",
"[0.05482161462707211537822558787512591459138992970460091703785607537371987968600453427636, 0.054821614627072115378225587875125914591389929704600917037856075373719879724843872425]",
"[0.05589889780454121750013741071566389825198551729038986514745807408843490358673435365642, 0.05589889780454121750013741071566389825198551729038986514745807408843490365399286177321]",
"[0.05644293137621420792920834353597234167921793583792045497115063646201173554400975480656, 0.05644293137621420792920834353597234167921793583792045497115063646201173567232879563415]",
"[0.05661472883061101144070082459625423173084163347328376003140286325161774253491225781304, 0.05661472883061101144070082459625423173084163347328376003140286325161774280213376135873]",
"[0.05678652628500781495219330565653612178246533110864706509165509004122374943436929922856, 0.05678652628500781495219330565653612178246533110864706509165509004122375002338415263315]"
]
},
{
"lower_level": 91,
"upper_level": 92,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.08169847139460724132259283757859626493382085774190671451309218958722438535001195272529683667854316746",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.0816984713946072413225928375785962649338208577419067145130921895872243853500119527253, 0.08169847139460724132259283757859626493382085774190671451309218958722438535455396198447]",
"[0.08187026884900404483408531863887815498544455537727001957334441637683039241006407885983, 0.0818702688490040448340853186388781549854445553772700195733444163768303924152093449708]",
"[0.08204206630340084834557779969916004503706825301263332463359664316643639947011620512615, 0.08204206630340084834557779969916004503706825301263332463359664316643639947586472782535]",
"[0.08219108241525635933293437935192363395793983931811384903452372798514570370234321171355, 0.08219108241525635933293437935192363395793983931811384903452372798514570370877374649072]",
"[0.082296555820916960516338166760183944283420308992856660262066052162720055253046566543, 0.08229655582091696051633816676018394428342030899285666026206605216272005526040605792788]",
"[0.08234678141041858524294938217459540412684542920496868136033707646971941060461607807005, 0.08234678141041858524294938217459540412684542920496868136033707646971941061345628322324]",
"[0.08275091401346124139264824860967767705426350442721383538663127604905700967144299934408, 0.08275091401346124139264824860967767705426350442721383538663127604905700968282509617411]",
"[0.08393121541918239421634757849231607635899059626869501933246057032047750347992585353558, 0.08393121541918239421634757849231607635899059626869501933246057032047750349575675513033]",
"[0.08575051133299473292090973474876422776771246902206456319413560158489986672080782056986, 0.08575051133299473292090973474876422776771246902206456319413560158489986674451745185099]",
"[0.08754072404857939318644084680268199020619771530190388624484239429055560961915553723001, 0.08754072404857939318644084680268199020619771530190388624484239429055560965733696573017]",
"[0.08873027937509173121167531955215950845389442167638823376258265790679325673816179526391, 0.08873027937509173121167531955215950845389442167638823376258265790679325680482373291795]",
"[0.08930403536669021396547565622905692004940725348423736677447223552508151059796954971641, 0.08930403536669021396547565622905692004940725348423736677447223552508151072534568351165]",
"[0.08944648448545862105851428241823445371351249612228052150534609109930449369159729635007, 0.08944648448545862105851428241823445371351249612228052150534609109930449395609895723541]",
"[0.08958893360422702815155290860741198737761773876032367623621994667352747669577871716702, 0.08958893360422702815155290860741198737761773876032367623621994667352747727629851935107]"
]
},
{
"lower_level": 90,
"upper_level": 91,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.1099820779302733660740340414775139701964697557137035952074706471996755817643972863202389143767105938",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.1099820779302733660740340414775139701964697557137035952074706471996755817643972863202, 0.1099820779302733660740340414775139701964697557137035952074706471996755817686158436837]",
"[0.1101245270490417731670726676666915038605749983517467499383445027738985649263135777218, 0.1101245270490417731670726676666915038605749983517467499383445027738985649310806057157]",
"[0.1102669761678101802601112938558690375246802409897899046692183583481215480882298691234, 0.1102669761678101802601112938558690375246802409897899046692183583481215480935453676159]",
"[0.1104559015688354369788578504605567259657882580000366473170252968023313148722398839117, 0.1104559015688354369788578504605567259657882580000366473170252968023313148781861093247]",
"[0.1106983862657332721063756810699435387749250144716274476196130184702638694400392357809, 0.1106983862657332721063756810699435387749250144716274476196130184702638694468728773248]",
"[0.1109782600709377853532874550712569810750845729225911854459088798903154198539984402579, 0.1109782600709377853532874550712569810750845729225911854459088798903154198622910066918]",
"[0.1116572912897744172801573877514266005946383496383063985081643371852451141528669078811, 0.1116572912897744172801573877514266005946383496383063985081643371852451141637142225977]",
"[0.1130963980018136834132534528631134211321245936317330334383314984878637781699370024488, 0.1130963980018136834132534528631134211321245936317330334383314984878637781853010439936]",
"[0.1151199752898871425889241095517803318587913272400757179629538352552688512896825651585, 0.11511997528988714258892410955178033185879132724007571796295383525526885131307190918]",
"[0.1170520846784369110306736905491265444078246324098306595486273455701349955371969325177, 0.1170520846784369110306736905491265444078246324098306595486273455701349955752965959942]",
"[0.1183223631241397705202573604447269320313318803471552277939649827103058762910346670972, 0.1183223631241397705202573604447269320313318803471552277939649827103058763579018092931]",
"[0.1189124316901877870322855140454765274705727536640339184773293478721414096721170588738, 0.1189124316901877870322855140454765274705727536640339184773293478721414097998018819297]",
"[0.119025078554559598768773148754325904070327379858445274192438242835282304120003341869, 0.1190250785545595987687731487543259040703273798584452741924382428352823043839869358228]",
"[0.1191377254189314105052607834631752806700820060528566299075471377984231984799045880255, 0.1191377254189314105052607834631752806700820060528566299075471377984231990561570764984]"
]
},
{
"lower_level": 89,
"upper_level": 90,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.1350569427326545171081475877939420696878212009149952689894056650324747688768454156722356897152973235",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.1350569427326545171081475877939420696878212009149952689894056650324747688768454156722, 0.1350569427326545171081475877939420696878212009149952689894056650324747688807728856876]",
"[0.135169589597026328844635222502791446287575827109406624704514559995615663392627160454, 0.1351695895970263288446352225027914462875758271094066247045145599956156633970624444545]",
"[0.1352822364613981405811228572116408228873304533038179804196234549587565579084089052357, 0.1352822364613981405811228572116408228873304533038179804196234549587565579133520029579]",
"[0.135497620689621364555751899341891544784073151460733912446163996534222266323621628879, 0.1354976206896213645557518993418915447840731514607339124461639965342222663291557630688]",
"[0.1358454721032611204182926877962717589744742113127654064774553535467095496553568269645, 0.1358454721032611204182926877962717589744742113127654064774553535467095496617415945024]",
"[0.1363060234057904564809363541863284522040227271900061491222405450254020382741325804402, 0.1363060234057904564809363541863284522040227271900061491222405450254020382819457807466]",
"[0.1371995721198398271477956693642424189708485248326238231829106459785749000254103895418, 0.1371995721198398271477956693642424189708485248326238231829106459785749000357592867978]",
"[0.1388342071236870816265178488322652947858837437810721071350158449735948547074237813946, 0.1388342071236870816265178488322652947858837437810721071350158449735948547222877997704]",
"[0.1410042714684843971334277761079181247638395413835395797013351454738881151821886564678, 0.1410042714684843971334277761079181247638395413835395797013351454738881152050947130594]",
"[0.1430325331998030217836500985673606516053825612945724733786840184556314715452731226236, 0.1430325331998030217836500985673606516053825612945724733786840184556314715828984663908]",
"[0.1443539796591140671096201868788244169370279672655164866626362162905955104421500057631, 0.1443539796591140671096201868788244169370279672655164866626362162905955105084258115658]",
"[0.1449478028527806078227744460494791235164462488044658090603391485879198774129397031663, 0.1449478028527806078227744460494791235164462488044658090603391485879198775394103406976]",
"[0.1450302296700975642230162007137598333705308288215747629154527115642214078308802557065, 0.1450302296700975642230162007137598333705308288215747629154527115642214080914813299719]",
"[0.1451126564874145206232579553780405432246154088386837167705662745405229381628872571675, 0.1451126564874145206232579553780405432246154088386837167705662745405229387294858729609]"
]
},
{
"lower_level": 88,
"upper_level": 89,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.1566098668765356368419614163079757830243870713280307738645343634331964986396768837020129406094116999",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.156609866876535636841961416307975783024387071328030773864534363433196498639676883702, 0.1566098668765356368419614163079757830243870713280307738645343634331964986434118299901]",
"[0.1566922936938525932422031709722564928784716513451397277196479264094980291244423039608, 0.1566922936938525932422031709722564928784716513451397277196479264094980291286579473289]",
"[0.1567747205111695496424449256365372027325562313622486815747614893857995596092077244831, 0.1567747205111695496424449256365372027325562313622486815747614893857995596139040646678]",
"[0.1570039641371266999499243880777920233539392454013643387347250544884599771379913700691, 0.157003964137126699949924388077792023353939245401364338734725054488459977143252112649]",
"[0.1574275296492519678718873020984612455606024910140826312493740397862250863504594154113, 0.1574275296492519678718873020984612455606024910140826312493740397862250863565455867889]",
"[0.1580228663421617440414961283585111417009124720291608511690717109270951425341541309714, 0.1580228663421617440414961283585111417009124720291608511690717109270951425416465690921]",
"[0.1590743718387837266830996222643183492660382113383679858981944217186768535415376081818, 0.1590743718387837266830996222643183492660382113383679858981944217186768535515488999823]",
"[0.1608453124369688306700342575602055737830995400155625986964776917935714199051638548757, 0.1608453124369688306700342575602055737830995400155625986964776917935714199196804240187]",
"[0.1631078219750433620574472025273676962669368974253857345631401401745397988930674684004, 0.1631078219750433620574472025273676962669368974253857345631401401745397989156179738166]",
"[0.1651894858053403044372838714646161648741298623401695430566521589396863615307650972918, 0.1651894858053403044372838714646161648741298623401695430566521589396863615679942325795]",
"[0.1665344828187313902108624366963744992620818650708015970994638245690328941121467993537, 0.1665344828187313902108624366963744992620818650708015970994638245690328941778250204024]",
"[0.1671203310117166476103521979758311170659727428454646957174291038225055849117147556358, 0.1671203310117166476103521979758311170659727428454646957174291038225055850368357625375]",
"[0.1671721558914291230794692504664294154166677588019806161343748600790548103590299764951, 0.167172155891429123079469250466429415416667758801980616134374860079054810615933375359]",
"[0.1672239807711415985485863029570277137673627747584965365513206163356040357224837284586, 0.1672239807711415985485863029570277137673627747584965365513206163356040362788924391543]"
]
},
{
"lower_level": 87,
"upper_level": 88,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.174357850998509619354217164532993365334377069150977509262967040128518823815926345407562923107146171",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.1743578509985096193542171645329933653343770691509775092629670401285188238159263454076, 0.1743578509985096193542171645329933653343770691509775092629670401285188238195635734274]",
"[0.1744096758782220948233342170235916636850720851074934296799127963850680493288995170409, 0.1744096758782220948233342170235916636850720851074934296799127963850680493330032731631]",
"[0.1744615007579345702924512695141899620357671010640093500968585526416172748418726889377, 0.1744615007579345702924512695141899620357671010640093500968585526416172748464429728989]",
"[0.1746928318260352396486734922635677570335302706812530596638762428311724209094244030647, 0.1746928318260352396486734922635677570335302706812530596638762428311724209145449510159]",
"[0.1751643945471733771549947629300372751282511730357792648757596282782323626136652983204, 0.1751643945471733771549947629300372751282511730357792648757596282782323626195971777787]",
"[0.1758516157940030839870889331484340009489129675018006218187061322558350015668895719759, 0.1758516157940030839870889331484340009489129675018006218187061322558350015742136169333]",
"[0.1770082290358965255269638766662578966146262699553630816410806062465845023566933537042, 0.1770082290358965255269638766662578966146262699553630816410806062465845023665217491762]",
"[0.17886019111283760305577474526455978919066912145771070711574047357074851317681628376, 0.1788601911128376030557747452645597891906691214577107071157404735707485131911326829196]",
"[0.1811647490989596256061783320659926432861340892496233358310995233911972105628175414755, 0.1811647490989596256061783320659926432861340892496233358310995233911972105851368417317]",
"[0.1832599732684892671386014457064679138073518738678866631946044607267685460071113974892, 0.1832599732684892671386014457064679138073518738678866631946044607267685460440226122407]",
"[0.184602785914085829281803642540718854905580876955079626150259097646773988714138848262, 0.1846027859140858292818036425407188549055808769550796261502590976467739887792194141875]",
"[0.1851697347072483136659664126776259761374419552959585845519336653188982636204178497986, 0.18516973470724831366596641267762597613744195529595858455193366531889826374406938869]",
"[0.1851906114425285419720265204104408202728394455696002675413110088074533638383073426478, 0.1851906114425285419720265204104408202728394455696002675413110088074533640912275628326]",
"[0.1852114881778087702780866281432556644082369358432419505306883522960084639744250561002, 0.1852114881778087702780866281432556644082369358432419505306883522960084645201575258601]"
]
},
{
"lower_level": 86,
"upper_level": 87,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.1880471369772394217405899942749054625832906279450131493003071251563935677243900563259507705244202948",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.188047136977239421740589994274905462583290627945013149300307125156393567724390056326, 0.188047136977239421740589994274905462583290627945013149300307125156393567728020597166]",
"[0.1880680137125196500466501020077203067186881182186548322896844686449486680066815338492, 0.1880680137125196500466501020077203067186881182186548322896844686449486680107767987581]",
"[0.1880888904477998783527102097405351508540856084922965152790618121335037682889730113725, 0.1880888904477998783527102097405351508540856084922965152790618121335037682935330003502]",
"[0.1883113414149677317356652363949747260925502493017415671064404922821962093817137608396, 0.1883113414149677317356652363949747260925502493017415671064404922821962093868218133871]",
"[0.1888050651426799709295528918450285548288828236597408756920664540886176074337314039522, 0.1888050651426799709295528918450285548288828236597408756920664540886176074396473293752]",
"[0.1895441758779844034431462164423766655615021925633022499096799887315643287446204153941, 0.1895441758779844034431462164423766655615021925633022499096799887315643287519221891677]",
"[0.1907566530637701250823604470681213779018604357612499795583056124751842815078444463226, 0.190756653063770125082360447068121377901860435761249979558305612475184281517638491624]",
"[0.1926381777930226157904639202918763338526580974749565116686038163031520466951767961455, 0.1926381777930226157904639202918763338526580974749565116686038163031520467094348589985]",
"[0.1949379275310427560533907850366797694896578879054553165804556811556620221807881227933, 0.1949379275310427560533907850366797694896578879054553165804556811556620222029968461988]",
"[0.1970096949705249444656511066717854231622270706756770576541058476532801903085787036912, 0.1970096949705249444656511066717854231622270706756770576541058476532801903452498465036]",
"[0.1983264169207524674633815625166634788731300924957802611629183495490001736523420793952, 0.1983264169207524674633815625166634788731300924957802611629183495490001737168300051211]",
"[0.1988643245437291931574089668256968008979084658624559650494324611983886841993181882649, 0.1988643245437291931574089668256968008979084658624559650494324611983886843213941324204]",
"[0.1988539423991062996708281835514506951279671251069269714721790884088491323928182972658, 0.198853942399106299670828183551450695127967125106926971472179088408849132641496256087]",
"[0.1988435602544834061842474002772045893580257843513979778949257156193095805066513737903, 0.1988435602544834061842474002772045893580257843513979778949257156193095810412653621545]"
]
},
{
"lower_level": 85,
"upper_level": 86,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.19743150418772854469281334015918827030971466803808205183283446710501920606902307911163131135957028",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.1974522684769743316659749067076804818495973495491400389873412126840983095558954936204, 0.1974522684769743316659749067076804818495973495491400389873412126840983095596533127882]",
"[0.197441886332351438179394123433434376079656008793611045410087839894558757812459286366, 0.197441886332351438179394123433434376079656008793611045410087839894558757816691817281]",
"[0.1974315041877285446928133401591882703097146680380820518328344671050192060690230791116, 0.1974315041877285446928133401591882703097146680380820518328344671050192060737303215103]",
"[0.1976348893578727278666735339527059214716398753941985772096963839421704346102194463235, 0.197634889357872727866673533952705921471639875394198577209696383942170434615486108084]",
"[0.1981267647166789095996682799466392399381079502886791081210242581315370763290367522766, 0.1981267647166789095996682799466392399381079502886791081210242581315370763351257985116]",
"[0.1988805919815514205452212173677399029925062394048698190821386116886883565976405840093, 0.198880591981551420545221217367739902992506239404869819082138611688688356605135165886]",
"[0.200103190391562237608195676348289870890990506062867692111506772683833219329676939698, 0.2001031903915622376081956763482898708909905060628676921115067726838332193396905386586]",
"[0.2019665333773388388570489761359493414895574275133109000574759498436866823043291147026, 0.2019665333773388388570489761359493414895574275133109000574759498436866823188411667774]",
"[0.204218055410646691794939004564704948950025850315398625155969042218989696728301224375, 0.2042180554106466917949390045647049489500258503153986251559690422189896967508012136871]",
"[0.2062320917510295367063159214824528140411282656754412149484512184686293694850223213313, 0.2062320917510295367063159214824528140411282656754412149484512184686293695219995428926]",
"[0.2075005924909692713388390177975738525544269714108598634078011238916551751691477832962, 0.2075005924909692713388390177975738525544269714108598634078011238916551752338420353857]",
"[0.2080000776896523898073199139545748113167254880827584447488913433436731383324660967285, 0.2080000776896523898073199139545748113167254880827584447488913433436731384542486183073]",
"[0.2079581611951020442408679246924233080192330225499594273875464216814155130148314844054, 0.2079581611951020442408679246924233080192330225499594273875464216814155132615280624243]",
"[0.2079162447005516986744159354302718047217405570171604100262015000191578876191137384309, 0.2079162447005516986744159354302718047217405570171604100262015000191578881468906299141]"
]
},
{
"lower_level": 84,
"upper_level": 85,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.202291337235829903121101434570047573947466236292963345679508964321754349055049874730240236495775399",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.2023751702249305942540054130943505805424511673585613804021988076462695995659009679578, 0.2023751702249305942540054130943505805424511673585613804021988076462695995698433907632]",
"[0.202333253730380248687553423832199077244958701825762363040853885984011974310475421344, 0.2023332537303802486875534238321990772449587018257623630408538859840119743149137826121]",
"[0.2022913372358299031211014345700475739474662362929633456795089643217543490550498747302, 0.2022913372358299031211014345700475739474662362929633456795089643217543490599841744611]",
"[0.2024662306893592191706687326437544913484054577088456930650791756752192112424548153124, 0.2024662306893592191706687326437544913484054577088456930650791756752192112479685988433]",
"[0.2029340224498440977419069533181377200230636479426820579075883380476031917396909116576, 0.2029340224498440977419069533181377200230636479426820579075883380476031917460435486846]",
"[0.2036681335583205200245031476399096432925729589836005746399299712069292375738447297158, 0.2036681335583205200245031476399096432925729589836005746399299712069292375816113914894]",
"[0.2048585096805829884315345599374144206243616399231166956496170273113212619929549829591, 0.2048585096805829884315345599374144206243616399231166956496170273113212620032337719632]",
"[0.2066595325285795182469045787091087977661233770333768297521981232932020359491433551225, 0.2066595325285795182469045787091087977661233770333768297521981232932020359638854068569]",
"[0.208822744085964012704011555185994523696528227294912804880496208817795877295286458296, 0.2088227440859640127040115551859945236965282272949128048804962088177958773179269819591]",
"[0.2107474374684512335652738713871567715953368785921843625589902890511989511548047183972, 0.2107474374684512335652738713871567715953368785921843625589902890511989511917169241153]",
"[0.2119473106740956738165442897202303038981211493772257505792668319859606962660280256678, 0.2119473106740956738165442897202303038981211493772257505792668319859606963301743367405]",
"[0.2123997310854820353075187996199221876716262356204131423431979854238083210819157234325, 0.2123997310854820353075187996199221876716262356204131423431979854238083212019673194226]",
"[0.2123260398374311894137994151715804260712953027347292285153259575548394196178295661474, 0.212326039837431189413799415171580426071295302734729228515325957554839419859851540149]",
"[0.2122523485893803435200800307232386644709643698490453146874539296858705180777937960063, 0.2122523485893803435200800307232386644709643698490453146874539296858705185936853529106]"
]
},
{
"lower_level": 83,
"upper_level": 84,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.2024968634161159621174885266230069819708755482945023451792712446567922862130418944893466429907486008",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.2026442459122176539049272955196905051715374140658701728350153003947300890197716087934, 0.2026442459122176539049272955196905051715374140658701728350153003947300890239455928215]",
"[0.2025705546641668080112079110713487435712064811801862590071432725257611876164067516414, 0.2025705546641668080112079110713487435712064811801862590071432725257611876211085455686]",
"[0.2024968634161159621174885266230069819708755482945023451792712446567922862130418944893, 0.2024968634161159621174885266230069819708755482945023451792712446567922862182714983156]",
"[0.2026345774344097056606309109398016559467667551693157388271833367538703024914703653807, 0.2026345774344097056606309109398016559467667551693157388271833367538703024973097676244]",
"[0.2030577730106645366622568300278515826046530017486939963371971014318376317226845861825, 0.2030577730106645366622568300278515826046530017486939963371971014318376317293883803968]",
"[0.203740395545443637786887602757842921165316820027518808988933096934324534159867653702, 0.203740395545443637786887602757842921165316820027518808988933096934324534168000490551]",
"[0.2048595054800099276038981525969075610216976262033980533247944198289316735840072194433, 0.2048595054800099276038981525969075610216976262033980533247944198289316735946471150975]",
"[0.2065575697959636619613601886653606888467912031849657721288924936064300903418568451875, 0.206557569795963661961360188665360688846791203184965772128892493606430090356918706093]",
"[0.208595626491842684555696062094976165256893001088251701792653042609847918019837159114, 0.2085956264918426845556960620949761652568930010882517017926530426098479180426894750067]",
"[0.2104019491776399574790408835062093031767853058347233685661129117333349396471415984815, 0.2104019491776399574790408835062093031767853058347233685661129117333349396840231575031]",
"[0.2115144622538775389737709280775272316312141364981596264083979009426260416449166154269, 0.2115144622538775389737709280775272316312141364981596264083979009426260417084872344646]",
"[0.2119118932685082119240697727712803682202795224614575988486377372018684062752866107349, 0.2119118932685082119240697727712803682202795224614575988486377372018684063934859164545]",
"[0.2118062217382453314200875488557476987101869764096568278647235862844869277536229227081, 0.2118062217382453314200875488557476987101869764096568278647235862844869279907225404985]",
"[0.2117005502079824509161053249402150292000944303578560568808094353671054491581527009679, 0.2117005502079824509161053249402150292000944303578560568808094353671054496617656858689]"
]
},
{
"lower_level": 82,
"upper_level": 83,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.1979021515677350424396939812035343990800929412755770275677983615947866247727281157413467379014293588",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.1981134946282608034476584290345997381002780333791785695356266634295495816977249731358, 0.1981134946282608034476584290345997381002780333791785695356266634295495817021832654834]",
"[0.1980078230979979229436762051190670685901854873273777985517125125121681032352265444386, 0.1980078230979979229436762051190670685901854873273777985517125125121681032402546660413]",
"[0.1979021515677350424396939812035343990800929412755770275677983615947866247727281157413, 0.1979021515677350424396939812035343990800929412755770275677983615947866247783260663358]",
"[0.1979947155532393535033615689877880361701162034736625384447760305188614434449798740067, 0.1979947155532393535033615689877880361701162034736625384447760305188614434512257167237]",
"[0.1983544746795629856665684223292168550511889025826406657182212949908814994952958239946, 0.1983544746795629856665684223292168550511889025826406657182212949908814995024330722737]",
"[0.1989564183182176040718890797142129958995869770339374803074631587078330960755439569275, 0.1989564183182176040718890797142129958995869770339374803074631587078330960841144881769]",
"[0.1999684204614185884335092908209273787996877324256016850714486254759987463485181674111, 0.1999684204614185884335092908209273787996877324256016850714486254759987463595590611289]",
"[0.2015262842794739077134317160070930076899174134124482497982846247933313138021623381873, 0.2015262842794739077134317160070930076899174134124482497982846247933313138175188835705]",
"[0.2034054840708622400315712622105612933394339814796768110890779178168463814070024497398, 0.2034054840708622400315712622105612933394339814796768110890779178168463814299234786244]",
"[0.2050669158528224853804406366106738854615453844785257353352658600211753434766546642036, 0.2050669158528224853804406366106738854615453844785257353352658600211753435131576974378]",
"[0.2060749606327451432162844464637997666923296077241593909014307192322428714696344331419, 0.2060749606327451432162844464637997666923296077241593909014307192322428715319253110512]",
"[0.2064101747457061095800656939581461341397914302072862021153468601356720093437746786721, 0.2064101747457061095800656939581461341397914302072862021153468601356720094587816376521]",
"[0.2062723520957197421770602852888385035174284363655157775569159004688746643612375190592, 0.206272352095719742177060285288838503517428436365515777556915900468874664590903306497]",
"[0.2061345294457333747740548766195308728950654425237453529984849408020773193075521018255, 0.2061345294457333747740548766195308728950654425237453529984849408020773197941732788213]"
]
},
{
"lower_level": 81,
"upper_level": 82,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.1883860004603359794876108948627191479147379177872695551396124922559368147601053447500187670855826576",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.1886616457603087142936217122013344091594639054708104042564744115895315046111422551273, 0.1886616457603087142936217122013344091594639054708104042564744115895315046158980809816]",
"[0.1885238231103223468906163035320267785371009116290399796980434519227341596856237999386, 0.1885238231103223468906163035320267785371009116290399796980434519227341596910010185196]",
"[0.18838600046033597948761089486271914791473791778726955513961249225593681476010534475, 0.1883860004603359794876108948627191479147379177872695551396124922559368147661039557942]",
"[0.1884261403537693795531423242240087549375620165108909903147076831938319432237508399087, 0.1884261403537693795531423242240087549375620165108909903147076831938319432304447215578]",
"[0.1887052459434637256728964398909569109662498696836106336139678893263645446497179678519, 0.1887052459434637256728964398909569109662498696836106336139678893263645446573387498531]",
"[0.189199826119271714876857654849894095198820612177865284382809482458943057572697699477, 0.1891998261192717148768576548498940951988206121778652843828094824589430575817627075133]",
"[0.190071986133145792453630396793036578330569641926554349620842420361916086134497026127, 0.1900719861331457924536303967930365783305696419265543496208424203619160861459990458615]",
"[0.1914557027800410519568658899616825615057788793917363484967923609134018846004293018504, 0.1914557027800410519568658899616825615057788793917363484967923609134018846161382850343]",
"[0.1931453921862996414356831123520698802579482654673064452450932431351790662757931608521, 0.1931453921862996414356831123520698802579482654673064452450932431351790662988293194992]",
"[0.1946378456075915564609413424061802640861693694965462789001541148620744876516942912284, 0.19463784560759155646094134240618026408616936949654627890015411486207448768784097577]",
"[0.1955258902166246592343558588244517557895125193316348844756148139679248147758743435777, 0.1955258902166246592343558588244517557895125193316348844756148139679248148368668056458]",
"[0.1957923368688947264446525105037518388390489327908020756273592296892550522435619850256, 0.1957923368688947264446525105037518388390489327908020756273592296892550523552996777002]",
"[0.1956222267776983802234327834514620690660380408590193222917806005628649992601088363898, 0.1956222267776983802234327834514620690660380408590193222917806005628649994821967066669]",
"[0.1954521166865020340022130563991722992930271489272365689562019714364749462081545122564, 0.1954521166865020340022130563991722992930271489272365689562019714364749466775948689623]"
]
},
{
"lower_level": 80,
"upper_level": 81,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.1738322103274535496910912357395490621851643225291359481837449953216610796107466741918519735817161873",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.1741913123128119901191969661499946593597052906465502654237482542059870747836063502335, 0.1741913123128119901191969661499946593597052906465502654237482542059870747889076460134]",
"[0.1740212022216156438979772390977048895866943987147675120881696250795970218549872821856, 0.1740212022216156438979772390977048895866943987147675120881696250795970218609706220654]",
"[0.1738510921304192976767575120454151198136835067829847587525909959532069689263682141378, 0.1738510921304192976767575120454151198136835067829847587525909959532069689330335981174]",
"[0.1738322103274535496910912357395490621851643225291359481837449953216610796107466741919, 0.1738322103274535496910912357395490621851643225291359481837449953216610796181676272496]",
"[0.1740150205186176605351708153285693079616843869189264215800771082467450649908851947175, 0.1740150205186176605351708153285693079616843869189264215800771082467450649992913253975]",
"[0.1743779839233421741988610978512162814538359844070522844484509494800203521514838313501, 0.1743779839233421741988610978512162814538359844070522844484509494800203521613864270282]",
"[0.1750805819994844176577247191431775092558267739903908624041096935807834193909956044139, 0.1750805819994844176577247191431775092558267739903908624041096935807834194033736362567]",
"[0.1762594014048423336077228810214431999607532716388686685625114343310791634495629215376, 0.1762594014048423336077228810214431999607532716388686685625114343310791634661586957001]",
"[0.1777318840002342931031542978070358675747690004202090830668344019076447497116767076852, 0.1777318840002342931031542978070358675747690004202090830668344019076447497355574769226]",
"[0.1790336313883505208061116670609662461302112858717534362127737210621071794943272894604, 0.1790336313883505208061116670609662461302112858717534362127737210621071795311709793256]",
"[0.1797876732787709173220843377384113042785001171168872998429068254493421352153374822064, 0.1797876732787709173220843377384113042785001171168872998429068254493421352766490855973]",
"[0.1799794591915862456690081487031855397122082095062768673383883012941657564229500519119, 0.1799794591915862456690081487031855397122082095062768673383883012941657565340811807789]",
"[0.1797769596876256154464752645160366892232558500532254025356306351592200899232920206311, 0.1797769596876256154464752645160366892232558500532254025356306351592200901424978600905]",
"[0.1795744601836649852239423803288878387343034906001739377328729690242744233567738927688, 0.1795744601836649852239423803288878387343034906001739377328729690242744238177746217515]"
]
},
{
"lower_level": 79,
"upper_level": 80,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.1541393193892542017681223450331692812999482483265130553807349997308085820579661302338238868699535642",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.1546281626264339822121999116286223159448216352448239940210186804814735746150286722282, 0.1546281626264339822121999116286223159448216352448239940210186804814735746209427503945]",
"[0.1544256631224733519896670274414734654558692757917725292182610143465279081690324077761, 0.1544256631224733519896670274414734654558692757917725292182610143465279081756976947675]",
"[0.1542231636185127217671341432543246149669169163387210644155033482115822417230361435876, 0.1542231636185127217671341432543246149669169163387210644155033482115822417304526388769]",
"[0.1541393193892542017681223450331692812999482483265130553807349997308085820579661302338, 0.1541393193892542017681223450331692812999482483265130553807349997308085820662066097762]",
"[0.1542117207847302215683571050737771903371385186288651098646845646346949581368450541043, 0.1542117207847302215683571050737771903371385186288651098646845646346949581461359706368]",
"[0.154421172724157273603877699986086066101117732251993135893084949104581133043695363769, 0.1544211727241572736038776999860860661011177322519931358930849491045811330545396049077]",
"[0.1549274131555708933283143411014532004072667899720593238704723944541788107436027028855, 0.1549274131555708933283143411014532004072667899720593238704723944541788107569611815392]",
"[0.1558736856232160304359950395374109695538240673852901015843562036795655704708577817689, 0.1558736856232160304359950395374109695538240673852901015843562036795655704884381582132]",
"[0.1571041328166263250329971665126509179043574409102674693289663923812562436048888700851, 0.1571041328166263250329971665126509179043574409102674693289663923812562436296945793528]",
"[0.1581957351445201600817434904943645350009335088826444661582717633155436373297920330095, 0.158195735144520160081743490494364535000933508882644466158271763315543637367379546363]",
"[0.1588032553081757499703858039524000555190918689675574163536124293103957251289000108191, 0.1588032553081757499703858039524000555190918689675574163536124293103957251905215253113]",
"[0.1589151253140412341281681048541531554535732904885553420208652710076225780624977713189, 0.1589151253140412341281681048541531554535732904885553420208652710076225781729272763254]",
"[0.1586801686193210602193812514797748481952934881150215576118945948940552720287611785482, 0.1586801686193210602193812514797748481952934881150215576118945948940552722448686038331]",
"[0.1584452119246008863105943981053965409370136857414877732029239187804879659298224240325, 0.1584452119246008863105943981053965409370136857414877732029239187804879663820121154881]"
]
},
{
"lower_level": 78,
"upper_level": 79,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.1292454496407336611961814776829203135651849370087048970647797661322388191054731703090484881654052044",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.1299201105034546596546803339661513920867888869906978108779267079517153804564603144576, 0.1299201105034546596546803339661513920867888869906978108779267079517153804630840609722]",
"[0.1296851538087344857458934805917730848285090846171640264689560318381480744751484828223, 0.1296851538087344857458934805917730848285090846171640264689560318381480744826006231278]",
"[0.1294501971140143118371066272173947775702292822436302420599853557245807684938366514505, 0.1294501971140143118371066272173947775702292822436302420599853557245807685021171852833]",
"[0.1292960875296567730522510647781977665217018235073645466307650712183401284909429978668, 0.1292960875296567730522510647781977665217018235073645466307650712183401285001235850268]",
"[0.129245449640733661196181477682920313565184937008704897064779766132238819105473170309, 0.1292454496407336611961814776829203135651849370087048970647797661322388191157760582505]",
"[0.129281783257568250349602243029030208558622125065277483747318456707060366545237770888, 0.129281783257568250349602243029030208558622125065277483747318456707060366557155275511]",
"[0.1295677063368312574972667070708211004959837135923670239505485507833510095233342141218, 0.1295677063368312574972667070708211004959837135923670239505485507833510095378052886731]",
"[0.1302567887971219366012416762889624172079781541316045106417066283027676999954920586388, 0.1302567887971219366012416762889624172079781541316045106417066283027677000141832978434]",
"[0.1312231529180247635477623980679329149214647012906052927067146555372078431997023901192, 0.1312231529180247635477623980679329149214647012906052927067146555372078432255434750024]",
"[0.1320873905079543472814015080944789276808277823927713760951820151873447761898749866098, 0.1320873905079543472814015080944789276808277823927713760951820151873447762282862778528]",
"[0.132537308877451681031555544166489707916605805440017767391944560717165206303612500726, 0.132537308877451681031555544166489707916605805440017767391944560717165206365572807198]",
"[0.1325646272524778936701228083348348566507599785936974533930390813592027053608347667463, 0.1325646272524778936701228083348348566507599785936974533930390813592027054705132858953]",
"[0.1322971796365904426897493195480018422600566845406661785571164027946857649793341907627, 0.1322971796365904426897493195480018422600566845406661785571164027946857651921833932216]",
"[0.1320297320207029917093758307611688278693533904876349037211937242301688245343043493577, 0.1320297320207029917093758307611688278693533904876349037211937242301688249773828115643]"
]
},
{
"lower_level": 77,
"upper_level": 78,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.09893352820505877056308715135442954217010863176049424112272014687791130796023525113075013659954247987",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.10003652377563366505864667392608754393325717303391626417162380660314776318061210897, 0.1000365237756336650586466739260875439332571730339162641716238066031477631877068251469]",
"[0.09976907615974621407827318513925452954255387898088498933570112803863082285024031286929, 0.0997690761597462140782731851392545295425538789808849893357011280386308228582480936858]",
"[0.09950162854385876309789969635242151515185058492785371449977844947411388251986851690032, 0.09950162854385876309789969635242151515185058492785371449977844947411388252878936209291]",
"[0.09927256991602216907584218129572407264953118279302496239131620908967253004033655066851, 0.09927256991602216907584218129572407264953118279302496239131620908967253005023541374958]",
"[0.09908770082218634231944951868549918360417958220517359495148770102509487871003971316012, 0.09908770082218634231944951868549918360417958220517359495148770102509487872112000254456]",
"[0.09893352820505877056308715135442954217010863176049424112272014687791130796023525113075, 0.09893352820505877056308715135442954217010863176049424112272014687791130797295073517173]",
"[0.09897792447229562953328386917529986920563183005705073314374087310677885000011310317266, 0.09897792447229562953328386917529986920563183005705073314374087310677885001533387427077]",
"[0.09938808924100006332425184893502599796085863906137472026895954675163968876790002040575, 0.09938808924100006332425184893502599796085863906137472026895954675163968878717713198244]",
"[0.100071018955933114669543664690992126498076356154886383338742289047652374630291182638, 0.1000710189559331146695436646909921264980763561548863833387422890476523746563617370401]",
"[0.1006928240457418784188039430685262797078739577603319435721543445318348704451157496452, 0.100692824045741878418803943068526279707873957760331943572154344531834870483063746605]",
"[0.1009754560970540555968400047924533345572271825004119451969592075857083184735968838581, 0.1009754560970540555968400047924533345572271825004119451969592075857083185337626881718]",
"[0.1009141884004460901123914849500359899802326909011119006271385509760291360698802166503, 0.1009141884004460901123914849500359899802326909011119006271385509760291361751187013525]",
"[0.1006142500457317110274026614438100099244254900175847518833581603317926085882162219292, 0.100614250045731711027402661443810009924425490017584751883358160331792608791143494319]",
"[0.1003143116910173319424138379375840298686182891340576031395777696875560810461090219547, 0.1003143116910173319424138379375840298686182891340576031395777696875560814676115088792]"
]
},
{
"lower_level": 76,
"upper_level": 77,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.06315499982431414073116134452234694550088089282022105896539301005766023009343932616396122370959128953",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.06496745138253095734999100218670780463629500912549601720451943740201462088104787909568, 0.06496745138253095734999100218670780463629500912549601720451943740201462088871529674961]",
"[0.06466751302781657826500217868048182458048780824196886846073904675777809344772593227362, 0.0646675130278165782650021786804818245804878082419688684607390467577780934563980549948]",
"[0.06436757467310219918001335517425584452468060735844171971695865611354156601440398545156, 0.06436757467310219918001335517425584452468060735844171971695865611354156602408081323998]",
"[0.06405948451262724159785042020555260782054117277026210600294257478220117148631744099157, 0.06405948451262724159785042020555260782054117277026210600294257478220117149705900468032]",
"[0.0637305877525941085639018315115556867196095283822836668584752070708109760669937158026, 0.06373058775259410856390183151155568671960952838228366685847520707081097607898915507342]",
"[0.06337067295448333157331632651117073811503508680086343838634296042765687934411107239708, 0.06337067295448333157331632651117073811503508680086343838634296042765687935778415408913]",
"[0.06315499982431414073116134452234694550088089282022105896539301005766023009343932616396, 0.06315499982431414073116134452234694550088089282022105896539301005766023010960530163702]",
"[0.06326734589964602306714678455524313206504133521466527897646016878829299233966426753024, 0.06326734589964602306714678455524313206504133521466527897646016878829299235978056310094]",
"[0.06365010398913413438742355322213934470397519883732886062323420195875874980808445670246, 0.06365010398913413438742355322213934470397519883732886062323420195875874983473054553374]",
"[0.0640164951852539112393553326531696121605283418451381374828916706013274957033507308429, 0.0640164951852539112393553326531696121605283418451381374828916706013274957413345143478]",
"[0.06412350975765051930021520675351882045126439083558035312938801221421872140788577379321, 0.06412350975765051930021520675351882045126439083558035312938801221421872146702378931596]",
"[0.06397020518543498404896809210780266249756295972156780234467234721581317601788600172711, 0.06397020518543498404896809210780266249756295972156780234467234721581317611995240653829]",
"[0.06363781006405774115386158112157130875461938543796153216442514356458890799547440836209, 0.06363781006405774115386158112157130875461938543796153216442514356458890819073599280915]",
"[0.06330541494268049825875507013533995501167581115435526198417793991336463991520422749933, 0.06330541494268049825875507013533995501167581115435526198417793991336464031937818990237]"
]
},
{
"lower_level": 75,
"upper_level": 76,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.02102893908981315639397593581468939760960804193042154477361880435147940012117906770358937326583942856",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.02472286906321017759197466884204849778752973041474745891955346638866464513565988572599, 0.02472286906321017759197466884204849778752973041474745891955346638866464514409127706064]",
"[0.02439047394183293469686815785581714404458615613114118873930626273744037715929443377291, 0.02439047394183293469686815785581714404458615613114118873930626273744037716882870689693]",
"[0.02405807882045569180176164686958579030164258184753491855905905908621610918292898181984, 0.02405807882045569180176164686958579030164258184753491855905905908621610919356613673321]",
"[0.02366745832380456473913048821809486103749660244378556408857114456884528687955096481659, 0.02366745832380456473913048821809486103749660244378556408857114456884528689134773093135]",
"[0.02318609103630653550463887318297098957691217815089089567533805860593385319389594330918, 0.02318609103630653550463887318297098957691217815089089567533805860593385320703135287595]",
"[0.02260728503070211690413997584205295469763509778050200666817448831151281860053467345549, 0.02260728503070211690413997584205295469763509778050200666817448831151281861541027882686]",
"[0.02211558583359874449449204273833469261073219729547478118661601703313594730153959045259, 0.02211558583359874449449204273833469261073219729547478118661601703313594731892860264668]",
"[0.02191395276972911691868496563303654457215330249368631716148094892484381375852314145073, 0.02191395276972911691868496563303654457215330249368631716148094892484381377980943426444]",
"[0.02198233630185973397572468259534616333943096367778628058662384133596030091491428478536, 0.02198233630185973397572468259534616333943096367778628058662384133596030094255190344022]",
"[0.02208235494834337554958142267320227445474199061650845544315617138952329155167558105273, 0.02208235494834337554958142267320227445474199061650845544315617138952329159025232682135]",
"[0.02200673330079282176923613303119060767123823597032964003542644760471381802268654477848, 0.02200673330079282176923613303119060767123823597032964003542644760471381808160257907029]",
"[0.02175850756225641002696109307321545959976684588508908302317261996846287187285705983661, 0.02175850756225641002696109307321545959976684588508908302317261996846287197302636743336]",
"[0.02139372332603478321046851444395242860468744390775531389839571215997113602489351335634, 0.02139372332603478321046851444395242860468744390775531389839571215997113621469549191253]",
"[0.02102893908981315639397593581468939760960804193042154477361880435147940012117906770359, 0.02102893908981315639397593581468939760960804193042154477361880435147940051211553002676]"
]
}
],
"pointwise_nonnegative_pair_energy_certified": true,
"second_is_unassigned_mathematical_control": false
},
{
"depth": 2,
"shell_levels": [
80,
94
],
"other_unsmoothed_chart_minimum_source_cost_lower_bound": "0.001662526762806632298585646064317141775172242321998606412727297239100576894396632750415485827289167804",
"common_smoothing_width_interval": "[0.00003970760187135478964154730942511701397745508053711967522862079237823054779163585056431, 0.00003970760187135478964154730942511701397745508053711967522862079237823054792301403910759]",
"smoothing_bands": [
{
"lower_level": 93,
"upper_level": 94,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.01399649425330866577714687110116946045114569126528215936557208478877755548067945183814169876270666492",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.014988892068035940177793541422232125307362681927476946037083841328329713083054623642, 0.01498889206803594017779354142223212530736268192747694603708384132832971308806891526472]",
"[0.01519180758841897242137017174048539016147715308654223381038337307555185654919850469494, 0.01519180758841897242137017174048539016147715308654223381038337307555185655488430958542]",
"[0.01539472310880200466494680205873865501559162424560752158368290482277400001534238574788, 0.01539472310880200466494680205873865501559162424560752158368290482277400002169970388965]",
"[0.01538310140671327222993738407844469669496908685195981408623834468750675289849819478586, 0.01538310140671327222993738407844469669496908685195981408623834468750675290560795614523]",
"[0.01505843343439050607393442395656493250847786819883207935573338527658272099605099574283, 0.01505843343439050607393442395656493250847786819883207935573338527658272100416837468224]",
"[0.01442060476181865974563171133009529807023248794205275761243846780039223613015978255078, 0.01442060476181865974563171133009529807023248794205275761243846780039223613985693424729]",
"[0.01399649425330866577714687110116946045114569126528215936557208478877755548067945183814, 0.01399649425330866577714687110116946045114569126528215936557208478877755549306196157836]",
"[0.01436522302006232951636673422795304485668760833085914466719925203273190140768216591901, 0.01436522302006232951636673422795304485668760833085914466719925203273190142476078487089]",
"[0.01550172172803055267805489475019402362283842903561758462676285631897794159218211228371, 0.01550172172803055267805489475019402362283842903561758462676285631897794161767644656898]",
"[0.01678290202780884877826838029732863776728426083273343003217383711703696387326515639149, 0.01678290202780884877826838029732863776728426083273343003217383711703696391467075974567]",
"[0.01765411099678467439768339046736287037092524860423670796253668827750617738029785708041, 0.01765411099678467439768339046736287037092524860423670796253668827750617745443248405691]",
"[0.01811106953606502522178046856645788417484640788508989736525208410735831598961637096927, 0.01811106953606502522178046856645788417484640788508989736525208410735831613695690301025]",
"[0.01828144437637600596430302095897659813345990849023236384412469773953324440635124982376, 0.01828144437637600596430302095897659813345990849023236384412469773953324472574068449017]",
"[0.01845181921668698670682557335149531209207340909537483032299731137170817270532904803343, 0.01845181921668698670682557335149531209207340909537483032299731137170817343228151238571]"
]
},
{
"lower_level": 92,
"upper_level": 93,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.04314701983205899396923541225069812984779067169161700124399680657673270304890691636848046380887683517",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.04347306793721348699510200553385077684911017592591533217599808812451673031405356600437, 0.04347306793721348699510200553385077684911017592591533217599808812451673031839747049668]",
"[0.04364344277752446773762455792636949080772367653105779865487070175669165881652519837076, 0.04364344277752446773762455792636949080772367653105779865487070175669165882144456079544]",
"[0.04381381761783544848014711031888820476633717713620026513374331538886658731899683080304, 0.0438138176178354484801471103188882047663371771362002651337433153888665873244916510942]",
"[0.04384434957456724535221026742715454799006629515004928282112049822454165727964103419454, 0.04384434957456724535221026742715454799006629515004928282112049822454165728579156305503]",
"[0.04366655574772311609461888114809043870509895745165843403526068395213128592944458232037, 0.04366655574772311609461888114809043870509895745165843403526068395213128593650328127565]",
"[0.04327550184413044166077957995137970755010188365757941818591513832241027801267359482838, 0.04327550184413044166077957995137970755010188365757941818591513832241027802120584972901]",
"[0.04314701983205899396923541225069812984779067169161700124399680657673270304890691636848, 0.04314701983205899396923541225069812984779067169161700124399680657673270306000442478604]",
"[0.04379413362567113833497510990454659503794128554492552459077599900028483220071564083554, 0.04379413362567113833497510990454659503794128554492552459077599900028483221636221532779]",
"[0.04515030611274150453669458675747321453807162329658498662578921947977581338731956942908, 0.04515030611274150453669458675747321453807162329658498662578921947977581341117916433251]",
"[0.04658387410418317820241473550093486734296612625708337549344505064680338688511727411327, 0.04658387410418317820241473550093486734296612625708337549344505064680338692455437900057]",
"[0.04754141025423447086383710604785159820347151661116260436045472870466020503894128420262, 0.04754141025423447086383710604785159820347151661116260436045472870466020511043186497826]",
"[0.048015145453088914555906049908435300083929421359058262409887960044494316104572141924, 0.04801514545308891455590604990843530008392942135905826240988796004449431624767754617716]",
"[0.04815250549885506854570690153738396601473582380721674897946357967905458953061559090836, 0.04815250549885506854570690153738396601473582380721674897946357967905458984179409983244]",
"[0.04828986554462122253550775316633263194554222625537523554903919931361486284184945615945, 0.04828986554462122253550775316633263194554222625537523554903919931361486355072019788541]"
]
},
{
"lower_level": 91,
"upper_level": 92,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.06820812296230599678998072371712241339603326434511216392061900078070441950008883769797886104888658385",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.06820812296230599678998072371712241339603326434511216392061900078070441950008883769798, 0.0682081229623059967899807237171224133960332643451121639206190007807044195038805753335]",
"[0.06834548300807215077978157534607107932683966679327065049019462041526469300991869763244, 0.06834548300807215077978157534607107932683966679327065049019462041526469301421076626923]",
"[0.06848284305383830476958242697501974525764606924142913705977024004982496651974855769867, 0.06848284305383830476958242697501974525764606924142913705977024004982496652454095720497]",
"[0.06854121417796598256633879860678735683175832904827140854374487090518002847369164170179, 0.06854121417796598256633879860678735683175832904827140854374487090518002847906628007984]",
"[0.06847660447032514516656148363752065390130583904110687097960146858967591117540785836421, 0.06847660447032514516656148363752065390130583904110687097960146858967591118162225831693]",
"[0.06828018394422435583879845401503061822689928818103064756884804686126834311475877184943, 0.06828018394422435583879845401503061822689928818103064756884804686126834312238940237187]",
"[0.06838302997288710200166109121950864062285387311862153281874112187686671828217861130812, 0.06838302997288710200166109121950864062285387311862153281874112187686671829233766044664]",
"[0.06924112916019247907525069818833523849003283857115948788386774182877983961179091978226, 0.06924112916019247907525069818833523849003283857115948788386774182877983962649470742322]",
"[0.07075540223603775588839102295976698227315413857166032346625059441351370113238387041753, 0.07075540223603775588839102295976698227315413857166032346625059441351370115533619961498]",
"[0.07229261774150588859581072581659263497573819429612427300107486281316035356239133458857, 0.07229261774150588859581072581659263497573819429612427300107486281316035360097116632208]",
"[0.07330499303098707346935987930626737306708262970187033005755323185355735125581384360731, 0.07330499303098707346935987930626737306708262970187033005755323185355735132636893352331]",
"[0.07378213012545689800965657334941260564837438549971321319057168517705872867085137229255, 0.07378213012545689800965657334941260564837438549971321319057168517705872881233332826967]",
"[0.0738860380350732805606013640228141236497102700760672656062126250603194302335735497701, 0.07388603803507328056060136402281412364971027007606726560621262506031943054048867340133]",
"[0.07398994594468966311154615469621564165104615465242131802185356494358013168412686987827, 0.07398994594468966311154615469621564165104615465242131802185356494358013238081284322155]"
]
},
{
"lower_level": 90,
"upper_level": 91,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.08886549600596971506783402699091634625392219715145465440437587080154755075204916202068658131640821118",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.08886549600596971506783402699091634625392219715145465440437587080154755075204916202069, 0.08886549600596971506783402699091634625392219715145465440437587080154755075550537404471]",
"[0.08896940391558609761877881766431786425525808172780870682001681068480825239726527329073, 0.088969403915586097618778817664317864255258081727808706820016810684808252401166825576]",
"[0.08907331182520248016972360833771938225659396630416275923565775056806895404248138456077, 0.0890733118252024801697236083377193822565939663041627592356577505680689540468282771073]",
"[0.08914609957524498770004365920727234606956707868563784460517127996899796511372135535317, 0.08914609957524498770004365920727234606956707868563784460517127996899796511859861836692]",
"[0.08916307321530560532708171767772603041850619465165292215943012768629214953367010735104, 0.08916307321530560532708171767772603041850619465165292215943012768629214953934383091562]",
"[0.08911237428393233286236745233718947366076601758321991208011037162027201223724439540649, 0.08911237428393233286236745233718947366076601758321991208011037162027201224430818116994]",
"[0.08938625609511351323346557282030198750615957000217604994855273433582929903334110488961, 0.08938625609511351323346557282030198750615957000217604994855273433582929904293677593917]",
"[0.09039219497939540668288118072438835246490856044588331459932276127953653593932082007994, 0.09039219497939540668288118072438835246490856044588331459932276127953653595351079443446]",
"[0.0920069328272862666494837336527876991639890551203249167804400239880938812829559731488, 0.09200693282728626664948373365278769916398905512032491678044002398809388130550645827126]",
"[0.0936021971838900147067606294681931581743084288118199236599207338812379430648474507458, 0.09360219718389001470676062946819315817430842881181992365992073388123794310319701728807]",
"[0.09463995622498234878944817974535706332328728316256404612215467241497323697050923114036, 0.09463995622498234878944817974535706332328728316256404612215467241497323704098081353913]",
"[0.0951079887331829869482567026102759558318432718687392564309695289751957571832038358354, 0.09510798873318298694825670261027595583184327186873925643096952897519575732438421471395]",
"[0.095178043711829991439352129074855084500170242067665780859075334793985664606932748534, 0.09517804371182999143935212907485508450017024206766578085907533479398566491194007498228]",
"[0.09524809869047699593044755553943421316849721226659230528718114061277557192051675050268, 0.09524809869047699593044755553943421316849721226659230528718114061277557260964090132706]"
]
},
{
"lower_level": 89,
"upper_level": 90,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.10514824491477761976957276266793377109173112975426429935104444442086348410706635784158300594023871",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.1051482449147776197695727626679337710917311297542642993510444444208634841070663578416, 0.1051482449147776197695727626679337710917311297542642993510444444208634841102662015334]",
"[0.1052182998934246242606681891325128997600580999531908237791502502396533916125039254959, 0.1052182998934246242606681891325128997600580999531908237791502502396533916161133645454]",
"[0.1052883548720716287517636155970920284283850701521173482072560560584432991179414931501, 0.1052883548720716287517636155970920284283850701521173482072560560584432991219605274257]",
"[0.1053630042712580545371536444655819377385297716573631655794873693577230316639850725873, 0.105363004271258054537153644465581937738529771657363165579487369357723031668499164525]",
"[0.1054319915337968545916013706893097200726818351959782215336451829952657369541358376834, 0.1054319915337968545916013706893097200726818351959782215336451829952657369594123484923]",
"[0.105481241601516663877885257737390405288605596068445626891383352519576938483490782579, 0.1054812416015166638778852577373904052886055960684456268913833525195769384901260057257]",
"[0.1058697625670366246787573298575683926885911250764848299620763931746034709367694232033, 0.1058697625670366246787573298575683926885911250764848299620763931746034709459097817313]",
"[0.1069645295742108413037931267951002747806849932904230793643260593382308044269675331777, 0.1069645295742108413037931267951002747806849932904230793643260593382308044406806746948]",
"[0.1086259226361905966296293526420909731635534291678133085057278870657642439522344823895, 0.1086259226361905966296293526420909731635534291678133085057278870657642439742828953349]",
"[0.1102366900821368949121151459339648208522397033692973158264263959807721265972434572604, 0.1102366900821368949121151459339648208522397033692973158264263959807721266350147198063]",
"[0.1112723530956532700608644346992371352682097345444213807989845492193429146674880973155, 0.1112723530956532700608644346992371352682097345444213807989845492193429147370844473333]",
"[0.1117196189199658162380773370802281796582603151371544000220962608401589987387556993699, 0.1117196189199658162380773370802281796582603151371544000220962608401589988780332073028]",
"[0.1117554564988386154333043027470195382665141797990258776795212309894109422872447482672, 0.1117554564988386154333043027470195382665141797990258776795212309894109425872296742318]",
"[0.1117912940777114146285312684138108968747680444608973553369462011386628857282911485304, 0.111791294077711414628531268413810896874768044460897355336946201138662886403868783865]"
]
},
{
"lower_level": 88,
"upper_level": 89,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.1167900577998736348908914825599555055783801176694145890381138252616571646909063219901026205919086172",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.1167900577998736348908914825599555055783801176694145890381138252616571646909063219901, 0.1167900577998736348908914825599555055783801176694145890381138252616571646939844341316]",
"[0.1168258953787464340861184482267468641866339823312860666955387954109091083195529413222, 0.1168258953787464340861184482267468641866339823312860666955387954109091083230233365558]",
"[0.1168617329576192332813454138935382227948878469931575443529637655601610519481995607861, 0.1168617329576192332813454138935382227948878469931575443529637655601610519520622388482]",
"[0.1169265327180071688773293569198841908175862977072607480411750457729793870318522690738, 0.1169265327180071688773293569198841908175862977072607480411750457729793870361925272834]",
"[0.1170199379306972138386488342504048949559217341247607217535640732215341108516112100399, 0.117019937930697213838648834250404894955921734124760721753564073221534110856695856536]",
"[0.1171264150548042185467559749912025303560499763172323041525988473807214913124120364102, 0.1171264150548042185467559749912025303560499763172323041525988473807214913188360550549]",
"[0.1175769639592437437457366837717325318990879600116726833793286889142329244353637778417, 0.1175769639592437437457366837717325318990879600116726833793286889142329244442706729391]",
"[0.1187055643266204197477558112664125415809753618972553979032049846898127530056238785293, 0.1187055643266204197477558112664125415809753618972553979032049846898127530190737071731]",
"[0.1203635205107147982944828065091646960701590250234692905344995720341374312455135766577, 0.1203635205107147982944828065091646960701590250234692905344995720341374312672447651155]",
"[0.1219502114242393127354466814037755528967952396714991340395522807232484036668507068933, 0.1219502114242393127354466814037755528967952396714991340395522807232484037041695096364]",
"[0.1229582183875167889325484804039629225863551650678439342955267645856018487522789718774, 0.1229582183875167889325484804039629225863551650678439342955267645856018488210245532117]",
"[0.1233738764172699670358539599595122549605028895373487258217763138634491273053899706507, 0.1233738764172699670358539599595122549605028895373487258217763138634491274426333131282]",
"[0.1233751682385115030547857266401189513384025848246343519956327885579589488575345765588, 0.1233751682385115030547857266401189513384025848246343519956327885579589491521496510939]",
"[0.1233764600597530390737174933207256477163022801119199781694892632524687703049621698262, 0.123376460059753039073717493320725647716302280111919978169489263252468770966382985887]"
]
},
{
"lower_level": 87,
"upper_level": 88,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.1235542836291506727328878703959161559811249052409195827893134190071210609242023696253592830330629211",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.1235542836291506727328878703959161559811249052409195827893134190071210609242023696254, 0.1235542836291506727328878703959161559811249052409195827893134190071210609272881816564]",
"[0.1235555754503922087518196370765228523590246005282052089631698937016308825548365708743, 0.1235555754503922087518196370765228523590246005282052089631698937016308825583149700081]",
"[0.123556867271633744770751403757129548736924295815490835137026368396140704185470772255, 0.1235568672716337447707514037571295487369242958154908351370263683961407041893417583598]",
"[0.1236009264256066172114308112305291805086405525171762295728283742178985124769954575163, 0.1236009264256066172114308112305291805086405525171762295728283742178985124813436039255]",
"[0.1236930721854685111758094089048880454364611018634680345039687678771067437303074029415, 0.1236930721854685111758094089048880454364611018634680345039687678771067437353972604461]",
"[0.1238170184209520092005239143501119703121001553451374201712530800502353542116094552278, 0.1238170184209520092005239143501119703121001553451374201712530800502353542180309640386]",
"[0.1242806615841710688475591930300268995181915914549120383771710066967613342188136798901, 0.1242806615841710688475591930300268995181915914549120383771710066967613342277004165919]",
"[0.1253920025411084046852670861137359278239327443483909887137753905812588928830715538493, 0.12539200254110840468526708611373592782393274434839098871377539058125889289646404137]",
"[0.1270000407410593723320006876363400395348481887223097282891678676194475608752972009213, 0.1270000407410593723320006876363400395348481887223097282891678676194475608968908735229]",
"[0.1285259567246066716386146761532302941342112491873580534240871852886179960429303377945, 0.1285259567246066716386146761532302941342112491873580534240871852886179960799219560448]",
"[0.1294826127079269211620897497260208795779810431727795895080569798839851934883604331421, 0.1294826127079269211620897497260208795779810431727795895080569798839851935562868722549]",
"[0.1298566199209136398703909617037457693851026373620758412446523939020580064642410406485, 0.1298566199209136398703909617037457693851026373620758412446523939020580065993382741556]",
"[0.1298230735286669061141553595322227030812797566150203259225591970568206644947217516967, 0.129823073528666906114155359532222703081279756615020325922559197056820664783657105079]",
"[0.1297895271364201723579197573606996367774568758679648106004660002115833224232305240657, 0.1297895271364201723579197573606996367774568758679648106004660002115833230699478894406]"
]
},
{
"lower_level": 86,
"upper_level": 87,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.1251658892014131134524367056785413832167049545569210903388255984737811247803899218133729440234282568",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.1252329819859065809649079100215875158243507160510321209830119921642558085660000807534, 0.1252329819859065809649079100215875158243507160510321209830119921642558085692178444686]",
"[0.1251994355936598472086723078500644495205278353039766056609187953190184666731950012834, 0.1251994355936598472086723078500644495205278353039766056609187953190184666768224690728]",
"[0.1251658892014131134524367056785413832167049545569210903388255984737811247803899218134, 0.125165889201413113452436705678541383216704954556921090338825598473781124784427093677]",
"[0.125179114239219953376280823129149684589150091700034234603103423275162550454974526026, 0.1251791142392199533762808231291496845891500917000342346031034232751625504595047290777]",
"[0.1252461868351209953791417153093230281322017793477837431728665293228245842629612924464, 0.125246186835120995379141715309323028132201779347783743172866529322824584268245228916]",
"[0.1253507234522874643068011563497567532459435074266734267722716602717677687275921503428, 0.1253507234522874643068011563497567532459435074266734267722716602717677687342112366789]",
"[0.1257820991842341859674619114574180247395941299490843281070634642870089483688376754768, 0.1257820991842341859674619114574180247395941299490843281070634642870089483779090330789]",
"[0.1268288776170711027633569641785093806340909479858286565096786171940306641830548006962, 0.1268288776170711027633569641785093806340909479858286565096786171940306641965883080361]",
"[0.1283440235379448911011438273838040702108711219903123900198704418715498178097415279912, 0.1283440235379448911011438273838040702108711219903123900198704418715498178313720358231]",
"[0.1297752643425583855920338760123579872341889459427354440934703114444040167375831302452, 0.1297752643425583855920338760123579872341889459427354440934703114444040167743717703341]",
"[0.1306586860310184854636542576708820058196978419219873888176311441916590664478994224949, 0.1306586860310184854636542576708820058196978419219873888176311441916590665150445084218]",
"[0.1309817750928241395319689752722113838218413882358049786445309391335805158744200272769, 0.1309817750928241395319689752722113838218413882358049786445309391335805160072766584037]",
"[0.1309131337308456445532150561247018780363799037435989049012876803322558237631531203086, 0.1309131337308456445532150561247018780363799037435989049012876803322558240461329209365]",
"[0.1308444923688671495744611369771923722509184192513928311580444215309311315526755050682, 0.130844492368867149574461136977192372250918419251392831158044421530931132184199832178]"
]
},
{
"lower_level": 85,
"upper_level": 86,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.1214817816563431251559738257634689927085748700046101900257912334508855671705317480979335262517044209",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.121645991867620197642173246477501405950700012275926938881249450412156191717271628275, 0.1216459918676201976421732464775014059507000122759269388812494504121561917207840342992]",
"[0.1215773505056417026634193273299919001652385277837208651380061916108314996808449255669, 0.1215773505056417026634193273299919001652385277837208651380061916108314996848001744056]",
"[0.1215087091436632076846654081824823943797770432915147913947629328095068076444182228588, 0.1215087091436632076846654081824823943797770432915147913947629328095068076488163143803]",
"[0.1214817816563431251559738257634689927085748700046101900257912334508855671705317480979, 0.1214817816563431251559738257634689927085748700046101900257912334508855671754563426813]",
"[0.1215017776953518870652602593916137114100986210407379737040105091494292499297009040181, 0.1215017776953518870652602593916137114100986210407379737040105091494292499354127576585]",
"[0.1215528222666538071979386663399275028121308676067596537677881896717482526935160215491, 0.1215528222666538071979386663399275028121308676067596537677881896717482527005950219444]",
"[0.1219100376500291275780526450719207957859154185642794634942006956052033135847390157561, 0.1219100376500291275780526450719207957859154185642794634942006956052033135942968530975]",
"[0.1228486302469624783719922813705831669271051950469350760858747338247204793790528279296, 0.1228486302469624783719922813705831669271051950469350760858747338247204793930856140277]",
"[0.1242313145330360530441906316275380261423133474875978541518213768323180955590085546581, 0.1242313145330360530441906316275380261423133474875978541518213768323180955811182331915]",
"[0.1255366968203639463272192303925700023423760741194522981195768133664088742938048044768, 0.1255366968203639463272192303925700023423760741194522981195768133664088743309689829577]",
"[0.126326760219702747112009198250545513946948604803542646734289481258288864167244059656, 0.126326760219702747112009198250545513946948604803542646734289481258288864234433467355]",
"[0.1265904175804986249907856782404630718670119149135780224295640635184114988040925363244, 0.1265904175804986249907856782404630718670119149135780224295640635184114989360303708868]",
"[0.1264864599968032648197779720749246693704549597185568143417365021423604481923046627046, 0.1264864599968032648197779720749246693704549597185568143417365021423604484717010859139]",
"[0.1263825024131079046487702659093862668738980045235356062539089407663093974834728445842, 0.1263825024131079046487702659093862668738980045235356062539089407663093981044157283105]"
]
},
{
"lower_level": 84,
"upper_level": 85,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.1122753186708032588400593364926905480910580306022011966599824621925713351934615779262241617361954217",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.1126400194182636711110979316996247161845598918538425111992035757813592486503230035622, 0.1126400194182636711110979316996247161845598918538425111992035757813592486542218366193]",
"[0.1125360618345683109400902255340863136880029366588213031113760144053081981120188178046, 0.112536061834568310940090225534086313688002936658821303111376014405308198116408890535]",
"[0.1124321042508729507690825193685479111914459814638000950235484530292571475737146321787, 0.1124321042508729507690825193685479111914459814638000950235484530292571475785959444507]",
"[0.1123564590786334651268699725313119862126065508675236433790628655858582363768174123999, 0.1123564590786334651268699725313119862126065508675236433790628655858582363822714090178]",
"[0.1123091333157425739691400070933685495390919273242801364142417029496529998155192189952, 0.1123091333157425739691400070933685495390919273242801364142417029496529998217998767938]",
"[0.1122753186708032588400593364926905480910580306022011966599824621925713351934615779262, 0.1122753186708032588400593364926905480910580306022011966599824621925713352011338832067]",
"[0.1125198486704332501483858898777518798235297333448902051132917991651274734915977170673, 0.1125198486704332501483858898777518798235297333448902051132917991651274735017449947876]",
"[0.1133102045455168933166153235359211768957843634342473540410128301192079192459827574807, 0.1133102045455168933166153235359211768957843634342473540410128301192079192605502645475]",
"[0.1145241632101195835216940413156513272163674628937146975824774139927271134281728624502, 0.1145241632101195835216940413156513272163674628937146975824774139927271134506700111671]",
"[0.1156751411520643380923023334853310215917481259356426549129798923963078312891831090339, 0.115675141152064338092302333485331021591748125935642654912979892396307831326404410019]",
"[0.1163534304786461701721208937043319565691624183385182795765747748548240284697675790854, 0.1163534304786461701721208937043319565691624183385182795765747748548240285362792031821]",
"[0.1165498749678263234755661572230923892350259753584962706474313522083322776589576181459, 0.1165498749678263234755661572230923892350259753584962706474313522083322777885180662322]",
"[0.1164104152268646032070341418829382997557819652470333185538004499166110442944459086522, 0.1164104152268646032070341418829382997557819652470333185538004499166110445674191741192]",
"[0.1162709554859028829385021265427842102765379551355703664601695476248898108356822487799, 0.1162709554859028829385021265427842102765379551355703664601695476248898114405721904795]"
]
},
{
"lower_level": 83,
"upper_level": 84,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.09739603833677693528833778844262840130698489373480538890873086987938413216541644299081200367955829794",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.0980877445085806084485395618044154090355894429067481371917639242440686923746914326175, 0.09808774450858060844853956180441540903558944290674813719176392424406869237905672209011]",
"[0.09794828476761888818000754646426131955634543279528518509813302195234745908160912139711, 0.09794828476761888818000754646426131955634543279528518509813302195234745908652848942232]",
"[0.09780882502665716791147553112410723007710142268382223300450211966062622578852681017671, 0.09780882502665716791147553112410723007710142268382223300450211966062622579400025662275]",
"[0.09767662891355675621188989116948778791030634908763212955039561694651717784996567157022, 0.09767662891355675621188989116948778791030634908763212955039561694651717785607195535305]",
"[0.09754344328611909888212943028420737794190254731202985411329366871111848250615622525833, 0.09754344328611909888212943028420737794190254731202985411329366871111848251314114180808]",
"[0.09739603833677693528833778844262840130698489373480538890873086987938413216541644299081, 0.09739603833677693528833778844262840130698489373480538890873086987938413217382705963958]",
"[0.0974926272380768515642189993316027487226941396366711689657674669256539328241923945856, 0.09749262723807685156421899933160274872269413963667116896576746692565393283507809015041]",
"[0.09809816303729528615107799358342465389371022989155430127864878331579521984430821912395, 0.09809816303729528615107799358342465389371022989155430127864878331579521985955400079602]",
"[0.09911034019780186732023475696129599133123913738852559398996617919444990911082805592065, 0.09911034019780186732023475696129599133123913738852559398996617919444990913383608258071]",
"[0.1000809279166604940204168924795260445683952065390788431824095966599022783435755290769, 0.1000809279166604940204168924795260445683952065390788431824095966599022783809355686814]",
"[0.1006306856736431078402957760964383623326268097570296750706812505810128356588932163422, 0.100630685673643107840295776096438362332626809757029675070681250581012835724737266428]",
"[0.100752847593463140176744913709230659769110911212246331082905978443607415014984122745, 0.1007528475934631401767449137092306597691109112122463310829059784436074151420694728075]",
"[0.1005777348963649835050830457552328969828662971246066239170230426066202825835449851099, 0.100577734896364983505083045755232896982866297124606623917023042606620282849852794515]",
"[0.1004026221992668268334211778012351341966216830369669167511401067696331500606544965509, 0.100402622199266826833421177801235134196621683036966916751140106769633150649087439605]"
]
},
{
"lower_level": 82,
"upper_level": 83,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.07673432295679285350060023409561524229096596190885415984014706947624370779895118488172300525495230372",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.07788694610118549810931626065818534798247502072496246077196510384076462223197639644676, 0.07788694610118549810931626065818534798247502072496246077196510384076462223687881999722]",
"[0.07771183340408734143765439270418758519623040663732275360608216800377748986983317186961, 0.07771183340408734143765439270418758519623040663732275360608216800377748987536626225007]",
"[0.07753672070698918476599252475018982240998579254968304644019923216679035750768994742424, 0.07753672070698918476599252475018982240998579254968304644019923216679035751385370450293]",
"[0.07734085146361704366236760540555972401100299251646628942786248755089409043004901986484, 0.07734085146361704366236760540555972401100299251646628942786248755089409043691728804857]",
"[0.07710492533381686538329050051513866496941155797886174496820982696331293241123226370331, 0.07710492533381686538329050051513866496941155797886174496820982696331293241903669105615]",
"[0.07681775777406893435608332063028279207317818069108194560464253607042324254168927361372, 0.07681775777406893435608332063028279207317818069108194560464253607042324255094734909121]",
"[0.07673432295679285350060023409561524229096596190885415984014706947624370779895118488172, 0.07673432295679285350060023409561524229096596190885415984014706947624370781065835697421]",
"[0.07712182045323581707905872998938742451155825046511089438265173337276750789844086165087, 0.0771218204532358170790587299893874245115582504651108943826517333727675079143895251313]",
"[0.07790227337820632588051946980927953042111449729034045920754226997970867868122470245473, 0.07790227337820632588051946980927953042111449729034045920754226997970867870465745094531]",
"[0.07866896923319309359864338465594770037797916842408549456303238837593447852427489239839, 0.07866896923319309359864338465594770037797916842408549456303238837593447856148847649463]",
"[0.07907504747687721776251242173183253276723076248571400695688510870267671963710211452438, 0.07907504747687721776251242173183253276723076248571400695688510870267671970163528551903]",
"[0.0791165481970957711618458644045223982940266123238874876527373991342546304815655631997, 0.0791165481970957711618458644045223982940266123238874876527373991342546306048711751517]",
"[0.07890566671055126348329592043985192998333677745866140709418637912139632583809085439628, 0.07890566671055126348329592043985192998333677745866140709418637912139632609517343715376]",
"[0.07869478522400675580474597647518146167264694259343532653563535910853802110654564407781, 0.07869478522400675580474597647518146167264694259343532653563535910853802167354621490283]"
]
},
{
"lower_level": 81,
"upper_level": 82,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.05017489012248894349229599905961996022608902032222497164907211407520553775624084139604869284311104982",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.05195964636137352643358161026728251087324334402376755738251999555528170671223538412144, 0.05195964636137352643358161026728251087324334402376755738251999555528170671771473281468]",
"[0.05174876487482901875503166630261204256255350915854147682396897554242340213528905940097, 0.05174876487482901875503166630261204256255350915854147682396897554242340214148858628906]",
"[0.0515378833882845110764817223379415742518636742933153962654179555295650975583427346805, 0.05153788338828451107648172233794157425186367429331539626541795552956509756526243976344]",
"[0.05127190956504254568260138304824502284727379193716609574908563759494636388909791021817, 0.0512719095650425456826013830482450228472737919371660957490856375949463638968064896863]",
"[0.05091797117586181435138834294332960603904574657741928168918961515862594700301398932909, 0.05091797117586181435138834294332960603904574657741928168918961515862594701172818945437]",
"[0.05046735206489495720690840316639288486764478611456258550124717694834695233541975598847, 0.05046735206489495720690840316639288486764478611456258550124717694834695234562576416173]",
"[0.05017489012248894349229599905961996022608902032222497164907211407520553775624084139605, 0.05017489012248894349229599905961996022608902032222497164907211407520553776887684365574]",
"[0.05031439631206444809715001870450879064244737865112501556284120564065469560883871503668, 0.05031439631206444809715001870450879064244737865112501556284120564065469562559872030278]",
"[0.05083620279164092600041509983792566262937560573725903903401373992199622732096279466599, 0.05083620279164092600041509983792566262937560573725903903401373992199622734492069095302]",
"[0.05137791552098213132980716315309578583845597561847467858272677642424149829576306548171, 0.05137791552098213132980716315309578583845597561847467858272677642424149833290941229602]",
"[0.05162672832347478645397608950941059873135694590977298844459968126886211695715695404695, 0.05162672832347478645397608950941059873135694590977298844459968126886211702042057887763]",
"[0.05158186037991106990080260194132431463757904061627475525533558800801845522306335493246, 0.05158186037991106990080260194132431463757904061627475525533558800801845534257641058138]",
"[0.05133512907429764358370232320411048606746196125300036496423316592790161173652019266829, 0.0513351290742976435837023232041104860674619612530003649642331659279016119843066332575]",
"[0.05108839776868421726660204446689665749734488188972597467313074384778476816526872249507, 0.0510883977686842172666020444668966574973448818897259746731307438477847687107451415064]"
]
},
{
"lower_level": 80,
"upper_level": 81,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.01754726088846412938771145401083486426581327642366493857940944123210370011745684244299469495282226121",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.02025127350039235976037237315560201446135090398400902592954280155410236023153140406258, 0.02025127350039235976037237315560201446135090398400902592954280155410236023787332455006]",
"[0.02000454219477893344327209441838818589123382462073463563844037947398551680871396005716, 0.02000454219477893344327209441838818589123382462073463563844037947398551681587785423578]",
"[0.01975781088916550712617181568117435732111674525746024534733795739386867338589651605174, 0.01975781088916550712617181568117435732111674525746024534733795739386867339388238388855]",
"[0.0194159719637479855291917042976244381632765637879893585052357383569638289333658709185, 0.01941597196374798552919170429762443816327656378798935850523573835696382894224054138292]",
"[0.01893031111621124440731980093446192879861201121384995860828219059537834357226719452361, 0.01893031111621124440731980093446192879861201121384995860828219059537834358224092931575]",
"[0.01829496135630126130071100643442089050979373211012399279032549919895053725505604558416, 0.01829496135630126130071100643442089050979373211012399279032549919895053726659947721357]",
"[0.01776745657565746747447225313138982982794169026090773153944407638927522715988130489255, 0.01776745657565746747447225313138982982794169026090773153944407638927522717390129137867]",
"[0.01763218628957340005248591831519730271456053301833370429124475164965517587309745584142, 0.01763218628957340005248591831519730271456053301833370429124475164965517589123068800928]",
"[0.01787135434471592551670270574491978203553423372958068952489541911966200805621810039631, 0.01787135434471592551670270574491978203553423372958068952489541911966200808143720077315]",
"[0.01816933107609129169305183692375684606685349281328972890568467445443693644576317153671, 0.01816933107609129169305183692375684606685349281328972890568467445443693648387417637561]",
"[0.018248808192735417111465712178662307052498821011142248228556405237445964718311906453, 0.01824880819273541711146571217866230705249882101114224822855640523744596478187635052999]",
"[0.01811251589364800920018850132499526990348794362302944357255095708566832693932768061231, 0.01811251589364800920018850132499526990348794362302944357255095708566832705766970650875]",
"[0.01782988839105606929394997766791506708465061002334719107598019915888601356963427805482, 0.01782988839105606929394997766791506708465061002334719107598019915888601381288989824781]",
"[0.01754726088846412938771145401083486426581327642366493857940944123210370011745684244299, 0.01754726088846412938771145401083486426581327642366493857940944123210370065059411852785]"
]
}
],
"pointwise_nonnegative_pair_energy_certified": true,
"second_is_unassigned_mathematical_control": false
},
{
"depth": 3,
"shell_levels": [
0,
3
],
"other_unsmoothed_chart_minimum_source_cost_lower_bound": "0.1990298784358011493755530332342368211362297768628027126996298628327662727819091915280639735707198151",
"common_smoothing_width_interval": "[0.0003924267933121276164437952255906639261229455238488610838033429377433115595597543549954, 0.0003924267933121276164437952255906639261229455238488610838033429377433115595597633158637]",
"smoothing_bands": [
{
"lower_level": 2,
"upper_level": 3,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.2353044183466917408543967868719109502831777189515338656131830149745054584040050796580263596589434687",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.2677072261287024859127741129842406007628161790611549722613211455561241745443770011544, 0.2677072261287024859127741129842406007628161790611549722613211455561241745443890545764]",
"[0.268729029578394098494306759978954471335367986550495064924370847861975568341812255553, 0.2687290295783940984943067599789544713353679865504950649243708478619755683418243738095]",
"[0.2697508330280857110758394069736683419079197940398351575874205501678269621392475104787, 0.2697508330280857110758394069736683419079197940398351575874205501678269621392596925155]",
"[0.2655603896673566473458596509754673348346238555217519362834388550431438298478578626282, 0.2655603896673566473458596509754673348346238555217519362834388550431438298478709665802]",
"[0.2539930239093748038600764190546330632162644958873257846408843275966848319945321527253, 0.2539930239093748038600764190546330632162644958873257846408843275966848319945484335687]",
"[0.235304418346691740854396786871910950283177718951533865613183014974505458404005079658, 0.2353044183466917408543967868719109502831777189515338656131830149745054584040288755072]",
"[0.2596454654593268453703608923590831539966319657454067457208416387542704566192424929972, 0.2596454654593268453703608923590831539966319657454067457208416387542704566192818148684]",
"[0.3770409639872853870681735026631398869294469767258704354365458032440037643552161221235, 0.3770409639872853870681735026631398869294469767258704354365458032440037643552882144171]",
"[0.5705574198265296577279063447116131400033752058350217415183186676715100410348806323555, 0.57055741982652965772790634471161314000337520583502174151831866767151004103503063729]",
"[0.7615593827457375317196239058993139164414165368803031107824145664286868248820704440144, 0.7615593827457375317196239058993139164414165368803031107824145664286868248824261767792]",
"[0.8833147472011008370954845660487614130751134913306104084272991077509924448066260705938, 0.8833147472011008370954845660487614130751134913306104084272991077509924448075401793064]",
"[0.933213394840338523394142908648414698245728308072642839981079074884477754787590200559, 0.9332133948403385233941429086484146982457283080726428399810790748844777547899738115442]",
"[0.9322635879708883927609190648884825313382154658776088798880577694034565046414485125793, 0.9322635879708883927609190648884825313382154658776088798880577694034565046474929334268]",
"[0.9313137811014382621276952211285503644307026236825749197950364639224352544928408115784, 0.931313781101438262127695221128550364430702623682574919795036463922435254507472295423]"
]
},
{
"lower_level": 1,
"upper_level": 2,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.6377420052136698559822167907624566551831768320445249877245882808863147973627123027580819281062403697",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.639641618952570117248664478282320988998202516434592907910630891848357297651331568093, 0.6396416189525701172486644782823209889982025164345929079106308918483572976513547493321]",
"[0.6386918120831199866154406345223888220906896742395589478176095863673360475070219348984, 0.6386918120831199866154406345223888220906896742395589478176095863673360475070452078546]",
"[0.6377420052136698559822167907624566551831768320445249877245882808863147973627123027581, 0.6377420052136698559822167907624566551831768320445249877245882808863147973627356663772]",
"[0.6546571880012688820703353406442905013657857973289400224308279200943191144234268856212, 0.6546571880012688820703353406442905013657857973289400224308279200943191144234524219872]",
"[0.6956269381185045689989867244348293233676728587468957648848839135289369812653776925095, 0.6956269381185045689989867244348293233676728587468957648848839135289369812654109162463]",
"[0.7583451523537247889980720385746880657562761993246875826455495671315400837408003972553, 0.7583451523537247889980720385746880657562761993246875826455495671315400837408519654708]",
"[0.87398433635738092774469343612384684342176429645664169319498177446870555071733005304, 0.8739843363573809277446934361238468434217642964566416931949817744687055507174192642817]",
"[1.068071259930995190156360613291841205935095116186441591238367413859453491339366162345, 1.068071259930995190156360613291841205935095116186441591238367413859453491339531929974]",
"[1.311089087887576992074417520284848058684827372502165596182837535972109570160213782952, 1.311089087887576992074417520284848058684827372502165596182837535972109570160550357381]",
"[1.528623717648202818765314019402218420626638659501244314525699431612886749774183217085, 1.528623717648202818765314019402218420626638659501244314525699431612886749774944441789]",
"[1.662568107485006846454689776371071784955643266394279436173473672868533161476544777608, 1.66256810748500684645468977637107178495564326639427943617347367286853316147841526503]",
"[1.711668903052820519244288164512652517735056654036454922018310865621042039558411580104, 1.711668903052820519244288164512652517735056654036454922018310865621042039563146173972]",
"[1.701806479833490966555657372876139187889451897600755968123354173447645298534046704151, 1.701806479833490966555657372876139187889451897600755968123354173447645298545859764056]",
"[1.691944056614161413867026581239625858043847141165057014228397481274248557504936485504, 1.691944056614161413867026581239625858043847141165057014228397481274248557533321863709]"
]
},
{
"lower_level": 0,
"upper_level": 1,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "0.4998337866253525063787921781478933814271748481516208064958089741213668739170870746698740163647564896",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[0.5195586330640116117560537614209200411183843610230187142857223584681603559587386341094, 0.5195586330640116117560537614209200411183843610230187142857223584681603559587611554068]",
"[0.5096962098446820590674229697844067112727796045873197603907656662947636149379128541261, 0.509696209844682059067422969784406711272779604587319760390765666294763614937935646358]",
"[0.4998337866253525063787921781478933814271748481516208064958089741213668739170870746699, 0.499833786625352506378792178147893381427174848151620806495808974121366873917110136255]",
"[0.5017988496345312040386673626755391926660203737740574553425209829826160359991457780425, 0.5017988496345312040386673626755391926660203737740574553425209829826160359991715958853]",
"[0.5161961869504759195046344804137364279482835341023788664185476372619836840588813929894, 0.5161961869504759195046344804137364279482835341023788664185476372619836840589166439908]",
"[0.5374239100443526233759159572475230521755977479133663176212441734300180104017028286948, 0.5374239100443526233759159572475230521755977479133663176212441734300180104017605936142]",
"[0.5921875921770327293851367059292683593256815790492132255617255267880817877335198139846, 0.5921875921770327293851367059292683593256815790492132255617255267880817877336252412352]",
"[0.6987705734254887760595688219883287056030036978063750822074159726923013749254969973044, 0.6987705734254887760595688219883287056030036978063750822074159726923013749257085539159]",
"[0.829759199820303148331047654456796600658224403323430346244541802683661207475225072045, 0.8297591998203031483310476544567966006582244033234303462445418026836612074757085825741]",
"[0.9314414758241047558331457663251918733316613656597612510309465644490349997103235755986, 0.9314414758241047558331457663251918733316613656597612510309465644490349997115752813328]",
"[0.972047294716189169965728192220500267455090267567441039705754926256577954052938460113, 0.9720472947161891699657281922205002674550902675674410397057549262565779540563777488785]",
"[0.9593862176868258238675352129469744253088736119211253423438268703919674012995566696124, 0.9593862176868258238675352129469744253088736119211253423438268703919674013089493178279]",
"[0.9147636029106943901992777611819988706433446067154916054906256206062944989057036436072, 0.9147636029106943901992777611819988706433446067154916054906256206062944989303077251691]",
"[0.8701409881345629565310203094170233159778156015098578686374243708206215965012177915458, 0.8701409881345629565310203094170233159778156015098578686374243708206215965622735276224]"
]
}
],
"pointwise_nonnegative_pair_energy_certified": true,
"second_is_unassigned_mathematical_control": false
},
{
"depth": 4,
"shell_levels": [
2,
19
],
"other_unsmoothed_chart_minimum_source_cost_lower_bound": "1.741738019508817798098454432504127094996496832485930876425380478907031101248858194415473756290703993",
"common_smoothing_width_interval": "[0.00000000002581063064296819424690279470796972440268404712337365137284454566576394061065317124291, 0.00000000002581063064296819424690279470796972440268404712337365137284454566576394561819719427741]",
"smoothing_bands": [
{
"lower_level": 18,
"upper_level": 19,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "1.926098825984006802454240639717299370562708660491531457106804132119492186572031647628358399097312348",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[1.930644251014710356328792687114968212214001684589646828170636131327476848849712443113, 1.930644251014710356328792687114968212214001684589646828170636131327476869297067843776]",
"[1.930646315693117369478257408712648866441801778181044232916723163090430402781206125648, 1.930646315693117369478257408712648866441801778181044232916723163090430423228983891038]",
"[1.930648380371524382627722130310329520669601871772441637662810194853383956712699808183, 1.9306483803715243826277221303103295206696018717724416376628101948533839771608999383]",
"[1.930011790799256676440798552400365757838913755072370522582680455588786229899810865463, 1.930011790799256676440798552400365757838913755072370522582680455588786250452830083579]",
"[1.928481081731622921389037805317532593750605903705780574646053656203487886943974624233, 1.928481081731622921389037805317532593750605903705780574646053656203487907873769597436]",
"[1.926098825984006802454240639717299370562708660491531457106804132119492186572031647628, 1.926098825984006802454240639717299370562708660491531457106804132119492208395936275758]",
"[2.141509343468161279046305789686571829555652769575309397066380654907111952975988769615, 2.141509343468161279046305789686571829555652769575309397066380654907111976556527021712]",
"[2.793484224434941701813396180385054631503816727417964927417753789951157757031193642938, 2.793484224434941701813396180385054631503816727417964927417753789951157783726634665899]",
"[3.795093233823450767795917170023024892594292578518367097887333237215174767870768254392, 3.795093233823450767795917170023024892594292578518367097887333237215174799820093775873]",
"[4.771091062291761127827797693979268615486905342060994303851812741740405174535967888083, 4.771091062291761127827797693979268615486905342060994303851812741740405215282741615435]",
"[5.398518515892129331966620991870064216011728099599558990758588550626622400765973674277, 5.398518515892129331966620991870064216011728099599558990758588550626622456662474547686]",
"[5.659947363859871275407876683304539400470613964447499549046734695317565485261180735084, 5.659947363859871275407876683304539400470613964447499549046734695317565568516919618344]",
"[5.659948797708642000477295519666230551633435976602934601897228525931867772031369180097, 5.659948797708642000477295519666230551633435976602934601897228525931867906970150862948]",
"[5.659950231557412725546714356027921702796257988758369654747722356546170034510125116812, 5.659950231557412725546714356027921702796257988758369654747722356546170269692035009233]"
]
},
{
"lower_level": 17,
"upper_level": 18,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "7.894593866768693826031827397751563232315823034832898971717707210281061266818275481253772794165054876",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[7.894593866768693826031827397751563232315823034832898971717707210281061266818275481254, 7.894593866768693826031827397751563232315823034832898971717707210281061324478891439161]",
"[7.894595300617464551101246234113254383478645046988334024568201040895363579458091998071, 7.89459530061746455110124623411325438347864504698833402456820104089536363711924647675]",
"[7.894596734466235276170665070474945534641467059143769077418694871509665892097908523323, 7.89459673446623527617066507047494553464146705914376907741869487150966594975960151434]",
"[8.118608649473570295811033474756996459353164578681086179742268278565594101657919636003, 8.118608649473570295811033474756996459353164578681086179742268278565594159679397449995]",
"[8.656234976951446453787877226252236123781845296490130774544932142736547823996531824037, 8.656234976951446453787877226252236123781845296490130774544932142736547883317778188773]",
"[9.492541380146209794762714523343006005735830654416333718358130775762380397509113151413, 9.492541380146209794762714523343006005735830654416333718358130775762380459921922434262]",
"[10.75566603422322170409535164175987962936586357819056431544712377238496908480492226238, 10.75566603422322170409535164175987962936586357819056431544712377238496915328488279682]",
"[12.52894459472714813490223054410483653225696810212777545958633201150225628743222462176, 12.528944594727148134902230544104836532256968102127775459586332011502256366574623867]",
"[14.57593931386353453191851426472826427253133135981949124625661063566666551927698955545, 14.57593931386353453191851426472826427253133135981949124625661063566666561596118096499]",
"[16.38772753132222667690647359783693185727727809456282600050125166615691898412068875958, 16.38772753132222667690647359783693185727727809456282600050125166615691910870684414961]",
"[17.55244765711357756576293490014590236605205068750166948255764278997302384343512677411, 17.55244765711357756576293490014590236605205068750166948255764278997302401214843955242]",
"[18.0377469986048535591335812262122443896514937016493836254276772188197183136937218517, 18.03774699860485355913358122621224438965149370164938362542767721881971855347637510281]",
"[18.03774617873384697444552544090607510751964779195316739618645089129212701159625667531, 18.0377461787338469744455254409060751075196477919531673961864508912921273697401347232]",
"[18.0377453588628403897574696555999058253878018822569511669452245637645356664561241143, 18.03774535886284038975746965559990582538780188225695116694522456376453622893614601925]"
]
},
{
"lower_level": 16,
"upper_level": 17,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "17.04292679384322606595774492035977738298537065573148223945774243026149599209919990563897661688005807",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[17.04292843358523923533385649097211594724906247512391469794019508531667847771031189425, 17.04292843358523923533385649097211594724906247512391469794019508531667855874318805312]",
"[17.04292761371423265064580070566594666511721656542769846869896875778908723490475589995, 17.04292761371423265064580070566594666511721656542769846869896875778908731593859792655]",
"[17.04292679384322606595774492035977738298537065573148223945774243026149599209919990564, 17.04292679384322606595774492035977738298537065573148223945774243026149607313400776625]",
"[17.45646963504428456046415507757160545796264706599480421348068236955066454133005543686, 17.45646963504428456046415507757160545796264706599480421348068236955066462306779188999]",
"[18.44897295128514297273334457069767133593407969380277538540627132971441885128595112722, 18.4489729512851429727333445706976713359340796938027753854062713297144189355568604494]",
"[19.99286640628980513309627325900398519783253289577966040108627379732176390554828750852, 19.99286640628980513309627325900398519783253289577966040108627379732176399583477519453]",
"[22.13977226321180418804338288546180754321342928959574430247461715216982839517510292058, 22.13977226321180418804338288546180754321342928959574430247461715216982849725079582878]",
"[24.85860370051281849305062376886728470224958569513928084909614725284593972270817142816, 24.85860370051281849305062376886728470224958569513928084909614725284593984545897576604]",
"[27.78684855970154820625620552109515012397958253462238728064174829912541039365808852673, 27.7868485597015482062562055210951501239795825346223872806417482991254105502777527557]",
"[30.30307305432351586874223359038167743460835842704755362278568497268861657753740943485, 30.30307305432351586874223359038167743460835842704755362278568497268861678756603406957]",
"[31.92064288561870972660870548416917049278851772224023158516384586200617848326606999065, 31.92064288561870972660870548416917049278851772224023158516384586200617877647958247457]",
"[32.59462666403650677767431995806999516679288435667534960860425083517113388648143368532, 32.59462666403650677767431995806999516679288435667534960860425083517113431059978555497]",
"[32.59462115741067357489880482414931711056088459075690018359234257608277019144711559278, 32.59462115741067357489880482414931711056088459075690018359234257608277082721192245383]",
"[32.59461565078484037212328969022863905432888482483845075858043431699440642542255144463, 32.59461565078484037212328969022863905432888482483845075858043431699440741505412776087]"
]
},
{
"lower_level": 15,
"upper_level": 16,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "27.46079150292779006807899147311806955018235234011669505106312888260129940893544779367572964684501266",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[27.46080251617945647363002174095942566264635187195359390108694540077802658753690734533, 27.46080251617945647363002174095942566264635187195359390108694540077802668908194163327]",
"[27.4607970095536232708545066070387476064143521060351444760750371416896629982361775695, 27.46079700955362327085450660703874760641435210603514447607503714168966309978307699997]",
"[27.46079150292779006807899147311806955018235234011669505106312888260129940893544779368, 27.46079150292779006807899147311806955018235234011669505106312888260129951048421236667]",
"[28.0304942393468458738201844273173940649436602227049413879408727022178361678404271067, 28.03049423934684587382018442731739406494366022270494138794087270221783627037151790092]",
"[29.39778727830032777175269967785438973859494691544269070405414361145002411661246809848, 29.39778727830032777175269967785438973859494691544269070405414361145002422268264588943]",
"[31.52468862623533873696692630707270891292611415988274011024906700263813669508176496481, 31.52468862623533873696692630707270891292611415988274011024906700263813680955783266671]",
"[34.39958781431158331706020653496804302734842848447696906953849620237580980588830057165, 34.39958781431158331706020653496804302734842848447696906953849620237580993684233076383]",
"[37.8969324941337361413831817883360162884429814378293875814411057075407368899816227709, 37.8969324941337361413831817883360162884429814378293875814411057075407370498361211037]",
"[41.5504075398665582173344172222107746409670993119311704412565017817664467902894878713, 41.55040753986655821733441722221077464096709931193117044125650178176644699746689653711]",
"[44.6461998354501522032525402093013251121743265145563183989394005145478001289131896145, 44.64619983545015220325254020930132511217432651455631839893940051454780041060921138481]",
"[46.63634522281894168948984643103347562954016593261676545988081497637204399489176141479, 46.63634522281894168948984643103347562954016593261676545988081497637204439230698666606]",
"[47.46556364412225891670172964902018095324763727935860816419668147937282829147806589812, 47.46556364412225891670172964902018095324763727935860816419668147937282887011562118205]",
"[47.46554979978216344267979874003634458097687009871784969405031854015274644276075900188, 47.4655497997821634426797987400363445809768700987178496940503185401527473124997493975]",
"[47.46553595544206796865786783105250820870610291807709122390395560093266449789654902634, 47.46553595544206796865786783105250820870610291807709122390395560093266585081949844782]"
]
},
{
"lower_level": 14,
"upper_level": 15,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "37.69296811524831482659000451295251345695227769761381403101307564064268816161921043632134628090427187",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[37.69299580392850577463386633092018620149381205889533097130580151908285156769495296143, 37.69299580392850577463386633092018620149381205889533097130580151908285168482581004833]",
"[37.69298195958841030061193542193634982922304487825457250115943857986276986465708169887, 37.69298195958841030061193542193634982922304487825457250115943857986276998179140991831]",
"[37.69296811524831482659000451295251345695227769761381403101307564064268816161921043632, 37.69296811524831482659000451295251345695227769761381403101307564064268827875700972081]",
"[38.38719112527389618188981969731372326712024482449515931688373351455321086126092203404, 38.38719112527389618188981969731372326712024482449515931688373351455321097941796105429]",
"[40.05334360469753668503187091072561954799112561413634266332619742998773149629878514897, 40.05334360469753668503187091072561954799112561413634266332619742998773161811652383612]",
"[42.64514061539510179187348022424743718037160630708019598922843091363962232931536375405, 42.64514061539510179187348022424743718037160630708019598922843091363962245981325264129]",
"[46.10031955505553618724821271083501238701849432657586237609116456616777321958181442996, 46.10031955505553618724821271083501238701849432657586237609116456616777336707754594964]",
"[50.21777041671751200580452125360478601762243817943203325568967555719033531070478339873, 50.21777041671751200580452125360478601762243817943203325568967555719033548799724712806]",
"[54.44849528046369050001935681263269500774552300082045390140572344504360031984133391481, 54.44849528046369050001935681263269500774552300082045390140572344504360054592826454459]",
"[58.00541037319877039427753177324229744284884792416075950939732264201852883493489091228, 58.00541037319877039427753177324229744284884792416075950939732264201852913792769496112]",
"[60.29198574492216169952437152079769448338590530578677455434817264697943521234001665002, 60.29198574492216169952437152079769448338590530578677455434817264697943563500537681342]",
"[61.24470811797679938634231307356796244985727771194103594820874622983613886931300336952, 61.24470811797679938634231307356796244985727771194103594820874622983613948004278567951]",
"[61.24468042665643870306427583025482489386981049450270623470134246839118001621527688479, 61.24468042665643870306427583025482489386981049450270623470134246839118093050269147201]",
"[61.24465273533607801978623858694168733788234327706437652119393870694622106154997355317, 61.2446527353360780197862385869416873378823432770643765211939387069462224826087805176]"
]
},
{
"lower_level": 13,
"upper_level": 14,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "46.68566718582036389610997287177664340060321890233837955567191928646717894119295178972166408103054721",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[46.68572256846108526266604735840291851257815333721503898268672680935709634427327842374, 46.68572256846108526266604735840291851257815333721503898268672680935709648076466100144]",
"[46.68569487714072457938801011508978095659068611977670926917932304791213764273311507299, 46.68569487714072457938801011508978095659068611977670926917932304791213777923064282439]",
"[46.68566718582036389610997287177664340060321890233837955567191928646717894119295178972, 46.68566718582036389610997287177664340060321890233837955567191928646717907769662464733]",
"[47.47447993659732936360798651274786840497623020843985612306019559638021889599706158948, 47.47447993659732936360798651274786840497623020843985612306019559638021903379273650157]",
"[49.36766582299360139607363481069426597986737040331916128483387531552519138247162540478, 49.36766582299360139607363481069426597986737040331916128483387531552519152491526632956]",
"[52.31263141833258592276815558309942339062870664563245790427506723703940057833267685082, 52.3126314183325859227681555830994233906287066456324579042750672370394007318160482905]",
"[56.20834692287423604176190534416842681541196469773597378097109286031704677559246263354, 56.20834692287423604176190534416842681541196469773597378097109286031704695072582242151]",
"[60.79601472476025412617642474704569347545830222547424395995444259832691554409934189658, 60.79601472476025412617642474704569347545830222547424395995444259832691575724348609664]",
"[65.46393816666725678786935527389253067042998625812415866601940205810373426894405810916, 65.4639381666672567878693552738925306704299862581241586660194020581037345444724499947]",
"[69.36986442827417481956597590414272126442919336227474854584114389591980813556582894966, 69.36986442827417481956597590414272126442919336227474854584114389591980850978637348696]",
"[71.88079442253844157681692462789860294171784822010557814728568963436340920101165181734, 71.88079442253844157681692462789860294171784822010557814728568963436340972975704067133]",
"[72.92698420706821622567998729800460291813150380819011849320310645368674475752582792644, 72.92698420706821622567998729800460291813150380819011849320310645368674553135222967642]",
"[72.92693427370637582177255420497604035100404415518443996482263102154872545076682193655, 72.92693427370637582177255420497604035100404415518443996482263102154872662490428842818]",
"[72.92688434034453541786512111194747778387658450217876143644215558941070600560714214043, 72.92688434034453541786512111194747778387658450217876143644215558941070785681275792351]"
]
},
{
"lower_level": 12,
"upper_level": 13,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "53.73122884042234100313416847775572876910887468090161116478753410150143978391783235058076514615319919",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[53.73132870714602181094903466381285390336379398691296822154848496577747799637030352778, 53.73132870714602181094903466381285390336379398691296822154848496577747815048781560033]",
"[53.73127877378418140704160157078429133623633433390728969316800953363945889014406793918, 53.7312787737841814070416015707842913362363343339072896931680095336394590442720254576]",
"[53.73122884042234100313416847775572876910887468090161116478753410150143978391783235058, 53.73122884042234100313416847775572876910887468090161116478753410150143993805623531486]",
"[54.58637592013771403224232315226272337408094235635550007974984292975489435579897248577, 54.58637592013771403224232315226272337408094235635550007974984292975489451171617538616]",
"[56.63879323900939336489518670714217171354819791259933548212812027970387328324397015717, 56.63879323900939336489518670714217171354819791259933548212812027970387344555850748368]",
"[59.83146115382138959487708609959910470768047861564429618229019456028754357214497539629, 59.83146115382138959487708609959910470768047861564429618229019456028754374965566080135]",
"[64.03578295181096816106008982576747152630670406836586581244211667140278061493083306795, 64.03578295181096816106008982576747152630670406836586581244211667140278082224961250697]",
"[68.95212327235535675463767514367542568067222437791640571770035043003021541182859729973, 68.95212327235535675463767514367542568067222437791640571770035043003021567152136116264]",
"[73.92495748235312487119083588886438513502258654950929294680961571637731124949438546916, 73.9249574823531248711908358888643851350225865495092929468096157163773115953227707566]",
"[78.0739818158483466333179970877026803631850622521814299143803193749399495913806764582, 78.07398181584834663331799708770268036318506225218142991438031937493995007409223861591]",
"[80.74117385188979344322978300891904412342195240605901022156293088197732453184061750138, 80.74117385188979344322978300891904412342195240605901022156293088197732523063120982902]",
"[81.85245118794373206711440781392362289132526661534577273382269750460182204481698021913, 81.85245118794373206711440781392362289132526661534577273382269750460182309058355579622]",
"[81.85236604212340988610657963693131101727553868324089885717899887128092021561172545968, 81.85236604212340988610657963693131101727553868324089885717899887128092183707615541698]",
"[81.85228089630308770509875145993899914322581075113602498053530023796001817960909238107, 81.85228089630308770509875145993899914322581075113602498053530023796002079114238227828]"
]
},
{
"lower_level": 11,
"upper_level": 12,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "58.41556617755729326604477046294556705129182080191570722404174533301486307834331173048608289841009591",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[58.41573646919793762806042681693019079939127666612545497732914259965666616286500189646, 58.41573646919793762806042681693019079939127666612545497732914259965666630758796809877]",
"[58.41565132337761544705259863993787892534154873402058110068544396633576462060415677974, 58.41565132337761544705259863993787892534154873402058110068544396633576476534437804682]",
"[58.41556617755729326604477046294556705129182080191570722404174533301486307834331173049, 58.41556617755729326604477046294556705129182080191570722404174533301486322310078799488]",
"[59.31041407531247838905350636007258890331235180314521864324598178430560751902765639334, 59.31041407531247838905350636007258890331235180314521864324598178430560766566372541066]",
"[61.45815936289872971951941643334120957992690930677205949191707820942641714776195041754, 61.45815936289872971951941643334120957992690930677205949191707820942641730114575560489]",
"[64.79912948770678112887531143274207536969494140148334746186499333334209040324702571236, 64.79912948770678112887531143274207536969494140148334746186499333334209057266761748563]",
"[69.18769439791551752829728138752009098770929924396971826135997714796847928585058823463, 69.187694397915517528297281387520090987709299243969718261359977147968479486763295604]",
"[74.29923891640334021313758373131466128389740509149765623222828969746799862949958830517, 74.29923891640334021313758373131466128389740509149765623222828969746799888586423809925]",
"[79.45220330920088974365237713702062030911747810520048035945153762304985232295181106155, 79.45220330920088974365237713702062030911747810520048035945153762304985267090750272736]",
"[83.74440309063269657326191620326012760109833105243009869190751718152209143499051591618, 83.74440309063269657326191620326012760109833105243009869190751718152209192968703339135]",
"[86.50361234845220196906386098808501988465825279018439243692282534125533712512871740349, 86.50361234845220196906386098808501988465825279018439243692282534125533785465031372016]",
"[87.65319603124594113651324552560407806502320098885200242190132622774059097423309751804, 87.65319603124594113651324552560407806502320098885200242190132622774059208834150798103]",
"[87.65305526956281385949566702631713017551791572678245128731418676105859178418502762905, 87.65305526956281385949566702631713017551791572678245128731418676105859355191468648977]",
"[87.65291450787968658247808852703018228601263046471290015272704729437659234486668467358, 87.65291450787968658247808852703018228601263046471290015272704729437659526489136324451]"
]
},
{
"lower_level": 10,
"upper_level": 11,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "60.56812350624164133274693385781556597955234628117110211245247277339700866728573945937110395515080114",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[60.56840502960789588678209085638946175856291680531020438162675170676100639321610179048, 60.56840502960789588678209085638946175856291680531020438162675170676100655232404740964]",
"[60.56826426792476860976451235710251386905763154324065324703961224007900753025092062492, 60.56826426792476860976451235710251386905763154324065324703961224007900768938688919418]",
"[60.56812350624164133274693385781556597955234628117110211245247277339700866728573945937, 60.56812350624164133274693385781556597955234628117110211245247277339700882644973097871]",
"[61.47757472456261449998807067749562426668222016774773319032875373230710637571763522085, 61.47757472456261449998807067749562426668222016774773319032875373230710653731288846846]",
"[63.66044056222290600785472926658631577384697576832747734938422310444088211203048390333, 63.66044056222290600785472926658631577384697576832747734938422310444088228232642011167]",
"[67.0560650424442268116211826050016248957649497738881186248710442000852185182972815984, 67.05606504244422681162118260500162489576494977388811862487104420008521870923399591217]",
"[71.51168157447737754123397355425836767847695696573766760787674062841048092992631086654, 71.51168157447737754123397355425836767847695696573766760787674062841048116136639297526]",
"[76.69260775152132858617949259927190835169424318075917813882393559522518888125258154744, 76.69260775152132858617949259927190835169424318075917813882393559522518918408509365246]",
"[81.9080203532746146623332387137580024869274846667592386751272317741205334860397456056, 81.90802035327461466233323871375800248692748466675923867512723177412053390730946267496]",
"[86.24913220251169270563891391898875332491314552210532265706664676922999509803554672268, 86.24913220251169270563891391898875332491314552210532265706664676922999571096443368267]",
"[89.03974645065213348413835951628314341130104508658702323526448614737006439839702260648, 89.03974645065213348413835951628314341130104508658702323526448614737006532349598029917]",
"[90.20236117943596902776276742497187972972922738323662382939186330644067347841484962142, 90.20236117943596902776276742497187972972922738323662382939186330644067492785188839464]",
"[90.20213197242968872113024622249582003538745244087230604443231005200268585586929307375, 90.20213197242968872113024622249582003538745244087230604443231005200268822318643769057]",
"[90.20190276542340841449772502001976034104567749850798825947275679756469785953969255487, 90.20190276542340841449772502001976034104567749850798825947275679756470189237020110493]"
]
},
{
"lower_level": 9,
"upper_level": 10,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "60.21394772295574005998316986963047398852431400356429269438584337955621798843447840900900796236611999",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[60.21440613696830067324821227458259337720786388829292826430494988843219231581002275369, 60.21440613696830067324821227458259337720786388829292826430494988843219248088393495075]",
"[60.21417692996202036661569107210653368286608894592861047934539663399420515212225058135, 60.21417692996202036661569107210653368286608894592861047934539663399420531724131651341]",
"[60.21394772295574005998316986963047398852431400356429269438584337955621798843447840901, 60.2139477229557400599831698696304739885243140035642926943858433795562181535986980086]",
"[61.11429762925052178530789822731754376332990209581710518454918384774312528972469729714, 61.11429762925052178530789822731754376332990209581710518454918384774312545828408332521]",
"[63.27543544224982659353592829468164777708850135603313575255118044236559325764475603353, 63.27543544224982659353592829468164777708850135603313575255118044236559343837831576464]",
"[66.63729589382991462738127506200153147468266424434722160834797761492808434539741647897, 66.63729589382991462738127506200153147468266424434722160834797761492808455506678868014]",
"[71.04928718915067263532539413570837239722473081360080766645844517654338941425020237305, 71.04928718915067263532539413570837239722473081360080766645844517654338968081082651781]",
"[76.18070591318435718710499661982262152734170663807277818057607301962593741659327771531, 76.1807059131843571871049966198226215273417066380727781805760730196259377837730541365]",
"[81.34730930142625800969289112867846119278210480907847665516104814885417762659889721209, 81.34730930142625800969289112867846119278210480907847665516104814885417816190692984753]",
"[85.64818345622141280645806864714832410339504139131093396945717335779171325786792032404, 85.6481834562214128064580686471483241033950413913109339694571733577917140690785277634]",
"[88.41286818185582816689874059276213702493500111052018002628835375522098911193081831951, 88.41286818185582816689874059276213702493500111052018002628835375522099038295059677555]",
"[89.56459106018233465278800662642208387543648540648286515002002428547559026174447348199, 89.5645910601823346527880066264220838754364854064828651500200242854755923292614897187]",
"[89.5642190914459347819856774990444265800574992212061156076764759352277261102273772739, 89.56421909144593478198567749904442658005749922120611560767647593522772961996191383048]",
"[89.56384712270953491118334837166676928467851303592936606533292758497986132997359316767, 89.56384712270953491118334837166676928467851303592936606533292758497986753860432817381]"
]
},
{
"lower_level": 8,
"upper_level": 9,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "57.52714794144668245308814845074687878894803218163498059764231011467943441649443552417653886331012296",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[57.52789187891948219469280670550219337970600455218847968232940681517516127759880767707, 57.52789187891948219469280670550219337970600455218847968232940681517516143677109194233]",
"[57.52751991018308232389047757812453608432701836691173013998585846492729784704662160062, 57.52751991018308232389047757812453608432701836691173013998585846492729800629172016924]",
"[57.52714794144668245308814845074687878894803218163498059764231011467943441649443552418, 57.52714794144668245308814845074687878894803218163498059764231011467943457581234839615]",
"[58.3958372430324152602491461221503838834678719051790136467170440125117895166160851315, 58.39583724303241526024914612215038388346787190517901364671704401251178967902733175783]",
"[60.48117467018132098261596165810702316290161135787679839311246588555143661620822092203, 60.48117467018132098261596165810702316290161135787679839311246588555143678959841454993]",
"[63.7251788765022622297398909528323683750062073350495331696248806462549917058659075528, 63.72517887650226222973989095283236837500620733504953316962488064625499190527932815726]",
"[67.98824952042745080189305866066516000334637939161597960732711445499347242734271822834, 67.98824952042745080189305866066516000334637939161597960732711445499347267793898794008]",
"[72.95698053005570339060127069974729097015969595717291400173288302937324126272988270614, 72.95698053005570339060127069974729097015969595717291400173288302937324160422845013165]",
"[77.96878642415071656120646050207491159753281251559075785564142503052407695592390996168, 77.96878642415071656120646050207491159753281251559075785564142503052407745093764969588]",
"[82.14445241660802099895809347679917790246358471394433461120341041956788968584898682693, 82.14445241660802099895809347679917790246358471394433461120341041956789043800634971789]",
"[84.82854228795122816655153965400521865430813360300375455233622778558812388784258437417, 84.82854228795122816655153965400521865430813360300375455233622778558812508252448259291]",
"[85.94653852970878312249282306111377110884257292624474047285167436529734391194406601407, 85.94653852970878312249282306111377110884257292624474047285167436529734590496468832121]",
"[85.94593080500239956499197707289201014053484568368511715962822947409838418913204265961, 85.94593080500239956499197707289201014053484568368511715962822947409838768964922633911]",
"[85.94532308029601600749113108467024917222711844112549384640478458289942375754395707631, 85.94532308029601600749113108467024917222711844112549384640478458289943018459033993959]"
]
},
{
"lower_level": 7,
"upper_level": 8,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "52.7843732997332914807419211205070851707287022630560368082735082640645369929583473761145653485251712",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[52.78558874914605859574361309695060710734415674817528343472039804646245493493118155728, 52.7855887491460585957436130969506071073441567481752834347203980464624551062584180457]",
"[52.78498102443967503824276710872884613903642950561566012149695315526349596394476443296, 52.78498102443967503824276710872884613903642950561566012149695315526349613539051121667]",
"[52.78437329973329148074192112050708517072870226305603680827350826406453699295834737611, 52.78437329973329148074192112050708517072870226305603680827350826406453716452260432017]",
"[53.59954113442216878989795312344784475008226768275725347560656033874452295810427504602, 53.59954113442216878989795312344784475008226768275725347560656033874452313293785959209]",
"[55.55673089068205387153299524119467331141555930508303269365612807927848457895458939685, 55.55673089068205387153299524119467331141555930508303269365612807927848476529978922816]",
"[58.60148302603998191614734319937531587090207607426483688812631013044721585822259905816, 58.60148302603998191614734319937531587090207607426483688812631013044721607181985650657]",
"[62.61367764909018302670750145733642911990688583503821926243896582694806982586171436605, 62.61367764909018302670750145733642911990688583503821926243896582694807009311447303963]",
"[67.31004933573315239824310848340947129367669620766233146291550438516751861417660894689, 67.31004933573315239824310848340947129367669620766233146291550438516751897719777644413]",
"[72.06426732260453559143674846881358194535856350622448540818884116786460405135556449875, 72.06426732260453559143674846881358194535856350622448540818884116786460457818312520413]",
"[76.03225990158899837473853501833525670166280077073848552918341026498037165772097955465, 76.03225990158899837473853501833525670166280077073848552918341026498037246582506365122]",
"[78.58266653173708373617173400907447379120204866972751134208375254176053599541779268418, 78.58266653173708373617173400907447379120204866972751134208375254176053730624986962377]",
"[79.64471278912943930075400617867897392940539830639553898879090229554145898799606782288, 79.64471278912943930075400617867897392940539830639553898879090229554146124781778717373]",
"[79.64370324722675583426342454689508114341108000545253159300893987220786337319350090121, 79.64370324722675583426342454689508114341108000545253159300893987220786750493199223477]",
"[79.64269370532407236777284291511118835741676170450952419722697744887426680968702595192, 79.64269370532407236777284291511118835741676170450952419722697744887427470751515810603]"
]
},
{
"lower_level": 6,
"upper_level": 7,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "46.31557919199071578069322641032799694022693158527783784094841663225587766983600811236331611095284956",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[46.31759827579608271367438967389578251221556818716385263251234147892306702833315336543, 46.31759827579608271367438967389578251221556818716385263251234147892306718916968068007]",
"[46.3165887338933992471838080421118897262212498862208452367303790555894723490845807389, 46.31658873389339924718380804211188972622124988622084523673037905558947251011751625185]",
"[46.31557919199071578069322641032799694022693158527783784094841663225587766983600811236, 46.31557919199071578069322641032799694022693158527783784094841663225587783106535175615]",
"[47.05521321612082562894708134878792351925404062556531361466377925628406089469783262051, 47.05521321612082562894708134878792351925404062556531361466377925628406106032766146459]",
"[48.83163560446166087790272499721915949808331212010919634676767992650333148341878536689, 48.83163560446166087790272499721915949808331212010919634676767992650333166448990101348]",
"[51.59533871966949068010065166974587471159776193473676568820252795402299350512021766267, 51.59533871966949068010065166974587471159776193473676568820252795402299372276220056704]",
"[55.25416687204731501024142544362419419574380431407408408404664783843525671701659840908, 55.25416687204731501024142544362419419574380431407408408404664783843525700686416777457]",
"[59.56784828847992287977580726389941116750060635561292767997741706414046081800101091658, 59.56784828847992287977580726389941116750060635561292767997741706414046123787820146925]",
"[63.96096812392750165885246466814665523410554727889202511196971637846419968247412234089, 63.96096812392750165885246466814665523410554727889202511196971637846420032949489547863]",
"[67.6381606293422990631938225164459167280635237049293208010288922787503600999979454521, 67.63816062934229906319382251644591672806352370492932080102889227875036115228559785187]",
"[70.00130207819093987072879741703780688045335929539540453884882948993909136103158864882, 70.00130207819093987072879741703780688045335929539540453884882948993909317733073655164]",
"[70.98487748557452950914995336159602712292086499992521209955849335266613090721687946073, 70.98487748557452950914995336159602712292086499992521209955849335266613425055120005125]",
"[70.98315365769815023737906082627288002326048460037243892960736646987802981126772880746, 70.98315365769815023737906082627288002326048460037243892960736646987803631835006931726]",
"[70.98142982982177096560816829094973292360010420081966575965623958708992700358452121312, 70.98142982982177096560816829094973292360010420081966575965623958708994011014953028382]"
]
},
{
"lower_level": 5,
"upper_level": 6,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "38.44629489611575402975728515121016104457596477143248539485277349820484297173240500768735593008031703",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[38.44974255186851257329907022185645524389672557053803173475502726378104200850665204386, 38.44974255186851257329907022185645524389672557053803173475502726378104214756794990106]",
"[38.44801872399213330152817768653330814423634517098525856480390038099294249011952852577, 38.44801872399213330152817768653330814423634517098525856480390038099294262951573706701]",
"[38.44629489611575402975728515121016104457596477143248539485277349820484297173240500769, 38.44629489611575402975728515121016104457596477143248539485277349820484311146352416549]",
"[39.08650846698147795253659179709964406647363731383126825791614609432991289590079566312, 39.08650846698147795253659179709964406647363731383126825791614609432991304119066108753]",
"[40.62522518836401962760180208224236432897651494053847832433390660372135434084081480891, 40.62522518836401962760180208224236432897651494053847832433390660372135450537527926251]",
"[43.01940515800431769889355337750601114855118404360713354793548746932192603135915893395, 43.01940515800431769889355337750601114855118404360713354793548746932192624132063786418]",
"[46.21399669064484006419231773879548760913544325923093762400723408519067067635861796475, 46.21399669064484006419231773879548760913544325923093762400723408519067097623306846929]",
"[50.02557223787409661841226186019093884999674557665817568785241186028402970486144343888, 50.02557223787409661841226186019093884999674557665817568785241186028403016881970888562]",
"[53.94545051242098465350261006434040212811304097288559316040229855721773112792386640485, 53.94545051242098465350261006434040212811304097288559316040229855721773188795477983966]",
"[57.24165358518765919453272056905350370335046715355870840218525689050200447494158529834, 57.24165358518765919453272056905350370335046715355870840218525689050200579347624403723]",
"[59.35925727586363066093538806117085366265621006543710822700680603236177404983564288137, 59.35925727586363066093538806117085366265621006543710822700680603236177649776322429146]",
"[60.23968727217878957686163700362027396095715545479110317058939830211993628092942682165, 60.23968727217878957686163700362027396095715545479110317058939830211994114244795896773]",
"[60.23662102004797233245129000834335735809058305212806216017171989106727623929233396474, 60.23662102004797233245129000834335735809058305212806216017171989106728636771234350863]",
"[60.23355476791715508804094301306644075522401064946502114975404148001461314163091725694, 60.23355476791715508804094301306644075522401064946502114975404148001463465436676124553]"
]
},
{
"lower_level": 4,
"upper_level": 5,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "29.41816843962395831569716859864956083296931110565822265058544753190153248842855554776067330230516394",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[29.42430094388559280451786258920339403870245591098430467142080435400684730208486165711, 29.42430094388559280451786258920339403870245591098430467142080435400684745998230933241]",
"[29.42123469175477556010751559392647743583588350832126366100312594295418989525670858557, 29.42123469175477556010751559392647743583588350832126366100312594295419005374941919062]",
"[29.41816843962395831569716859864956083296931110565822265058544753190153248842855554776, 29.41816843962395831569716859864956083296931110565822265058544753190153264751652901509]",
"[29.92941565620386933612794725151721470370252527535093846523222373482161557326413718062, 29.92941565620386933612794725151721470370252527535093846523222373482161574050918323195]",
"[31.16028527424225661309698091650310756638620086346291649216130583005952542057506251468, 31.16028527424225661309698091650310756638620086346291649216130583005952561583261729196]",
"[33.0760038652987436180875372340111274428048110204120218045860196097124394026908961609, 33.07600386529874361808753723401112744280481102041202180458601960971243966400744039701]",
"[35.66988601829572340465317891927441816498873849490441876789371888385506105398165425804, 35.66988601829572340465317891927441816498873849490441876789371888385506144683593429726]",
"[38.83237213208444947036895229537200702896681806888601158231647523419136042271966571431, 38.83237213208444947036895229537200702896681806888601158231647523419136106119615656652]",
"[42.14086884210489587405883016936437986116307475938906516012636070066733736682585045961, 42.14086884210489587405883016936437986116307475938906516012636070066733847208739805725]",
"[44.94475992611669528163933147722985061995668203536574256745028605645947459389492874108, 44.94475992611669528163933147722985061995668203536574256745028605645947665302052921786]",
"[46.74460322336329343444873897675149566686143138378082731018686186304096866818583331928, 46.74460322336329343444873897675149566686143138378082731018686186304097283193607925306]",
"[47.49092551277301187612082723184442817921122344497991892010964860299832104466910891293, 47.49092551277301187612082723184442817921122344497991892010964860299833004056480250391]",
"[47.48514129421308968500470085233087213214254331889412892436573983366486468931838795123, 47.48514129421308968500470085233087213214254331889412892436573983366488476007495605006]",
"[47.47935707565316749388857447281731608507386319280833892862183106433140154928276338983, 47.47935707565316749388857447281731608507386319280833892862183106433144629994818872227]"
]
},
{
"lower_level": 3,
"upper_level": 4,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "19.25461493097994296131649977786566094420547855666618678592073231949119781981202584076267370648450893",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[19.26618336809978734354875253689277303834283880883776677740854985815809947936780506364, 19.26618336809978734354875253689277303834283880883776677740854985815809964533059254779]",
"[19.2603991495398651524326261573792169912741586827519767816646410888246486495899154522, 19.26039914953986515243262615737921699127415868275197678166464108882464881667515895385]",
"[19.25461493097994296131649977786566094420547855666618678592073231949119781981202584076, 19.25461493097994296131649977786566094420547855666618678592073231949119798801972535991]",
"[19.59245303624318061945815511454260882024536870496352305939146430315619851659430443413, 19.5924530362431806194581551145426088202453687049635230593914643031561986969049166151]",
"[20.41045118783068359461113499695854801189398335898292564328959380683883051630821449761, 20.41045118783068359461113499695854801189398335898292564328959380683883073771366042406]",
"[21.68463815595447581437923098142888507744639763588266459944355715999457334817487014356, 21.68463815595447581437923098142888507744639763588266459944355715999457366646446210698]",
"[23.47368715786944089301111546867780259983817586976805846931184751791046786571280375076, 23.47368715786944089301111546867780259983817586976805846931184751791046837949908974334]",
"[25.76740824888105336388546079884551774918112689903329356800542998861639978894561812683, 25.76740824888105336388546079884551774918112689903329356800542998861640068510819093341]",
"[28.25793489568489187312727553425340126739153591260161257851657612431294483354069008725, 28.25793489568489187312727553425340126739153591260161257851657612431294652757340983071]",
"[30.40254687875998295196665552882532831467900842563232613142776337370215798925096217508, 30.40254687875998295196665552882532831467900842563232613142776337370216152260938902761]",
"[31.77563033235106617932931559806937222408415706478129166969535062040649507225618266834, 31.77563033235106617932931559806937222408415706478129166969535062040650312153671809821]",
"[32.34027374564794011304841294744144090969525175733095345504232750482137057045533886545, 32.34027374564794011304841294744144090969525175733095345504232750482138977441375582736]",
"[32.32839271316814546889133916974971700483988525361415317125143158862034787590296439534, 32.32839271316814546889133916974971700483988525361415317125143158862039378112354056104]",
"[32.31651168068835082473426539205799309998451874989735288746053567241930803479255694914, 32.31651168068835082473426539205799309998451874989735288746053567241941491067247454004]"
]
},
{
"lower_level": 2,
"upper_level": 3,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "7.477716078786367377955731393862372349806803509362465731590524447237105742910859357758900332643062687",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[7.501478143745956666269878949245820159517536516796066299172316279639124400012474024468, 7.501478143745956666269878949245820159517536516796066299172316279639124595889339589831]",
"[7.489597111266162022112805171554096254662170013079266015381420363438115071461666691114, 7.489597111266162022112805171554096254662170013079266015381420363438115269643702314201]",
"[7.477716078786367377955731393862372349806803509362465731590524447237105742910859357759, 7.477716078786367377955731393862372349806803509362465731590524447237105943398065030138]",
"[7.556751435241029665326573621525147659930539921018384744448565560316210260356556836101, 7.556751435241029665326573621525147659930539921018384744448565560316210476274360669264]",
"[7.760788053200692387709921652586172583934545527541301964898058946313675817053080055037, 7.760788053200692387709921652586172583934545527541301964898058946313676083096952712118]",
"[8.081102876565874200690532615829694972222163817336069448148018185524236887488429910703, 8.081102876565874200690532615829694972222163817336069448148018185524237270628198150394]",
"[8.674718393402075172290417775516517483027491651842415831687196038788857611853561783786, 8.674718393402075172290417775516517483027491651842415831687196038788858236862405457524]",
"[9.679675083595849351213570650533403302489586072558301245063072465995721819690235604737, 9.679675083595849351213570650533403302489586072558301245063072465995722959913353144046]",
"[10.95671330869209110219005964007342720305932731170133622110649304364781218465954739979, 10.95671330869209110219005964007342720305932731170133622110649304364781456812622143845]",
"[12.12094042840468278573028134266264771952117021362815398912717569146329993567437860484, 12.12094042840468278573028134266264771952117021362815398912717569146330564177538334733]",
"[12.85585276616127699374913168429012118721696575661091789810243133859315315171870143792, 12.85585276616127699374913168429012118721696575661091789810243133859316792710425609113]",
"[13.14442984419179169572685179325087827420480917605914430841878295029179870826672706426, 13.14442984419179169572685179325087827420480917605914430841878295029183736483466944881]",
"[13.11668636489847201541470485647272665727034334113744768356647232815852143232329083845, 13.1166863648984720154147048564727266572703433411374476835664723281586194174953793966]",
"[13.08894288560515233510255791969457504033587750621575105871416170602520472029678155906, 13.08894288560515233510255791969457504033587750621575105871416170602544125270795738386]"
]
}
],
"pointwise_nonnegative_pair_energy_certified": true,
"second_is_unassigned_mathematical_control": false
},
{
"depth": 4,
"shell_levels": [
2,
71
],
"other_unsmoothed_chart_minimum_source_cost_lower_bound": "1.741738019508817798098454432504127094996496832485930876425380478907031101248858194415473756290703993",
"common_smoothing_width_interval": "[0.00000000002581063064296819424690279470796972440268404712337365137284454566576394061065317124291, 0.00000000002581063064296819424690279470796972440268404712337365137284454566576394561819719427741]",
"smoothing_bands": [
{
"lower_level": 70,
"upper_level": 71,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "1.909221310520880847551791968276440524188353002168696526350705349863511732578937186218408798265276223",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[1.983819672050005285251697201387331920332845197554522700953784072065559872710156718982, 1.983819672050005285251697201387331920332845197554522700953784072065559879401256575145]",
"[1.983819676216670732717402117795852649946372988821083673758777750610476018585650017163, 1.983819676216670732717402117795852649946372988821083673758777750610476025276750697726]",
"[1.983819680383336180183107034204373379559900780087644646563771429155392164461143317454, 1.983819680383336180183107034204373379559900780087644646563771429155392171152244820308]",
"[1.973361967452099883456427910146770540096490558176177655241754574303182633400746320429, 1.973361967452099883456427910146770540096490558176177655241754574303182640095456729688]",
"[1.948263450487884024194848505082388613605006083212164072632274630861248477801886453545, 1.948263450487884024194848505082388613605006083212164072632274630861248484509583754282]",
"[1.909221310520880847551791968276440524188353002168696526350705349863511732578937186218, 1.909221310520880847551791968276440524188353002168696526350705349863511739317418499831]",
"[2.132812755880909854381101113523573200884677448968795178305379084487602963817615160935, 2.132812755880909854381101113523573200884677448968795178305379084487602970616255253014]",
"[2.897706538081507123049420212387795465106974068303145420378602123467379506452817033523, 2.897706538081507123049420212387795465106974068303145420378602123467379513356317096245]",
"[4.101916819678423944183985963670006102504763260711450331861992351199053571774410532852, 4.101916819678423944183985963670006102504763260711450331861992351199053578847368305802]",
"[5.28320034223143180716316186589124361765600768232999164873312413471687102275656994263, 5.28320034223143180716316186589124361765600768232999164873312413471687103008942978414]",
"[6.042596893423523249068478670368352138701580749038787273468703931709535822726268223466, 6.042596893423523249068478670368352138701580749038787273468703931709535830443845068014]",
"[6.359012124997026286316037581041801106859022026568097056431393926767656557290109008406, 6.359012124997026286316037581041801106859022026568097056431393926767656565564999180958]",
"[6.359012128446731468966046594243800996281253061071635434088884616533354733184404725974, 6.359012128446731468966046594243800996281253061071635434088884616533354742259419503061]",
"[6.35901213189643665161605560744580088570348409557517381174637530629905290890299537621, 6.359012131896436651616055607445800885703484095575173811746375306299052919129547768408]"
]
},
{
"lower_level": 69,
"upper_level": 70,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "9.472139501175391295426021074444308037550870076671562808466079196200803541894293013561324584448521712",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[9.472139501175391295426021074444308037550870076671562808466079196200803541894293013561, 9.47213950117539129542602107444430803755087007667156280846607919620080356234294821452]",
"[9.472139504625096478076030087646307926973101111175101186123569885966501718188664181626, 9.472139504625096478076030087646307926973101111175101186123569885966501738637320242828]",
"[9.472139508074801660726039100848307816395332145678639563781060575732199894483035349691, 9.472139508074801660726039100848307816395332145678639563781060575732199914931692254269]",
"[9.754717695737131935541294537085132177368166712150626995560719136893962894128251124394, 9.754717695737131935541294537085132177368166712150626995560719136893962914587395002665]",
"[10.43290534105959951810475819534153818830901536325994530976099202636523655322147643101, 10.43290534105959951810475819534153818830901536325994530976099202636523657371838303581]",
"[11.48786389815282789025518753368216940587463609192272664785243064504500708729082075279, 11.48786389815282789025518753368216940587463609192272664785243064504500710787727442307]",
"[13.07506142171652560634535229361920367877829044819919024287338436875909654038153267165, 13.07506142171652560634535229361920367877829044819919024287338436875909656114298787357]",
"[15.29345032945449476526591597982673364626945950325311325658681945618584306426900037941, 15.29345032945449476526591597982673364626945950325311325658681945618584308533527454809]",
"[17.84724543367490066158391016179600035673042084283376565336107890378666857631930493516, 17.84724543367490066158391016179600035673042084283376565336107890378666859787704780326]",
"[20.1050809793369627842304901086760589814794749395740342948976911783975011282582992286, 20.10508097933696278423049010867605898147947493957403429489769117839750115056582547953]",
"[21.55654668752741904748625246579281777443059788535806641680021697810549187274395695513, 21.5565466875274190474862524657928177744305978853580664168002169781054918961496927418]",
"[22.16132406687819495483502417997782294384026702486089332288901332077119710762121074574, 22.16132406687819495483502417997782294384026702486089332288901332077119713258816771505]",
"[22.1613240687706714705899814209533935300398639542936630763217674776349896536163110209, 22.16132406877067147058998142095339353003986395429366307632176747763498968075691267555]",
"[22.16132407066314798634493866192896411623946088372643282975452163449878219920430507665, 22.16132407066314798634493866192896411623946088372643282975452163449878222933279060735]"
]
},
{
"lower_level": 68,
"upper_level": 69,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "23.74883046382254463875555538371697215738950979364291906274076384618275272268781239045808729700949775",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[23.74883046382254463875555538371697215738950979364291906274076384618275272268781239046, 23.74883046382254463875555538371697215738950979364291906274076384618275275384822847288]",
"[23.74883046571502115451051262469254274358910672307568881617351800304654526976947582203, 23.74883046571502115451051262469254274358910672307568881617351800304654530092989295023]",
"[23.74883046760749767026546986566811332978870365250845856960627215991033781685113925359, 23.74883046760749767026546986566811332978870365250845856960627215991033784801155742759]",
"[24.30825550689925706840489004859145102817201284944945748048242150033016112644230646793, 24.30825550689925706840489004859145102817201284944945748048242150033016115761873903337]",
"[25.65087559815282386348425301498878647381541073556071098978797107883197629936416910227, 25.65087559815282386348425301498878647381541073556071098978797107883197633059827896037]",
"[27.73939573841315999394006506522073270369709609089083737869229539572189853483356439507, 27.73939573841315999394006506522073270369709609089083737869229539572189856620447220887]",
"[30.61496299848522160592489563324781405956886749912990772471632543054979412716724348209, 30.61496299848522160592489563324781405956886749912990772471632543054979415880553817318]",
"[34.20683944163435203654252183894074614404583386430125790628165692622368350316804889979, 34.20683944163435203654252183894074614404583386430125790628165692622368353527209357793]",
"[38.03610820848336847941671762195563218490537943151235625360505858542583727070015775979, 38.03610820848336847941671762195563218490537943151235625360505858542583730355494018487]",
"[41.31145688943534906298722464613456272221844121895697870574852379929279725171987083145, 41.31145688943534906298722464613456272221844121895697870574852379929279728571898728658]",
"[43.41703818352741930744199347750261623421828213327698088018650933821243849626878130093, 43.41703818352741930744199347750261623421828213327698088018650933821243853194080281505]",
"[44.29436372214166389336800012284957758168483644088311112885671555169752450166875000835, 44.2943637221416638933680001228495775816848364408831111288567155516975245397103851085]",
"[44.29436372153605884453803024786211917289361839695296983545468492033691291080540334748, 44.29436372153605884453803024786211917289361839695296983545468492033691295212577097213]",
"[44.29436372093045379570806037287466076410240035302282854205265428897630131934986772684, 44.29436372093045379570806037287466076410240035302282854205265428897630136513309642617]"
]
},
{
"lower_level": 67,
"upper_level": 68,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "43.82247933987921998155570934542617400487743501702446045371866417840481530393492028147360609054146982",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[43.82247934109043007921564909540109082245987110488474304052272544112603848238162573064, 43.82247934109043007921564909540109082245987110488474304052272544112603852449198039675]",
"[43.82247934048482503038567922041363241366865306095460174712069480976542689315827297232, 43.82247934048482503038567922041363241366865306095460174712069480976542693526862919024]",
"[43.82247933987921998155570934542617400487743501702446045371866417840481530393492028147, 43.82247933987921998155570934542617400487743501702446045371866417840481534604527791626]",
"[44.64334808282992936239748907451406998008976995618741545253360135645851407937960284374, 44.64334808282992936239748907451406998008976995618741545253360135645851412151579442977]",
"[46.61343306618246230919403686167225025149598602025103364797317099898391071232855167938, 46.61343306618246230919403686167225025149598602025103364797317099898391075455777369236]",
"[49.67800970636123750664507917133863191294393514192365439739785662304361111321212899282, 49.67800970636123750664507917133863191294393514192365439739785662304361115566196287612]",
"[53.77035150700440840197284212329866435609973229273228317589769289733782837157319134716, 53.7703515070044084019728421232986643560997322927322831758976928973378284144541540997]",
"[58.65955822308520496364734501174172827115766192377215384361444600068935525895330777757, 58.65955822308520496364734501174172827115766192377215384361444600068935530258504950127]",
"[63.69373562506924743374040493695396764766315870810753874210562519372049785635398386096, 63.69373562506924743374040493695396764766315870810753874210562519372049790119544357455]",
"[67.93037434541188399008664420014506178517908594884424698090493053189646525755159644354, 67.93037434541188399008664420014506178517908594884424698090493053189646530423585185645]",
"[70.65392780621462889705130544387457986673739842130989861742577084391078176133259114358, 70.65392780621462889705130544387457986673739842130989861742577084391078181070795507848]",
"[71.78874174547249530561218405579610333064931057516237647414144160032032541863757415437, 71.7887417454724953056121840557961033306493105751623764741414416003203254718179443544]",
"[71.78874174131507580687058961048632011752280243199967407645266108237352888841352342003, 71.78874174131507580687058961048632011752280243199967407645266108237352894684333537492]",
"[71.78874173715765630812899516517653690439629428883697167876388056442673235725762928895, 71.78874173715765630812899516517653690439629428883697167876388056442673242280039113144]"
]
},
{
"lower_level": 66,
"upper_level": 67,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "68.78195887587009744002716462601791326180640498890936006022127525098812283125596341845497526576398256",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[68.7819588841849364375103535166374796880594212752347648555988362868817158864547479519, 68.78195888418493643751035351663747968805942127523476485559883628688171594163279226678]",
"[68.78195888002751693876875907132769647493291313207206245791005576893491935885535568518, 68.78195888002751693876875907132769647493291313207206245791005576893491941403340215911]",
"[68.78195887587009744002716462601791326180640498890936006022127525098812283125596341845, 68.78195887587009744002716462601791326180640498890936006022127525098812288643401191649]",
"[69.84958706383710661070180916868006746376137711615210818117560063806013174190061773579, 69.84958706383710661070180916868006746376137711615210818117560063806013179711300013155]",
"[72.41189471999886320142494431491279247194077950572153671505424840419605396999877006741, 72.41189471999886320142494431491279247194077950572153671505424840419605402533481254625]",
"[76.39770663063880989958098486880660073640583401092821626160085614714309109087522355348, 76.39770663063880989958098486880660073640583401092821626160085614714309114650455004657]",
"[81.63855875644293706527982396348340186723339811957079436829980626221321564893331846343, 81.63855875644293706527982396348340186723339811957079436829980626221321570513584190212]",
"[87.75246141983875729880921645883363771021491922731967860607648226710647809955035037261, 87.75246141983875729880921645883363771021491922731967860607648226710647815675108467903]",
"[93.92422759773148743357405023444738754904568309549143981466485907954324867022102463663, 93.92422759773148743357405023444738754904568309549143981466485907954324872903006775523]",
"[99.06851032676114785878285818946332906430958830079140362019063627919627038144613773396, 99.06851032676114785878285818946332906430958830079140362019063627919627044270464654463]",
"[102.3755492198042937930972333004273886298649950824194630619093969246698080333256662508, 102.3755492198042937930972333004273886298649950824194630619093969246698080981595528914]",
"[103.7534820863111837176728484948007101843040937814116737338150141318671014080550196132, 103.7534820863111837176728484948007101843040937814116737338150141318671014779397182911]",
"[103.7534820774214418216685020678265375439501891511071654925258500307807580761633989181, 103.7534820774214418216685020678265375439501891511071654925258500307807581530056654039]",
"[103.753482068531699925664155640852364903596284520802657251236685929694414743048027876, 103.7534820685316999256641556408523649035962845208026572512366859296944148292947519897]"
]
},
{
"lower_level": 65,
"upper_level": 66,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "97.79067988209619469036262983142951433931702275417512614673948897308521377586557167919475967604914841",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[97.79067989987567848237132268537785962002483201478414262931781717525790043269103758867, 97.79067989987567848237132268537785962002483201478414262931781717525790049439121949062]",
"[97.79067989098593658636697625840368697967092738447963438802865307417155710427830456646, 97.79067989098593658636697625840368697967092738447963438802865307417155716597848957204]",
"[97.79067988209619469036262983142951433931702275417512614673948897308521377586557167919, 97.79067988209619469036262983142951433931702275417512614673948897308521383756575951852]",
"[99.09104181419301147904790606109713583141416613113886298687509361236371641833738621343, 99.09104181419301147904790606109713583141416613113886298687509361236371648007828576096]",
"[102.2119104626637587669807312982565821785465835547760152957309153602378532076011584026, 102.2119104626637587669807312982565821785465835547760152957309153602378532694886318124]",
"[107.0665950302683934461806239401053328757515568672909184207450781610492189229597443967, 107.0665950302683934461806239401053328757515568672909184207450781610492189851947438413]",
"[113.3907449467172143465935526796748126274295549606798145862711950350290277890070300938, 113.3907449467172143465935526796748126274295549606798145862711950350290278519210809465]",
"[120.6599372538253596783900314688313381552664623861606107671103033729477363128800674357, 120.6599372538253596783900314688313381552664623861606107671103033729477363769764402601]",
"[127.9049463085809128186130270717717671656604009277997001121361985846049426447298615501, 127.9049463085809128186130270717717671656604009277997001121361985846049427107308010116]",
"[133.905588912438230876812200341807080720711915147815821457086745737215056231549366503, 133.905588912438230876812200341807080720711915147815821457086745737215056300450239741]",
"[137.7631448654546055575296556433608862144227545694259327285666307493502105460078444403, 137.7631448654546055575296556433608862144227545694259327285666307493502106191400187173]",
"[139.370459836649534803519028458557920966151126490572343201458084940434874937017582738, 139.3704598366495348035190284585579209661511264905723432014580849404348750161235373014]",
"[139.3704598217044636626412900436725990732557109868604872933476449467873887465035408798, 139.3704598217044636626412900436725990732557109868604872933476449467873888338304413322]",
"[139.3704598067593925217635516287872771803602954831486313852372049531399025545527574135, 139.3704598067593925217635516287872771803602954831486313852372049531399026529749252193]"
]
},
{
"lower_level": 64,
"upper_level": 65,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "130.0813708805599180075112413692153537381645824260620290571626375810623141879411505749398145998957455",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[130.0813709104500602892667181989859975239554134334857408733835175683572865607496766664, 130.0813709104500602892667181989859975239554134334857408733835175683572866311851355239]",
"[130.0813708955049891483889797841006756310599979297738849652730775747098003743454136207, 130.0813708955049891483889797841006756310599979297738849652730775747098004447808767963]",
"[130.0813708805599180075112413692153537381645824260620290571626375810623141879411505749, 130.0813708805599180075112413692153537381645824260620290571626375810623142583766177987]",
"[131.6010450682143699041697866560956905245083807730810608365649753995029470080580285951, 131.6010450682143699041697866560956905245083807730810608365649753995029470785458601474]",
"[135.2482631382446154797691105591108876900010002527572689228321830097459128065409343461, 135.2482631382446154797691105591108876900010002527572689228321830097459128772173323207]",
"[140.9217134756705146491550318357969049138553617103115193557252981482049696750339437747, 140.9217134756705146491550318357969049138553617103115193557252981482049697461574977282]",
"[148.2667487003722686867784518395185719380063432678518642319525835478791541523260364139, 148.2667487003722686867784518395185719380063432678518642319525835478791542243234051884]",
"[156.6247865921656719763878038744744961668528258396762544908019587828325891266627038355, 156.6247865921656719763878038744744961668528258396762544908019587828325892001815876584]",
"[164.8814220958009066956886778117564468901883409182602256183795129614513226542505516915, 164.88142209580090669568867781175644689018834091826022561837951296145132273022040363]",
"[171.6893083327620045383782512735559068938019310845656383965298959306391433255833428739, 171.6893083327620045383782512735559068938019310845656383965298959306391434052848125364]",
"[176.0658066183679791583546041332636431358497711876043626756786169966728928134582736484, 176.0658066183679791583546041332636431358497711876043626756786169966728928986035232823]",
"[177.8893475569632034263941162726196686506505870800584183650314661819665938736263664495, 177.8893475569632034263941162726196686506505870800584183650314661819665939664543510904]",
"[177.8893475344794790159803344063481288397390976722930257437109396155937083995017027046, 177.8893475344794790159803344063481288397390976722930257437109396155937085028957292102]",
"[177.8893475119957546055665525400765890288276082645276331223904130492208229235371010899, 177.8893475119957546055665525400765890288276082645276331223904130492208230411768821922]"
]
},
{
"lower_level": 63,
"upper_level": 64,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "164.9513243850887327071560633765437278718433914006900832107008887953616832647735233214638845486373786",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[164.95132443005618152798362710908680749366637021622086845334194192810745420245916797, 164.9513244300561815279836271090868074936663702162208684533419419281074542853435571969]",
"[164.9513244075724571175698452428152676827548808084554758320214153617345687336163455108, 164.9513244075724571175698452428152676827548808084554758320214153617345688165007404052]",
"[164.9513243850887327071560633765437278718433914006900832107008887953616832647735233215, 164.9513243850887327071560633765437278718433914006900832107008887953616833476579236135]",
"[166.6774445824672803345677743187037838855041276674619101212278836156656169449300870984, 166.6774445824672803345677743187037838855041276674619101212278836156656170278664199106]",
"[170.8201330861011458989725772490307768672149847206573424230014203922578665918281639045, 170.8201330861011458989725772490307768672149847206573424230014203922578666749515580167]",
"[177.264315212856076003761201670418624843525632896280967117509099113200015016633760203, 177.2643152128560760037612016704186248435256328962809671175090991132000151002008320771]",
"[185.5703965464866351501986021845083122202158411018835227881659867891144878404750104217, 185.5703965464866351501986021845083122202158411018835227881659867891144879249092259467]",
"[194.9535586274035698844846073732209614905477218824097845685918923086413947180894462194, 194.9535586274035698844846073732209614905477218824097845685918923086413948040337179464]",
"[204.1627131739797973107687914950727082517378476527943062480034371443065473909671709362, 204.1627131739797973107687914950727082517378476527943062480034371443065474793441048002]",
"[211.7307197396903409485086828350085296871493521102872561822290834182963524593304173359, 211.7307197396903409485086828350085296871493521102872561822290834182963525514111502057]",
"[216.5958668044571753777467231288826107621139277790519676957059171459442560732798834348, 216.5958668044571753777467231288826107621139277790519676957059171459442561707634970012]",
"[218.6230113955392664905538047941644370992508791011003094101662997859241012634283888119, 218.6230113955392664905538047941644370992508791011003094101662997859241013685357283345]",
"[218.6230113638530263272770291447101941894306473859661161202522286076616438854294648396, 218.6230113638530263272770291447101941894306473859661161202522286076616440010181658956]",
"[218.623011332166786164000253495255951279610415670831922830338157429399186505608528175, 218.6230113321667861640002534952559512796104156708319228303381574293991866353206484518]"
]
},
{
"lower_level": 62,
"upper_level": 63,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "201.7580568386995550648346524927782838865891260234976127291322924903316425566971390872272140590978736",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[201.7580569020720353913882037916867697062295894537659993089604348468565573022094045711, 201.7580569020720353913882037916867697062295894537659993089604348468565573882114460585]",
"[201.7580568703857952281114281422325267964093577386318060190463636685940999294532718292, 201.7580568703857952281114281422325267964093577386318060190463636685941000154553206033]",
"[201.7580568386995550648346524927782838865891260234976127291322924903316425566971390872, 201.7580568386995550648346524927782838865891260234976127291322924903316426426991948783]",
"[203.6782679103554064152048701998625155447700024314298187294281839432873603727025570076, 203.6782679103554064152048701998625155447700024314298187294281839432873604587543690043]",
"[208.2867745248139245115608245673600396737588374719823697477685222665120424440966480839, 208.2867745248139245115608245673600396737588374719823697477685222665120425303276276527]",
"[215.4555626063301970956251411313575939241585583705262728799582451330425167784549277032, 215.4555626063301970956251411313575939241585583705262728799582451330425168651107986685]",
"[224.6652197406009572815894664154993188636624397754065689637199669245242601245255621368, 224.6652197406009572815894664154993188636624397754065689637199669245242602120118082653]",
"[235.012291293478573520925263810166707181439715558223427653901175031149048782425105339, 235.0122912934785735209252638101667071814397155582234276539011750311490488713573799255]",
"[245.1171677190066484263745220165072747094136179464522840331454840084929373087452545349, 245.1171677190066484263745220165072747094136179464522840331454840084929374000071234445]",
"[253.4000064694981278954992473602733282625928809568635479155593044960029237316686041924, 253.4000064694981278954992473602733282625928809568635479155593044960029238264775067569]",
"[258.724688505882261241546289790329930948127084227058954671195205560071155379463403603, 258.7246885058822612415462897903299309481270842270589546711952055600711554794466554923]",
"[260.943305995202771312767533923027683510815533230853375886939785439964962010347239096, 260.9433059952027713127675339230276835108155332308533758869397854399649621176316001808]",
"[260.943305952446631073469000346789207651335959757127845289518613402323778209601238989, 260.9433059524466310734690003467892076513359597571278452895186134023237783269223079583]",
"[260.9433059096904908341704667705507317918563862834023146920974413646825944071131628359, 260.9433059096904908341704667705507317918563862834023146920974413646825945379551041964]"
]
},
{
"lower_level": 61,
"upper_level": 62,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "239.9153360449648641932841440279693029669563985422889640846266749041127719911618520757662689341220818",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[239.9153361304771446718812111804462546859155454897400252794690189793951395826210865464, 239.91533613047714467188121118044625468591554548974002527946901897939513967553521373]",
"[239.9153360877210044325826776042077788264359720160144946820478469417539557868914691761, 239.9153360877210044325826776042077788264359720160144946820478469417539558798056060754]",
"[239.9153360449648641932841440279693029669563985422889640846266749041127719911618520758, 239.915336044964864193284144027969302966956398542288964084626674904112772084075998151]",
"[242.0177541936143097963764385220116938054716284798010509483818904346472916594978577639, 242.0177541936143097963764385220116938054716284798010509483818904346472917524657602101]",
"[247.0635578079902443596505752778084509995651679998301309096026299549588658345259888713, 247.0635578079902443596505752778084509995651679998301309096026299549588659276876299951]",
"[254.9125856727174134739612451332479096780020478182092527306728148819779585790537815144, 254.9125856727174134739612451332479096780020478182092527306728148819779586726751507193]",
"[264.9705329751341720843620740140631932004919314148175499442069557904711941096956084452, 264.9705329751341720843620740140631932004919314148175499442069557904711942042158289939]",
"[276.2226112653423352297521921365668935145720425532106630861781583228343924765715750995, 276.2226112653423352297521921365668935145720425532106630861781583228343925726575518988]",
"[287.168543430736918612561272351226660678027921031914571538216426496878156256586525775, 287.1685434307369186125612723512266606780279210319145715382164264968781563551955262923]",
"[296.1226191194945056474105111236900215052281288355148310850529703416621050212368569114, 296.1226191194945056474105111236900215052281288355148310850529703416621051236879290498]",
"[301.8788106110855006104089367954031790428024314263168250703629848225945170556636602707, 301.8788106110855006104089367954031790428024314263168250703629848225945171637198200862]",
"[304.2772236988987603660912342336345795268309563297062136727392279986356855530968163823, 304.2772236988987603660912342336345795268309563297062136727392279986356856690616873502]",
"[304.2772236429756496464384265250515634365196258238339756965044257578328545174799086147, 304.2772236429756496464384265250515634365196258238339756965044257578328546443153824086]",
"[304.2772235870525389267856188164685473462082953179617377202696235170300234799753745944, 304.2772235870525389267856188164685473462082953179617377202696235170300236214513028759]"
]
},
{
"lower_level": 60,
"upper_level": 61,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "278.8895357117162902408965511446160388885950584257471058734241111996808180480473470717685834630795149",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[278.8895358235625116802021665617820710692177194374915818258937156812864801083945607389, 278.8895358235625116802021665617820710692177194374915818258937156812864802021731994311]",
"[278.8895357676394009605493588531990549789063889316193438496589134404836490782209539053, 278.8895357676394009605493588531990549789063889316193438496589134404836491719996044723]",
"[278.8895357117162902408965511446160388885950584257471058734241111996808180480473470718, 278.8895357117162902408965511446160388885950584257471058734241111996808181418260095134]",
"[281.1627126421543072912498405618732997895515842866072851568021970495347991759872056188, 281.1627126421543072912498405618732997895515842866072851568021970495347992698234691457]",
"[286.6183373508455871659695680054785743535213969953947442583319138071882009270338602721, 286.6183373508455871659695680054785743535213969953947442583319138071882010210775634882]",
"[295.1048647022715070641288963989590335419391201142211381821297259720216072077103221781, 295.1048647022715070641288963989590335419391201142211381821297259720216073022460176612]",
"[305.9578352213288321642372746585922998262867738808391085152061196343119644274379779596, 305.9578352213288321642372746585922998262867738808391085152061196343119645229352913801]",
"[318.0581540369355303911163689743795971345947658793885539834484309121253129003516400727, 318.0581540369355303911163689743795971345947658793885539834484309121253129975236895548]",
"[329.7924452977923182137771469334538523858583880779638435755838619517884116551899584578, 329.7924452977923182137771469334538523858583880779638435755838619517884117550602654552]",
"[339.3757273436997387737734742213464980181772540455697368586032790968700088529007982251, 339.3757273436997387737734742213464980181772540455697368586032790968700089568796571592]",
"[345.5364086303163294996750002937273509376451946629027925625930452409938604235112199289, 345.5364086303163294996750002937273509376451946629027925625930452409938605334835404377]",
"[348.1033591234851104298859527098301084616783047798700742391742074618464909729075128114, 348.103359123485110429885952709830108461678304779870074239174207461846491091336005231]",
"[348.1033590520384382559683215398318257001783519039884108886529278331915237171993532061, 348.103359052038438255968321539831825700178351903988410888652927833191523847249941931]",
"[348.1033589805917660820506903698335429386783990281067475381316482045365564594757304631, 348.1033589805917660820506903698335429386783990281067475381316482045365566051767476796]"
]
},
{
"lower_level": 59,
"upper_level": 60,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "318.196281678367001000634691826169045262577254510368631585548141110514853978851706583708065134845546",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[318.1962818212603453484699541661656107855771602621319582865907003678247884786395721894, 318.1962818212603453484699541661656107855771602621319582865907003678247885896613609806]",
"[318.1962817498136731745523229961673280240772073862502949360694207391698212287456391167, 318.1962817498136731745523229961673280240772073862502949360694207391698213397674430212]",
"[318.1962816783670010006346918261690452625772545103686315855481411105148539788517065837, 318.1962816783670010006346918261690452625772545103686315855481411105148540898735250618]",
"[320.6291723195388488180187286363276712777902892730003644310175841957045155861012061078, 320.6291723195388488180187286363276712777902892730003644310175841957045156971932344772]",
"[326.4681099552614184034159911121590553164326861584101300707303223888240433900925202801, 326.4681099552614184034159911121590553164326861584101300707303223888240435014374232214]",
"[335.550901867725382892377419681510077222097726671789739010182876494649800312562090131, 335.5509018677253828923774196815100772220977266717897390101828764946498004245067674218]",
"[347.1474978135801944628847084154332174336486601794614760075554776972483620064150864076, 347.1474978135801944628847084154332174336486601794614760075554776972483621195320188662]",
"[360.0412694085258819826287019558241056502352470452952939969049193844773364023662877102, 360.0412694085258819826287019558241056502352470452952939969049193844773365175246636004]",
"[372.5130470950357584891315621551634152408816130140617467221312109558926732543995153212, 372.5130470950357584891315621551634152408816130140617467221312109558926733728466607855]",
"[382.6849540550193853594090251671431586510194456869746826122482730842254663268421303538, 382.6849540550193853594090251671431586510194456869746826122482730842254664502963800712]",
"[389.2240370651105396147951678137800116598104204026920800460073611826440444881008737192, 389.224037065110539614795167813780011659810420402692080046007361182644044618858302074]",
"[391.9486549322529518407977873447972306099147627332040706569952354650499937516830585158, 391.948654932252951840797787344797230609914762733204070656995235465049993892742712138]",
"[391.9486548426325287388821094703085058608485739550603816856894460038844106484843108839, 391.9486548426325287388821094703085058608485739550603816856894460038844108037001863239]",
"[391.9486547530121056369664315958197811117823851769166927143836565427188275428368640198, 391.9486547530121056369664315958197811117823851769166927143836565427188277171104322352]"
]
},
{
"lower_level": 58,
"upper_level": 59,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "357.3973586569698191754916907035676286347803823201584593690278917173162263619470147754688275571784727",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[357.3973588362106653793230464525450781329127598764458373116394706396473925541996280505, 357.3973588362106653793230464525450781329127598764458373116394706396473926770863767803]",
"[357.3973587465902422774073685780563533838465710983021483403336811784818094580733211431, 357.3973587465902422774073685780563533838465710983021483403336811784818095809600887645]",
"[357.3973586569698191754916907035676286347803823201584593690278917173162263619470147755, 357.3973586569698191754916907035676286347803823201584593690278917173162264848338002089]",
"[359.9792921042226017770042009902386300043467799591561516874850718326427216134922878977, 359.9792921042226017770042009902386300043467799591561516874850718326427217364621505739]",
"[366.1759324994610156889703854212729118920794349860528247452822762384645244475335743522, 366.1759324994610156889703854212729118920794349860528247452822762384645245708027337051]",
"[375.815150935983333511175982903983539432188149190908165697813460926873997591168690087, 375.815150935983333511175982903983539432188149190908165697813460926873997715147916298]",
"[388.1057090755951646297590545106166811380306441000343207340104229363277179092759902631, 388.1057090755951646297590545106166811380306441000343207340104229363277180346433790944]",
"[401.7399818746188087737087402153726965151953341919413703074983829843515386040042438631, 401.7399818746188087737087402153726965151953341919413703074983829843515387317896238701]",
"[414.900066278951203961359812345480477469988830048477426703740523481869040690690198201, 414.9000662789512039613598123454804774699888300484774267037405234818690408223717575841]",
"[425.6213618361545591985768433471501810758711766872223011887388581808861218842981959882, 425.6213618361545591985768433471501810758711766872223011887388581808861220219126871202]",
"[432.5136232220396313248833335198037801195487694105427174811126493532543512700748179485, 432.5136232220396313248833335198037801195487694105427174811126493532543514163441808778]",
"[435.3853987331893886687304234518774595929495639940901757244257272810394441360591598694, 435.3853987331893886687304234518774595929495639940901757244257272810394442945390217785]",
"[435.3853986224124323942837425163504124572543216576856167891347894033417819287401543917, 435.3853986224124323942837425163504124572543216576856167891347894033417821039999298752]",
"[435.3853985116354761198370615808233653215590793212810578538438515256441197185188376274, 435.3853985116354761198370615808233653215590793212810578538438515256441199163696943949]"
]
},
{
"lower_level": 57,
"upper_level": 58,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "396.0978499945436816377543798434676977294900816011215481507130860014957126492739351452323885155029442",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[396.0978502160975941866477417145217920008805662739306660212949617568910370471463280839, 396.0978502160975941866477417145217920008805662739306660212949617568910371691517428583]",
"[396.0978501053206379122010607789947448651853239375261070860040238791933748482101313447, 396.0978501053206379122010607789947448651853239375261070860040238791933749702155687891]",
"[396.0978499945436816377543798434676977294900816011215481507130860014957126492739351452, 396.0978499945436816377543798434676977294900816011215481507130860014957127712793947198]",
"[398.8185033690024980245524229139559358806893092716921838640821227101633768869594966578, 398.8185033690024980245524229139559358806893092716921838640821227101633770090519575342]",
"[405.3480716185662704782135024632986867381435310828916302655315565550356090843745158445, 405.3480716185662704782135024632986867381435310828916302655315565550356092067802996149]",
"[415.5051778392893003614935915991431633812662182976631003919008402809385056307988460316, 415.5051778392893003614935915991431633812662182976631003919008402809385057539478109688]",
"[428.4416484056609851697079945027857205552634957228819650837385845009553702247265843036, 428.441648405660985169707994502785720555263495722881965083738584500955370349328265062]",
"[442.76517899737295103847419551945668617733221278609621609244470586440141390418612479, 442.7651789973729510384741955194566861773322127860962160924447058644014140313180728528]",
"[456.5659655181654704892109892754393473498764323828718407870757749626877227928087340798, 456.5659655181654704892109892754393473498764323828718407870757749626877229240176818375]",
"[467.7986649164754675578029831651030255277849678821679270210222537292175927043661060776, 467.7986649164754675578029831651030255277849678821679270210222537292175928417833827439]",
"[475.0196859050939910404937431976006499117422513779947853484115129772088187929014337647, 475.0196859050939910404937431976006499117422513779947853484115129772088189393756239422]",
"[478.0284445694863007179417954226642679160806283684574278183857247262381715103245790007, 478.0284445694863007179417954226642679160806283684574278183857247262381716695771664093]",
"[478.0284444341927338169467185499073054059608623899694463967312392639624386607825821952, 478.0284444341927338169467185499073054059608623899694463967312392639624388375967865148]",
"[478.0284442988991669159516416771503428958410964114814649750767538016867058081989565115, 478.0284442988991669159516416771503428958410964114814649750767538016867060086589109901]"
]
},
{
"lower_level": 56,
"upper_level": 57,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "433.9434861524395039747758640337012305451445655069652532617647231768674553192977999488934422423162512",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[433.9434864230266377767660177792151555653840974639412161050736941014189210008206062983, 433.9434864230266377767660177792151555653840974639412161050736941014189211076362814361]",
"[433.9434862877330708757709409064581930552643314854532346834192086391431881600592028537, 433.9434862877330708757709409064581930552643314854532346834192086391431882668749055193]",
"[433.9434861524395039747758640337012305451445655069652532617647231768674553192977999489, 433.9434861524395039747758640337012305451445655069652532617647231768674554261135296025]",
"[436.7928611050441700804342912651002409699660029997840897745684901636251919860196359005, 436.7928611050441700804342912651002409699660029997840897745684901636251920929260939023]",
"[443.6313611758173241601824819044893695725389544139228796019974020821813961358345933097, 443.6313611758173241601824819044893695725389544139228796019974020821813962430677683633]",
"[454.269028019861061863389843981545815866961738185805094573633459627393880300041282973, 454.2690280198610618633898439815458158669617381858050945736334596273938804080493382502]",
"[467.8048658758186055577310834101709788949301157864594836332393576390540063957948806528, 467.8048658758186055577310834101709788949301157864594836332393576390540065053174597299]",
"[482.7680039674074714253927674465557943130601881441102043007543466594047033846898900299, 482.768003967407471425392767446555794313060188144110204300754346659404703496850123389]",
"[497.1633571947654977575982634457321599081555334644812515572846159633127020642826976792, 497.1633571947654977575982634457321599081555334644812515572846159633127021806925515499]",
"[508.8706431559609426556146662640560766821056673951312226940204239435228759818467366855, 508.8706431559609426556146662640560766821056673951312226940204239435228761047272420051]",
"[516.3967554955913204197009909783531824386434689680445115683904653911069570254260965815, 516.3967554955913204197009909783531824386434689680445115683904653911069571577455773502]",
"[519.5326355394318654939869362857835854880629165056491042991164651918278862135207237931, 519.5326355394318654939869362857835854880629165056491042991164651918278863591570674421]",
"[519.5326353758329706252438698645231140005322572684135833321594636887430872369288386907, 519.5326353758329706252438698645231140005322572684135833321594636887430874008666279649]",
"[519.5326352122340757565008034432626425130015980311780623652024621856582882571658960712, 519.5326352122340757565008034432626425130015980311780623652024621856582884457463759107]"
]
},
{
"lower_level": 55,
"upper_level": 56,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "470.6181803734135127079537607985009083817002001405337050014035295148366769176189008982371619550361001",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[470.6181807006113024454398936410218513567615186150047469353175325210062748524923437183, 470.6181807006113024454398936410218513567615186150047469353175325210062749837701730167]",
"[470.6181805370124075766968272197613798692308593777692259683605310179214758850556220384, 470.6181805370124075766968272197613798692308593777692259683605310179214760163334848019]",
"[470.6181803734135127079537607985009083817002001405337050014035295148366769176189008982, 470.6181803734135127079537607985009083817002001405337050014035295148366770488967960474]",
"[473.5865819880454996594654639684819660389222140325216255301667591166934128811316953994, 473.5865819880454996594654639684819660389222140325216255301667591166934130125038775381]",
"[480.7107460865617415359326448389049593369193657154488542583115249028017925044577728793, 480.7107460865617415359326448389049593369193657154488542583115249028017926361694735702]",
"[491.7927792105004243406911255614510014443197050400206623256498629373375281110495735324, 491.7927792105004243406911255614510014443197050400206623256498629373375282435665197553]",
"[505.8828461312989834035238472831584015467134501014962014780822580233169373974541995149, 505.8828461312989834035238472831584015467134501014962014780822580233169375315450550713]",
"[521.437431267860001732735553412058962966889751778544084143039975045966101282936527461, 521.4374312678600017327355534120589629668897517785440841430399750459661014197685509555]",
"[536.3825899101562659329487600649102305258000113034953529440370853871336935953866575332, 536.3825899101562659329487600649102305258000113034953529440370853871336937366352608076]",
"[548.5287371629332770325955448706135807310458104974515598363962335079998342711329703992, 548.528737162933277032595544870613580731045810497451559836396233507999834419106791304]",
"[556.3369746061150799242382949793244580034843371927435740138399467942374408739693328727, 556.3369746061150799242382949793244580034843371927435740138399467942374410317541305678]",
"[559.5904067570958993757953308231937388930990520179559107756411842463360460514917014906, 559.5904067570958993757953308231937388930990520179559107756411842463360462231194342735]",
"[559.5904065609152277134656323755245720029337599770607617701261227672632513097790256931, 559.5904065609152277134656323755245720029337599770607617701261227672632515004335235125]",
"[559.5904063647345560511359339278554051127684679361656127646110612881904565647676994653, 559.5904063647345560511359339278554051127684679361656127646110612881904567810459285304]"
]
},
{
"lower_level": 54,
"upper_level": 55,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "505.841732431237933915995742307196141402874415308621665733688751726445782084267478166371048857440601",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[505.8417328235992772406551392025344751832049993904119637447188746845913715486640433216, 505.8417328235992772406551392025344751832049993904119637447188746845913716840117884977]",
"[505.8417326274186055783254407548653082930397073495168147392038132055185768164657604741, 505.8417326274186055783254407548653082930397073495168147392038132055185769518135450527]",
"[505.8417324312379339159957423071961414028744153086216657336887517264457820842674781664, 505.8417324312379339159957423071961414028744153086216657336887517264457822196153016077]",
"[508.9197503050918645800593422143096090834307907752390206526396851134658026851941548882, 508.9197503050918645800593422143096090834307907752390206526396851134658028206611196724]",
"[516.306993470507314134531647944871745913911851963270477572897655368147888256376946815, 516.3069934705073141345316479448717459139118519632704775728976553681478883922727578211]",
"[527.7982607152461588236096301782347433483581877999236734478165093326506536679896948251, 527.7982607152461588236096301782347433483581877999236734478165093326506538049022764999]",
"[542.398737763596831564607542314945291853279507339385047393159589138911915498969001699, 542.3987377635968315646075423149452918532795073393850473931595891389119156378683782103]",
"[558.4980067294696504971882524775091574841923670735855120616869408538916965287747544493, 558.4980067294696504971882524775091574841923670735855120616869408538916966711335555434]",
"[573.9494983874724533271424030331618857566175028164416768297512489918261209046098306435, 573.9494983874724533271424030331618857566175028164416768297512489918261210525412976187]",
"[586.4998060198658951232123653165604028225063376553583608445984056943056978236125286974, 586.4998060198658951232123653165604028225063376553583608445984056943056979800280510728]",
"[594.5678608356446788909664508430924636657966122637055110779922414122297881470303076309, 594.5678608356446788909664508430924636657966122637055110779922414122297883158207438233]",
"[597.9295502030057109824681319364519453939671035518227884317885810675891461997193639789, 597.9295502030057109824681319364519453939671035518227884317885810675891463859682888152]",
"[597.9295499694109337935503343045517928038849979401744278311872534392322994519650701323, 597.9295499694109337935503343045517928038849979401744278311872534392322996622085378454]",
"[597.9295497358161566046325366726516402138028923285260672305859258108754527000490552374, 597.9295497358161566046325366726516402138028923285260672305859258108754529426061855214]"
]
},
{
"lower_level": 53,
"upper_level": 54,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "539.3676834829947342745680568544204609827986282414684766472999870430773083480894388347529993737436755",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[539.3676839501842886524036521182207661629628394647651978485026422997910018196017467019, 539.3676839501842886524036521182207661629628394647651978485026422997910019586733133008]",
"[539.3676837165895114634858544863206135728807338531168372479013146714341550838455922285, 539.3676837165895114634858544863206135728807338531168372479013146714341552229172063264]",
"[539.3676834829947342745680568544204609827986282414684766472999870430773083480894388348, 539.3676834829947342745680568544204609827986282414684766472999870430773084871610982725]",
"[542.5461747833487664916606214353442536007912557758504649545828306217399892444625630757, 542.5461747833487664916606214353442536007912557758504649545828306217399893836678650628]",
"[550.1745542237844231834914554044055998734358880430279184567412000839936189310419927037, 550.1745542237844231834914554044055998734358880430279184567412000839936190707284858099]",
"[562.0409223600161004900941200907984918787677313209863512068163973887812427957664919763, 562.0409223600161004900941200907984918787677313209863512068163973887812429365941079422]",
"[577.1092314239272348441524160932369718687463330216378703822000206890648182051813312851, 577.1092314239272348441524160932369718687463330216378703822000206890648183482390575003]",
"[593.7077353448262680095893086700772694584546281746794990527470728712139419265244263274, 593.70773534482626800958930867007726945845462817467949905274707287121394207346561624]",
"[609.6233002311581027267817848407096908742838035275203715517470539552029945288586341445, 609.6233002311581027267817848407096908742838035275203715517470539552029946820559757491]",
"[622.544031150895211266490627844453620114767440494406263614465889164578059682655427187, 622.5440311508952112664906278444536201147674404944062636144658891645780598453778884027]",
"[630.8502152064482186884690622602830464554979744072913791801012205608921075432645519798, 630.85021520644821868846906226028304645549797440729137918010122056089210771988118991]",
"[634.3111250649412323254680595226104505768307822953440761564008311048736410781093893261, 634.3111250649412323254680595226104505768307822953440761564008311048736412743294065971]",
"[634.3111247884653782134110865658393837143956328623883914486871970679604050373232291434, 634.3111247884653782134110865658393837143956328623883914486871970679604052604889991041]",
"[634.3111245119895241013541136090683168519604834294327067409735630310471689918572134234, 634.3111245119895241013541136090683168519604834294327067409735630310471692513183018093]"
]
},
{
"lower_level": 52,
"upper_level": 53,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "570.9813069138367737714134666506231007045911861405793652281550114850290512387386677313241877252778636",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[570.9813074667884819955274125641652344294614850064907346435822795588555232933396745072, 570.981307466788481995527412564165234429461485006490734643582279558855523435807624897]",
"[570.9813071903126278834704396073941675670263355735350499358686455219422872660391711193, 570.9813071903126278834704396073941675670263355735350499358686455219422874085071765647]",
"[570.9813069138367737714134666506231007045911861405793652281550114850290512387386677313, 570.9813069138367737714134666506231007045911861405793652281550114850290513812067271528]",
"[574.2513812290260123575717645055648786316594121983106432020394851293572325452496007568, 574.2513812290260123575717645055648786316594121983106432020394851293572326878318076567]",
"[582.099559964012025592060102848806599260736852831486760070627439960595133403702593057, 582.0995599640120255920601028488065992607368528314867600706274399605951335466957552761]",
"[594.3078381360590932950278715560135154820951419864880727245198234191446086421596916624, 594.3078381360590932950278715560135154820951419864880727245198234191446087861274314692]",
"[609.8025717858899272335811725692431920756534231089781539284321512483485586246747384891, 609.8025717858899272335811725692431920756534231089781539284321512483485587705472478829]",
"[626.8561020407731105997999690262971256599976632686868547618002356845106211874819446046, 626.8561020407731105997999690262971256599976632686868547618002356845106213366717574734]",
"[643.1946248250003465044335261765661504250356272654240350632980512808602052430803096063, 643.1946248250003465044335261765661504250356272654240350632980512808602053976149996949]",
"[656.4529516773384061794336731641018130932352496214728501969770122345533414094668123043, 656.4529516773384061794336731641018130932352496214728501969770122345533415721406907538]",
"[664.976161670835199239939517996336898629341810029932905542854983997983054846219062104, 664.9761616708351992399395179963368986293418100299329055428549839979830550207681980435]",
"[668.5274989743615250488954300465258732794561445395437736647042611347708275413653761159, 668.5274989743615250488954300465258732794561445395437736647042611347708277326742418243]",
"[668.5274986488117456932353198085853055973991793722526827116011325137038194237418535145, 668.5274986488117456932353198085853055973991793722526827116011325137038196380964138173]",
"[668.5274983232619663375752095706447379153422142049615917584980038926368113021129363905, 668.527498323261966337575209570644737915342214204961591758498003892636811547525010196]"
]
},
{
"lower_level": 51,
"upper_level": 52,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "600.497721714005866261415886448843603440520709576293497621260376170260569760351598730333168062131722",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[600.4977223651054249727361069247247388046346399108756795274666334123945859725495013485, 600.49772236510542497273610692472473880463463991087567952746663341239458611046010457]",
"[600.4977220395556456170759966867841711225776747435845885743635047913275778664505494996, 600.4977220395556456170759966867841711225776747435845885743635047913275780043612174924]",
"[600.4977217140058662614158864488436034405207095762934976212603761702605697603515987303, 600.4977217140058662614158864488436034405207095762934976212603761702605698982623304149]",
"[603.8507275330193544843536168874595812087270960876543291903650120633091018151569107352, 603.8507275330193544843536168874595812087270960876543291903650120633091019531849161911]",
"[611.8979419446529568218371148804033502707415346081073373957732749108243872547285882895, 611.897941944652956821837114880403350270741534608107337395773274910824387393178658416]",
"[624.4158311945378496446003597892870542633992269111400537096205313188465802961986896979, 624.4158311945378496446003597892870542633992269111400537096205313188465804356494272772]",
"[640.2966900923218450227779333311401793555948315876000517669518387902952008859700965897, 640.2966900923218450227779333311401793555948315876000517669518387902952010273762041472]",
"[657.7622122243724815813042912364331906373269003391041291184263915868240452559922063908, 657.7622122243724815813042912364331906373269003391041291184263915868240454008032000471]",
"[674.4836612575012384667420878738022058659388044289841546779019238129149445601766907954, 674.4836612575012384667420878738022058659388044289841546779019238129149447104730278736]",
"[688.0476182081728704908761167381484714204298940263032494247226137151942059397773651659, 688.0476182081728704908761167381484714204298940263032494247226137151942060984261597079]",
"[696.7673046720566025052463979352549540559394507033748776927732147712798397503176086617, 696.7673046720566025052463979352549540559394507033748776927732147712798399211525336147]",
"[700.4005071383047184534149614768218215784649070011528570388632938996258555627494244346, 700.400507138304718453414961476821821578464907001152857038863293899625855750783585649]",
"[700.4005067566563618449219827308219012434813545384763788577849952261847095348761367124, 700.4005067566563618449219827308219012434813545384763788577849952261847097465636516925]",
"[700.4005063750080052364290039848219809084978020757999006767066965527435635028849662131, 700.4005063750080052364290039848219809084978020757999006767066965527435637464575069693]"
]
},
{
"lower_level": 50,
"upper_level": 51,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "627.7601163884673386570795329485422972357865908581731339206508639839349373424992611285933964414907412",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[627.7601171517640518740654904405421379057536957835260902828074613308172293745798955916, 627.7601171517640518740654904405421379057536957835260902828074613308172295307914089958]",
"[627.7601167701156952655725116945422175707701433208496121017291626573760833585395783601, 627.7601167701156952655725116945422175707701433208496121017291626573760835147511673308]",
"[627.7601163884673386570795329485422972357865908581731339206508639839349373424992611286, 627.7601163884673386570795329485422972357865908581731339206508639839349374987109256658]",
"[631.1876290584408787078602936220661105744073066717300860880782563785971405383140799694, 631.1876290584408787078602936220661105744073066717300860880782563785971406946690325767]",
"[639.4136599895144129926226801107617073504739195203125118331170260109845889441659441222, 639.4136599895144129926226801107617073504739195203125118331170260109845891010367134868]",
"[652.2097082985458805388188223786873778567031341941946040576764866730429859402486720516, 652.2097082985458805388188223786873778567031341941946040576764866730429860983425830482]",
"[668.4374454611869716564074071417789303504868645476759781123287074383973104018445839952, 668.4374454611869716564074071417789303504868645476759781123287074383973105623288234402]",
"[686.2730403492532346989932672829764422663454784447768934679741531781406654857168154363, 686.2730403492532346989932672829764422663454784447768934679741531781406656503635693775]",
"[703.3384135872044184489553575928898854018904591423997665844869000460603994214151921272, 703.338413587204418448955357592889885401890459142399766584486900046060399592768056176]",
"[717.1768534301215429632589855875780391152270377700652742855024432541400642399250586286, 717.1768534301215429632589855875780391152270377700652742855024432541400644214894449652]",
"[726.0729931574426576753705642800742177204665733497733880258976784895575019832229158302, 726.0729931574426576753705642800742177204665733497733880258976784895575021796862711841]",
"[729.7797177787872846997702978221122841965025151259151483949807084772129786501485174005, 729.7797177787872846997702978221122841965025151259151483949807084772129788676414170958]",
"[729.7797173330606116579202466595013812942201148075862022876563907873848849559244620557, 729.7797173330606116579202466595013812942201148075862022876563907873848852023423882538]",
"[729.7797168873339386160701954968904783919377144892572561803320730975567912566653261295, 729.7797168873339386160701954968904783919377144892572561803320730975567915420842758841]"
]
},
{
"lower_level": 49,
"upper_level": 50,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "652.6380726960411341209589687910873592470876452436582588296773284618653312259118785273316696125702992",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[652.6380735874944802046590711163091650516524458803161510443259638415215185854554552626, 652.6380735874944802046590711163091650516524458803161510443259638415215187364297704351]",
"[652.6380731417678071628090199536982621493700455619872049370016461516934249056836663552, 652.6380731417678071628090199536982621493700455619872049370016461516934250566580700485]",
"[652.6380726960411341209589687910873592470876452436582588296773284618653312259118785273, 652.6380726960411341209589687910873592470876452436582588296773284618653313768863685823]",
"[656.1318837202337034151638527325937789292565101484278253752375043258589403761165413439, 656.1318837202337034151638527325937789292565101484278253752375043258589405272368217987]",
"[664.5170307895470198533422456874717212951702308515782603079629128252749627436517511341, 664.517030789547019853342245687471721295170230851578260307962912825274962895297257452]",
"[677.5605931244243257514376199856261335562928778479825257350205886806100993232933339552, 677.5605931244243257514376199856261335562928778479825257350205886806100994761850599065]",
"[694.0969644038488530327610087683580909358221725464558020168975871947788931061481257001, 694.0969644038488530327610087683580909358221725464558020168975871947788932614764494523]",
"[712.2617760202815625780675888096415386117660468341324230713189168472197613220349138626, 712.2617760202815625780675888096415386117660468341324230713189168472197614816079554815]",
"[729.6330530250176955374386297322747018152358674616330170810683421843509272296214552156, 729.6330530250176955374386297322747018152358674616330170810683421843509273960352264579]",
"[743.7156091211359748110162445666065513634686164452563436422102756279536141320076127531, 743.7156091211359748110162445666065513634686164452563436422102756279536143088408889714]",
"[752.7686806976239572770925137299364750776959083254780947582182162610908897126736591351, 752.7686806976239572770925137299364750776959083254780947582182162610908899047136812253]",
"[756.5407935460704289530615757285892768459066958286041959167205528238359518349346460211, 756.540793546070428953061575728589276845906695828604195916720552823835952048445452656]",
"[756.5407930271867669319003558114008910719887147228225743170245543866680032989692611247, 756.5407930271867669319003558114008910719887147228225743170245543866680035420236479604]",
"[756.5407925083031049107391358942125052980707336170409527173285559495000547578493336863, 756.5407925083031049107391358942125052980707336170409527173285559495000550407596168133]"
]
},
{
"lower_level": 48,
"upper_level": 49,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "675.025979668788254891441849471339512420508059915148747181661751766211035966891740832739790978044597",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[675.025980706555578933764289305716283968344022126711990381053748640546933009286958823, 675.0259807065555789337642893057162839683440221267119903810537486405469331545366374563]",
"[675.0259801876719169126030693885278981944260410209303687813577502033789844880893498279, 675.0259801876719169126030693885278981944260410209303687813577502033789846333391310157]",
"[675.0259796687882548914418494713395124205080599151487471816617517662110359668917408327, 675.0259796687882548914418494713395124205080599151487471816617517662110361121416234955]",
"[678.5780872196039498250698131886183798239070532552339807363794599447012432798079903431, 678.5780872196039498250698131886183798239070532552339807363794599447012434252229501292]",
"[687.1031460534141817371032809761007574690646642275585208673241074841503135659079031878, 687.1031460534141817371032809761007574690646642275585208673241074841503137119175430636]",
"[700.3643489485553391511740759413173793380643169774099235930851161532881466421636617619, 700.3643489485553391511740759413173793380643169774099235930851161532881467895842140849]",
"[717.1720691472089789159239918825830695188257672113621475347102901946666254145314446898, 717.1720691472089789159239918825830695188257672113621475347102901946666255647103816927]",
"[735.6262582861868046006451872596548071265988981450696456588787334793400100633291453819, 735.6262582861868046006451872596548071265988981450696456588787334793400102183129885633]",
"[753.266357736400597821038570841299529091663628941986871640220324540455881356286249896, 753.2663577364005978210385708412995290916636289419868716402203245404558815190130691382]",
"[767.5634103322760409591041448337794761373517413212395148649586164255814750531258102402, 767.5634103322760409591041448337794761373517413212395148649586164255814752276458692797]",
"[776.7543724839180731911167885097641757243334870196895994887198331515570131823865206261, 776.7543724839180731911167885097641757243334870196895994887198331515570133741183351328]",
"[780.5839396891600244193592961722489218526274125113265188588283813838499965553594539603, 780.583939689160024419359296172248921852627412511326518858828381383849996771395209639]",
"[780.5839390867734879632205642194993298883231682104600786623753064520502314690519433392, 780.5839390867734879632205642194993298883231682104600786623753064520502317185371969543]",
"[780.5839384843869515070818322667497379240189239095936384659222315202504663768927387081, 780.5839384843869515070818322667497379240189239095936384659222315202504666715221676242]"
]
},
{
"lower_level": 47,
"upper_level": 48,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "694.8415293917581253403273783914821371983612208150955971293403707608643355287227925485037498587708185",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[694.8415305965311982526048422969813211269697094168284775222465206244638656678729413151, 694.8415305965311982526048422969813211269697094168284775222465206244638658233212462776]",
"[694.8415299941446617964661103442317291626654651159620373257934456926641005982978669318, 694.8415299941446617964661103442317291626654651159620373257934456926641007537462906416]",
"[694.8415293917581253403273783914821371983612208150955971293403707608643355287227925485, 694.8415293917581253403273783914821371983612208150955971293403707608643356841713339261]",
"[698.4441299241748137679488388014313369889633805980125550458408524277796445405747629979, 698.4441299241748137679488388014313369889633805980125550458408524277796446962323374378]",
"[707.0903720286556437548393180406412017635971134563534472216656080451949608693723676256, 707.0903720286556437548393180406412017635971134563534472216656080451949610257829144885]",
"[720.540082276774893449461131980637780141236520007467630244975745104864177306106615584, 720.5400822767748934494611319806377801412365200074676302449757451048641774643035020954]",
"[737.5827863667508280019600952909182971727791467983134865559048618376626186784146959093, 737.5827863667508280019600952909182971727791467983134865559048618376626188401037024581]",
"[756.2874897796752130276556548868464623498783054118000276433670774251350137904059717916, 756.2874897796752130276556548868464623498783054118000276433670774251350139581776207701]",
"[774.1602319710399866369469117243550595196778270764810411743123866216429110539073962157, 774.1602319710399866369469117243550595196778270764810411743123866216429112314805826522]",
"[788.6428784836798335588969209936664486455969286171857847773411927080909108266485144838, 788.6428784836798335588969209936664486455969286171857847773411927080909110191499940479]",
"[797.9531509740487378671944879054981580373280269555640670937925864155339657931146618821, 797.9531509740487378671944879054981580373280269555640670937925864155339660074039888857]",
"[801.8324307639039721055182709260014221141697028022783916229297180988533253123506997293, 801.8324307639039721055182709260014221141697028022783916229297180988533255574090954444]",
"[801.8324300662040609088307402766425039956678358133355575648053706477932127178796019586, 801.8324300662040609088307402766425039956678358133355575648053706477932130052957520532]",
"[801.8324293685041497121432096272835858771659688243927235066810231967331001159964952532, 801.8324293685041497121432096272835858771659688243927235066810231967331004606045337887]"
]
},
{
"lower_level": 46,
"upper_level": 47,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "712.0242869433830073404568334201924732978816534511307499967673237034140919563278636869682879362649155",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[712.0242883387828297338318947189103095348853874290164181130160186055343171029416602653, 712.0242883387828297338318947189103095348853874290164181130160186055343172602934998427]",
"[712.0242876410829185371443640695513914163835204400735840548916711544742045296347619761, 712.0242876410829185371443640695513914163835204400735840548916711544742046869867386527]",
"[712.024286943383007340456833420192473297881653451130749996767323703414091956327863687, 712.0242869433830073404568334201924732978816534511307499967673237034140921136799763832]",
"[715.6697678039156177261855081157895504036050470716085263983870859601987297804014916667, 715.6697678039156177261855081157895504036050470716085263983870859601987299379278498587]",
"[724.4189228269394503599001878146777530268606398715648040991022068983916998317381602759, 724.4189228269394503599001878146777530268606398715648040991022068983916999898921703695]",
"[738.0287198863638395487086990073708886799926770471916980630083750188770761398659715554, 738.0287198863638395487086990073708886799926770471916980630083750188770762995091399425]",
"[755.270928845589130966361195757730710185064156699337586475344225061661717604960067902, 755.2709288455891309663611957577307101850641566993375864753442250616617177675146841023]",
"[774.1882232676472423986965867289384560367421575019577296763515087712261077481123792175, 774.1882232676472423986965867289384560367421575019577296763515087712261079157387807951]",
"[792.258297126185005122625320401676068449237906495547252285814598117266273013658617462, 792.2582971261850051226253204016760684492379064955472522858145981172662731894587844602]",
"[806.8983260152871172564060609816405400323575154058616431813963158673546584388207347956, 806.8983260152871172564060609816405400323575154058616431813963158673546586270722230326]",
"[816.3097728490340698699414270884393468832737478713600280404790393566520823744113618348, 816.3097728490340698699414270884393468832737478713600280404790393566520825808400439014]",
"[820.2312085507616504831921709670804668929451486887743030915121798738313756327809481614, 820.2312085507616504831921709670804668929451486887743030915121798738313758648887840855]",
"[820.2312077442410243675958778361561133278149557904764486616401152027091603783732949078, 820.2312077442410243675958778361561133278149557904764486616401152027091606458502363725]",
"[820.2312069377203982519995847052317597626847628921785942317680505315869451177559050502, 820.2312069377203982519995847052317597626847628921785942317680505315869454330245429204]"
]
},
{
"lower_level": 45,
"upper_level": 46,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "726.5343277208952315415168178641877317501056724720787714582217598722860348081186043212092988142195093",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[726.5343293339364837727094041260364388803660582686744803179658892145304652815700236927, 726.5343293339364837727094041260364388803660582686744803179658892145304654406511070493]",
"[726.5343285274158576571131109951120853152358653703766258880938245434082500448443134672, 726.5343285274158576571131109951120853152358653703766258880938245434082502039255555134]",
"[726.5343277208952315415168178641877317501056724720787714582217598722860348081186043212, 726.534327720895231541516817864187731750105672472078771458221759872286034967200002898]",
"[730.2152606560778344679684039989356454067323108101328093133983651895338438246344396388, 730.2152606560778344679684039989356454067323108101328093133983651895338439838920300878]",
"[739.0495008078906123094626391347267510463148312768934128709684953083510630360205338282, 739.0495008078906123094626391347267510463148312768934128709684953083510631959125631278]",
"[752.7916525681714143483760960944541925361268801549628926279032971173072229968123772721, 752.7916525681714143483760960944541925361268801549628926279032971173072231582095147889]",
"[770.1987433880228304516390275613049114921759611897945051326118727482612382376987395753, 770.1987433880228304516390275613049114921759611897945051326118727482612384020386493683]",
"[789.2916139831369463567423492319499780498078192137191119418434103997001203957206927021, 789.2916139831369463567423492319499780498078192137191119418434103997001205651876852597]",
"[807.5245481548063625150933030257866974883079673425345386333180301281243510593942649342, 807.5245481548063625150933030257866974883079673425345386333180301281243512371258915985]",
"[822.2944160348075596547648029341357762388202361156471316632871373097925988437310384956, 822.2944160348075596547648029341357762388202361156471316632871373097925990340559196698]",
"[831.7893307438728397566375561752897933065099290802549363990449047407753152703791323267, 831.789330743872839756637556175289793306509929080254936399044904740775315479094991365]",
"[835.7455446532644420160140819454113208229129213759046452594675822901388010656909352523, 835.7455446532644420160140819454113208229129213759046452594675822901388013004001988903]",
"[835.7455437224449166080416195947833045289024979793302393773123945886608170884412119107, 835.7455437224449166080416195947833045289024979793302393773123945886608173589750990383]",
"[835.7455427916253912000691572441552882348920745827558334951572068871828331048761542936, 835.7455427916253912000691572441552882348920745827558334951572068871828334238591564424]"
]
},
{
"lower_level": 44,
"upper_level": 45,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "738.3509361142988321603087499966744216429679568187498191950791597295401155105916910910006833592566525",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[738.3509379759378829762536746979304542309888036118986309593895351324960834292600997703, 738.3509379759378829762536746979304542309888036118986309593895351324960835899097682626]",
"[738.3509370451183575682812123473024379369783802153242250772343474310180994699258954307, 738.350937045118357568281212347302437936978380215324225077234347431018099630575746362]",
"[738.350936114298832160308749996674421642967956818749819195079159729540115510591691091, 738.3509361142988321603087499966744216429679568187498191950791597295401156712417233819]",
"[742.0600715907198968301919839173118567334005122836957324515552336018843816900206176053, 742.0600715907198968301919839173118567334005122836957324515552336018843818508756757762]",
"[750.9619980124005455868423259345144368865767679949346628253116622334983646235063577485, 750.9619980124005455868423259345144368865767679949346628253116622334983647850992707294]",
"[764.8094395898327038269899443701673696796598128223855237652779620193232928130100922537, 764.8094395898327038269899443701673696796598128223855237652779620193232929763526444054]",
"[782.3476190457807686262872020532390855286951057974164321406567620397333029545025985824, 782.3476190457807686262872020532390855286951057974164321406567620397333031212646794567]",
"[801.5799318363847350807225544627635807573578535778865693076320384134546242214971973734, 801.5799318363847350807225544627635807573578535778865693076320384134546243942150078623]",
"[819.9420694519782987522531916475728840780535046738894761011494101349894720180361828874, 819.9420694519782987522531916475728840780535046738894761011494101349894722003517280516]",
"[834.8148811248457474631023560408479861846817027789376500030211242115020659121120272657, 834.8148811248457474631023560408479861846817027789376500030211242115020661090490937372]",
"[844.3759739322703806254257077453822896980282412467104415350784316640009767868954002975, 844.3759739322703806254257077453822896980282412467104415350784316640009770051829538038]",
"[848.3597619650453342983196614208385079189128356672099654538814498524873221261305205065, 848.3597619650453342983196614208385079189128356672099654538814498524873223745945666214]",
"[848.3597608921535764512977741276765602244190472037359540195459420144408076817586393571, 848.3597608921535764512977741276765602244190472037359540195459420144408079718201892974]",
"[848.3597598192618186042758868345146125299252587402619425852104341763942932300405860243, 848.3597598192618186042758868345146125299252587402619425852104341763942935763827207863]"
]
},
{
"lower_level": 43,
"upper_level": 44,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "747.4713601561940837646329370635410473098715565315916320635395975142926607064010656665873128293483544",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[747.4713623019775994586767116498649426988591334585396549322106131903856895535243994307, 747.4713623019775994586767116498649426988591334585396549322106131903856897070530730395]",
"[747.4713612290858416116548243567029950043653449950656434978751053523391751299627320089, 747.4713612290858416116548243567029950043653449950656434978751053523391752834916161243]",
"[747.4713601561940837646329370635410473098715565315916320635395975142926607064010656666, 747.4713601561940837646329370635410473098715565315916320635395975142926608599301581296]",
"[751.2016224114530029953492604140545578646701253181736309079348109376629005569871815356, 751.2016224114530029953492604140545578646701253181736309079348109376629007107222034378]",
"[760.154253297652520372108941956771214201435636918849024630713081771699317345576876652, 760.1542532976525203721089419567712142014356369188490246307130817716993175000534960637]",
"[774.0805685596985484340051764874925864268034031032095234980731371964517038637391937063, 774.0805685596985484340051764874925864268034031032095234980731371964517040199753882007]",
"[791.7168503705000079434147510495441041262881410724581844645258778123472066949025562886, 791.716850370500007943414751049544104126288141072458184464525877812347206854579459709]",
"[811.0533282543339173282728441277710513494786941202146564370028291805011823015279623471, 811.0533282543339173282728441277710513494786941202146564370028291805011824672001695449]",
"[829.5118050015862850026234963142403235120841395953280519414617795037114043796294566176, 829.511805001586285002623496314240323512084139595328051941461779503711404554967142756]",
"[844.4612961172893060045966425077472315212080979358716458112116876289732767821312358634, 844.4612961172893060045966425077472315212080979358716458112116876289732769721996401038]",
"[854.0716827902260663103469228097762701806485786657659454075244577180807980615616816129, 854.0716827902260663103469228097762701806485786657659454075244577180807982731496690684]",
"[858.0760098372231804517386630663736093783114948839535927975168854243970651683155710523, 858.076009837223180451738663066373609378311494883953592797516885424397065410335725966]",
"[858.0760086018056238526753203751260628930951984028113682087279486376472688941871703037, 858.0760086018056238526753203751260628930951984028113682087279486376472691781877049395]",
"[858.076007366388067253611977683878516407878901921669143619939011850897472612625172358, 858.0760073663880672536119776838785164078789019216691436199390118508974729534810774113]"
]
},
{
"lower_level": 42,
"upper_level": 43,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "753.9096173713157830293388623632402340113827366759151217141290550935167673179676224743710955030367746",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[753.9096198421508962274655477457353269818153296381995708917069286670163598242559416512, 753.9096198421508962274655477457353269818153296381995708917069286670163599789889645892]",
"[753.9096186067333396284022050544877804965990331570573463029179918802665635711117820628, 753.909618606733339628402205054487780496599033157057346302917991880266563725845045734]",
"[753.9096173713157830293388623632402340113827366759151217141290550935167673179676224744, 753.9096173713157830293388623632402340113827366759151217141290550935167674727011268788]",
"[757.6541001219623885166441295011533165781796465963791575350962239318764014240714079847, 757.6541001219623885166441295011533165781796465963791575350962239318764015790409485915]",
"[766.6408604204849543051579083709970500340276954622949778289519211457400627670862418008, 766.6408604204849543051579083709970500340276954622949778289519211457400629229044273854]",
"[780.6202659630943488795466635505560709933394486998664731765356420783009430210980244058, 780.6202659630943488795466635505560709933394486998664731765356420783009431789271882578]",
"[798.3224509950192320410260587950601703678443338305776023127786348286334140549426110515, 798.3224509950192320410260587950601703678443338305776023127786348286334142167000635542]",
"[817.7286529837758600846986169918637213380076537485120538024043043418022955023760383765, 817.7286529837758600846986169918637213380076537485120538024043043418022956709727458768]",
"[836.2513781485514428028925362552117076676847392539893897130184087677951226879297782738, 836.2513781485514428028925362552117076676847392539893897130184087677951228675453192576]",
"[851.251900223901275519426718108493036575946900124244069589366494891849226618045159294, 851.2519002239012755194267181084930365759469001242440695893664948918492268144456066371]",
"[860.8950924426904981694771027923714661494343500885311257934993764268835986167433950133, 860.8950924426904981694771027923714661494343500885311257934993764268835988376560889934]",
"[864.9130883567095277495829967646568106770342785858834184870461204850707480537885000341, 864.913088356709527749582996764656810677034278585883418487046120485070748309360761662]",
"[864.9130869351735664053784454866155139753647511229684110349235196315794368042442370212, 864.9130869351735664053784454866155139753647511229684110349235196315794371076342287848]",
"[864.9130855136376050611738942085742172736952236600534035828009187780881255462129790722, 864.9130855136376050611738942085742172736952236600534035828009187780881259143935303586]"
]
},
{
"lower_level": 41,
"upper_level": 42,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "757.6953475860344180975489283541815835740880470647403654007439932544400881456224697522576008297244622",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[757.6953504291063407859580309102641769774271019905703803049891949614227105968920047618, 757.6953504291063407859580309102641769774271019905703803049891949614227107786399992804]",
"[757.6953490075703794417534796322228802757575745276553728528665941079313993712572367173, 757.6953490075703794417534796322228802757575745276553728528665941079313995530055086728]",
"[757.6953475860344180975489283541815835740880470647403654007439932544400881456224697523, 757.6953475860344180975489283541815835740880470647403654007439932544400883273710180652]",
"[761.4473103246717261551675349864089946954399893078390231132645770833428051806513832173, 761.447310324671726155167534986408994695439989307839023113264577083342805362637659342]",
"[770.4520228501479914819448743937079084930661454484259784387381419073622270000156171845, 770.4520228501479914819448743937079084930661454484259784387381419073622271828569009842]",
"[784.4593541748120603546290557785109443276894023480079207811860728908873204440119009262, 784.4593541748120603546290557785109443276894023480079207811860728908873206288799768975]",
"[802.196013375700013604740289377156561605020251230870093655315611140496009121054226148, 802.1960133757000136047402893771565616050202512308700936553156111404960093098827864064]",
"[821.638316720199151217469094631220399311181555177929880099096917071657111976433650363, 821.6383167201991512174690946312203993111815551779298800990969170716571121721596345323]",
"[840.1939568860243537184391972341122091523024561146863130957915793744628383716319982689, 840.193956886024353718439197234112209152302456114686313095791579374462838578473902649]",
"[855.2204644342840411125917690000904271159765000003532702946504938144952136827900113324, 855.2204644342840411125917690000904271159765000003532702946504938144952139065702900256]",
"[864.8803615184178592873443719646317514543590780436214845335741985618366741146296958566, 864.8803615184178592873443719646317514543590780436214845335741985618366743631562559571]",
"[868.9053176663775074380542328627820292529255695799251921272344719564987729709209089238, 868.9053176663775074380542328627820292529255695799251921272344719564987732544566665584]",
"[868.9053160314429134006480685021087324663330959188339180655921272279421831521009757315, 868.9053160314429134006480685021087324663330959188339180655921272279421834839732036022]",
"[868.905314396508319363241904141435435679740622257742644003949782499385593324662726024, 868.9053143965083193632419041414354356797406222577426440039497824993855937220990442398]"
]
},
{
"lower_level": 40,
"upper_level": 41,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "758.8727089403293903701618320324552298541700314872774875904214003139973488870959278773941338177366774",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[758.8727122101985784449741607538018234273549788094600357137060897711105284763904320108, 758.8727122101985784449741607538018234273549788094600357137060897711105286331485911352]",
"[758.8727105752639844075679963931285266407625051483687616520637450425539386817431799441, 758.8727105752639844075679963931285266407625051483687616520637450425539388385016575271]",
"[758.8727089403293903701618320324552298541700314872774875904214003139973488870959278774, 758.8727089403293903701618320324552298541700314872774875904214003139973490438547239191]",
"[762.6255737596579763635391919493826091650079794596571986742802148412772758482759234501, 762.6255737596579763635391919493826091650079794596571986742802148412772760052739705079]",
"[771.6324515720004808010906638122590690845550209636003944635712088296501495941262955206, 771.6324515720004808010906638122590690845550209636003944635712088296501497519849184231]",
"[785.6431512302903260318940744235785708732769115739506122162966524316847478169958220109, 785.6431512302903260318940744235785708732769115739506122162966524316847479768946933151]",
"[803.383611004132740104390937617031960108525688090346960986323796483655802277473277155, 803.3836110041327401043909376170319601085256880903469609863237964836558024413593400976]",
"[822.8291958980011754912612420715521871006608242330913152837987881907336579175366797661, 822.8291958980011754912612420715521871006608242330913152837987881907336580883673244179]",
"[841.3871610182673462732274009977237502043619131814441544440173745267639620631672387002, 841.3871610182673462732274009977237502043619131814441544440173745267639622451910130688]",
"[856.4152005617946114661466292354581372573849022899125507805563627765100538325157031874, 856.4152005617946114661466292354581372573849022899125507805563627765100540315981558561]",
"[866.0760824063592522051306547732211837533970345256209937804935960375662510447568983266, 866.0760824063592522051306547732211837533970345256209937804935960375662512687676957899]",
"[870.1014487257554060370915837872074877056034454185663832661414026231509003800448997624, 870.1014487257554060370915837872074877056034454185663832661414026231509006393372967885]",
"[870.101446845795967539104263494700252572759307353997348987365077828886632566234999023, 870.1014468457959675391042634947002525727593073539973489873650778288866328742732163566]",
"[870.1014449658365290411169432021930174399151692894283147085887530346223647437087213131, 870.1014449658365290411169432021930174399151692894283147085887530346223651179365186127]"
]
},
{
"lower_level": 39,
"upper_level": 40,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "757.4993137780732134931612975535184288853727889198829692147752260609227698191421528390467288636370383",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[757.4993175379920904891359381385328991510610650490210377723278756494513053980560946417, 757.4993175379920904891359381385328991510610650490210377723278756494513055643995102573]",
"[757.4993156580326519911486178460256640182169269844520034935515508551870376085991237404, 757.4993156580326519911486178460256640182169269844520034935515508551870377749429053136]",
"[757.499313778073213493161297553518428885372788919882969214775226060922769819142152839, 757.4993137780732134931612975535184288853727889198829692147752260609227699854863003699]",
"[761.2466626647788408469077880514707083271666437266214813053922140934919027928469009523, 761.2466626647788408469077880514707083271666437266214813053922140934919029594048303586]",
"[770.2403025754105952729347626887741940516709255560168685853331014874607416432584511821, 770.2403025754105952729347626887741940516709255560168685853331014874607418105855307142]",
"[784.2304100678829115890437123878633400924285121311919362079932757199520053848967579067, 784.2304100678829115890437123878633400924285121311919362079932757199520055540479991876]",
"[801.9447398243303598943560363185947285961943240042819415230073578524060560800131218356, 801.9447398243303598943560363185947285961943240042819415230073578524060562527305199474]",
"[821.3615764031392571408620684876140311302048424861908713668539599765077356624943478832, 821.3615764031392571408620684876140311302048424861908713668539599765077358414251054718]",
"[839.8920079832168817490165542494031894000786524644996236507261600881424306877505857938, 839.8920079832168817490165542494031894000786524644996236507261600881424308766994100969]",
"[854.8977087395580515401254653896055677167251813340445988137589657234659483709659317088, 854.8977087395580515401254653896055677167251813340445988137589657234659485751886750823]",
"[864.544229827412997752830185672408801886676180947384643991058276074435394827583425323, 864.544229827412997752830185672408801886676180947384643991058276074435395054137583062]",
"[868.5636123309200229896887246111710770253455167970476293207072627116483132664629447697, 868.5636123309200229896887246111710770253455167970476293207072627116483135246448449488]",
"[868.563610169170358018372465226091882989879144137358484095761831527655740570138610286, 868.5636101691703580183724652260918829898791441373584840957618315276557408720606639018]",
"[868.5636080074206930470562058410126889544127714776693388708164003436631678659410620015, 868.5636080074206930470562058410126889544127714776693388708164003436631682273387988903]"
]
},
{
"lower_level": 38,
"upper_level": 39,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "753.6452014803244130377926413874283365404181762046911295434312629101139152837246702907019994298398989",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[753.6452058038237429804251601575867246113509215240694199933221252780990606326075633889, 753.6452058038237429804251601575867246113509215240694199933221252780990607909601006457]",
"[753.6452036420740780091089007725075305758845488643802747683766940941064879581661163, 753.6452036420740780091089007725075305758845488643802747683766940941064881165190745701]",
"[753.6452014803244130377926413874283365404181762046911295434312629101139152837246702907, 753.6452014803244130377926413874283365404181762046911295434312629101139154420780484945]",
"[757.3807740263955202440660828070439722417910605954416183982466563161713508672521694153, 757.3807740263955202440660828070439722417910605954416183982466563161713510258204403217]",
"[766.3461511064935521181746222623431248397155666630956586104975024397205708323876336978, 766.3461511064935521181746222623431248397155666630956586104975024397205709917300669463]",
"[780.2922943403524869371912731976340543542268192989685640349923487660738845254161081987, 780.292294340352486937191273197634054354226819298968564034992348766073884686596509191]",
"[797.9512959752185212737961512578539572059286050663629509495295798641520487707340998816, 797.9512959752185212737961512578539572059286050663629509495295798641520489355104740767]",
"[817.308133350846639963044149453154289740148466130975673592189729965183679731865041984, 817.3081333508466399630441494531542897401484661309756735921897299651836799029105588277]",
"[835.7818944982701230911462900775648208159734975095364453063100698166634894425440564256, 835.7818944982701230911462900775648208159734975095364453063100698166634896237026810187]",
"[850.7419605466894391685512110593674937972732755174624718518344766768021747307661263346, 850.7419605466894391685512110593674937972732755174624718518344766768021749273508490037]",
"[860.3591449122894261069990521278867063229658654453064639645265043938546280112754622307, 860.359144912289426106999052127886706322965865445306463964526504393854628230425784089]",
"[864.3663035887797756739251645178813005416981502756193119763408314897416484180917898804, 864.3663035887797756739251645178813005416981502756193119763408314897416486692226589366]",
"[864.3663011023758078102083756653033740294874922413770512731810023839903221804621158748, 864.3663011023758078102083756653033740294874922413770512731810023839903224758619104574]",
"[864.3662986159718399464915868127254475172768342071347905700211732782389959348286837445, 864.3662986159718399464915868127254475172768342071347905700211732782389962905030913941]"
]
},
{
"lower_level": 37,
"upper_level": 38,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "747.391845654519108196978721151083369014711033631082585243753569950628563932019104407455910218924062",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[747.3918506273270439244122988562392220391323496995671066500732281621312163629922469986, 747.3918506273270439244122988562392220391323496995671066500732281621312165308425218145]",
"[747.391848140923076060695510003661295526921691665324845946913399056379890147505675703, 747.3918481409230760606955100036612955269216916653248459469133990563798903153564341444]",
"[747.3918456545191081969787211510833690147110336310825852437535699506285639320191044075, 747.3918456545191081969787211510833690147110336310825852437535699506285640998703453948]",
"[751.1095371378556251627810385802572818563352587906598066359059280005527896813373536126, 751.109537137855625162781038580257281856335258790659806635905928000552789849405943213]",
"[760.0320001131196994268642975923716125441446303460370503556315517597188734954188844164, 760.0320001131196994268642975923716125441446303460370503556315517597188736642698374805]",
"[773.9113882389991880944598320924827795386359591404257121163399609834910285556175662903, 773.9113882389991880944598320924827795386359591404257121163399609834910287263250397473]",
"[791.4865873215994004964663066773048078221491448892573352218940359952991886709829824289, 791.4865873215994004964663066773048078221491448892573352218940359952991888453215286367]",
"[810.7529444123779979364376225092217614213555472182143607407792210895203386353238486849, 810.752944412377997936437622509221761421355547218214360740779221089520338815991398064]",
"[829.1416115322945852822007801339094202350856359699091424940620659425509658573396254347, 829.1416115322945852822007801339094202350856359699091424940620659425509660482158633589]",
"[844.0333152827856370609511469693613518245675204196593897931384965575782462246705876712, 844.0333152827856370609511469693613518245675204196593897931384965575782464311192397981]",
"[853.6065523132310639208925318133429820677026339185705299656308399865057245704075929774, 853.606552313231063920892531813342982067702633918570529965630839986505724799640656737]",
"[857.5953993775166083748244939592212351808988491168860966344982042228942109487639797909, 857.5953993775166083748244939592212351808988491168860966344982042228942112103026885185]",
"[857.595396516329845480196654036859006413759075793457309299832133676809069685209200743, 857.5953965163298454801966540368590064137590757934573092998321336768090699915040530823]",
"[857.5953936551430825855688141144967776466193024700285219651660631307239284135243261402, 857.5953936551430825855688141144967776466193024700285219651660631307239287808390097696]"
]
},
{
"lower_level": 36,
"upper_level": 37,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "738.8311934031865809594342613861750071314170842786978164313458908323108480289833261344676786562517241",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[738.8311991255601067486899412308994646656966309255553911006780319244811305113527844608, 738.8311991255601067486899412308994646656966309255553911006780319244811306798124953399]",
"[738.8311962643733438540621013085372358985568576021266037660119613783959892701680547579, 738.8311962643733438540621013085372358985568576021266037660119613783959894386283226698]",
"[738.8311934031865809594342613861750071314170842786978164313458908323108480289833261345, 738.8311934031865809594342613861750071314170842786978164313458908323108481974441499997]",
"[742.5250531932457002384497499687037904490497146261589375625701654482816722087424613615, 742.5250531932457002384497499687037904490497146261589375625701654482816723773943593765]",
"[751.390320619035658085800958010275723227520720000083316077586165450998927524782512521, 751.3903206190356580858009580102757232275207200000833160775861654509989276941223968702]",
"[765.1807380817889549849733119143277629162069929940038490598510965437312799015297964032, 765.1807380817889549849733119143277629162069929940038490598510965437312800725032606131]",
"[782.6443765429056566657392133520270884007906266266378233219809852630866949202109360752, 782.6443765429056566657392133520270884007906266266378233219809852630866950943815455083]",
"[801.7905344789432577245188190345112765248573550672828243711888195882742578317170924189, 801.7905344789432577245188190345112765248573550672828243711888195882742580114640845242]",
"[820.0663904092391869925233405585764018915111617297685891865159302963493266222766103335, 820.0663904092391869925233405585764018915111617297685891865159302963493268110245487199]",
"[834.867567209675663510290082356151679578900211319889650088166034567731453107665465071, 834.8675672096756635102900823561516795789002113198896500881660345677314533101539956299]",
"[844.3826081773222196275257601961961021627415830933402613189558064422922971427913569103, 844.3826081773222196275257601961961021627415830933402613189558064422922973654023167331]",
"[848.3472066245580294852574150725477300143038199176868241663600445828216258291505782908, 848.3472066245580294852574150725477300143038199176868241663600445828216260803257206651]",
"[848.3472033297729522969061287707259416062642573718925197894124700482576963403828099898, 848.3472033297729522969061287707259416062642573718925197894124700482576966311918354318]",
"[848.3472000349878751085548424689041531982246948260982154124648955136937668443570739335, 848.3472000349878751085548424689041531982246948260982154124648955136937671893165095314]"
]
},
{
"lower_level": 35,
"upper_level": 36,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "728.0647346717436450477708141851522317687973879826060289058263969162650515590069024300177703907740267",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[728.0647412613137994244733867887958085848765130741946376597215459853929104968963811257, 728.0647412613137994244733867887958085848765130741946376597215459853929106570394217439]",
"[728.0647379665287222361221004869740201768369505284003332827739714508289810279516412381, 728.0647379665287222361221004869740201768369505284003332827739714508289811880953230918]",
"[728.06473467174364504777081418515223176879738798260602890582639691626505155900690243, 728.0647346717436450477708141851522317687973879826060289058263969162650517191512233602]",
"[731.7289649194715494476861562608997213664786145202392580096860802631922695425346747572, 731.728964919471549447686156260899721366478614520239258009686080263192269702898110397]",
"[740.523122038579409501143270100265145499075733486862039097814399828497992543526839279, 740.5231220385794095011432701002651454990757334868620390978143998284979927046789892049]",
"[754.2029236900696223151565756497161808122925289164543631119609029270150601716636241203, 754.2029236900696223151565756497161808122925289164543631119609029270150603346884429946]",
"[771.5279538205108106946033994612464732481731333725783615959526043386503002193385280547, 771.5279538205108106946033994612464732481731333725783615959526043386503003860287840742]",
"[790.5249497205298659118477125313578185970116788320213823493104297021755480265745983569, 790.5249497205298659118477125313578185970116788320213823493104297021755481996592830017]",
"[808.6609781164765204457788972655475203367306637935184238658353980624109983086707938623, 808.660978116476520445778897265547520336730663793518423865835398062410998492079776202]",
"[823.350021845733556186578842263563914307279076498882965863428787682141580621936966611, 823.3500218457335561865788422635639143072790764988829658634287876821415808211129025657]",
"[832.7929770745123387056969655825356186880385809876316757561040082359518473887383440467, 832.7929770745123387056969655825356186880385809876316757561040082359518476110169819444]",
"[836.7275394984536607808835187292198066169931046773182647403127328545226238489536763879, 836.7275394984536607808835187292198066169931046773182647403127328545226241040535374368]",
"[836.7275357008233788202433904324368363464164460771594918027522320823300840511677364405, 836.727535700823378820243390432436836346416446077159491802752232082330084351862454485]",
"[836.7275319031930968596032621356538660758397874770007188651917313101375442449943765803, 836.7275319031930968596032621356538660758397874770007188651917313101375446080914836619]"
]
},
{
"lower_level": 34,
"upper_level": 35,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "715.2025999181498719044732117786370283790031538102763369012971361021555039856182005446828592471743794",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[715.2026075134104358257534683722029689201564710105938827764181376465405835356750605041, 715.2026075134104358257534683722029689201564710105938827764181376465405837052523142642]",
"[715.2026037157801538651133400754199986495798124104351098388576368743480437606466305244, 715.2026037157801538651133400754199986495798124104351098388576368743480439302246226768]",
"[715.2025999181498719044732117786370283790031538102763369012971361021555039856182005447, 715.20259991814987190447321177863702837900315381027633690129713610215550415519693001]",
"[718.8315544925701116381010731804999269791933496452991952646775709154132901189559150583, 718.8315544925701116381010731804999269791933496452991952646775709154132902888376326227]",
"[727.541050685404187620132566153305272664610791032257236951860212366663398650599081091, 727.5410506854041876201325661533052726646107910322572369518602123666633988215714096447]",
"[741.0891578189802066829993403518669594867475010406391460588452656171678018575663274675, 741.0891578189802066829993403518669594867475010406391460588452656171678020311270258483]",
"[758.249237403099598419695376055173221485978042957773038666910430303361100146090363948, 758.2492374030995984196953760551732214859780429577730386669104303033611003247145850518]",
"[777.0688593341239229935202323640120700939139823016064080744899699882405094370469185022, 777.0688593341239229935202323640120700939139823016064080744899699882405096244993797883]",
"[795.0387401259990832204934767704714440100609354610613507043659402742900843200239212444, 795.0387401259990832204934767704714440100609354610613507043659402742900845217221894839]",
"[809.5945996315873474921895683083357833659611733105109368114526506100409518543377813, 809.5945996315873474921895683083357833659611733105109368114526506100409520777814091887]",
"[818.9519362060647765676031272862527698115471104023898325035417149303555609397564759233, 818.9519362060647765676031272862527698115471104023898325035417149303555611950530915618]",
"[822.8508238432225829483322192442432404418302349588685895211945432406544224655731838924, 822.8508238432225829483322192442432404418302349588685895211945432406544227661217412613]",
"[822.8508194609193133186417488642084586462811593013224848976694842327631913031595471915, 822.8508194609193133186417488642084586462811593013224848976694842327631916665986962058]",
"[822.8508150786160436889512784841736768507320836437763802741444252248719601291178795183, 822.8508150786160436889512784841736768507320836437763802741444252248719605787209771298]"
]
},
{
"lower_level": 33,
"upper_level": 34,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "700.3626845592684729373342789382758654000746510590581638012559416391128704507633776808771020985439307",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[700.3626933238750121967152196983454289911728023741503730483060596548953327127501211473, 700.362693323875012196715219698345428991172802374150373048306059654895332873931929835]",
"[700.3626889415717425670247493183106471956237267166042684247810006470041015817567494141, 700.3626889415717425670247493183106471956237267166042684247810006470041017429394098439]",
"[700.3626845592684729373342789382758654000746510590581638012559416391128704507633776809, 700.3626845592684729373342789382758654000746510590581638012559416391128706119468887733]",
"[703.9508681958236621737906291242147015731588546847021615958154570372919790434634627399, 703.950868195823662173790629124214701573158854684702161595815457037291979205071553787]",
"[712.5625149393493114730168500528273589078060071450717362522811794721076380416486444382, 712.5625149393493114730168500528273589078060071450717362522811794721076382047830325421]",
"[725.9584121159161008561513726734473434896541390794712902685498939114992958783976129451, 725.9584121159161008561513726734473434896541390794712902685498939114992960451498237583]",
"[742.9279005370108116939837298649778817418099270473730123877756034575542191696395798247, 742.9279005370108116939837298649778817418099270473730123877756034575542193434614834415]",
"[761.5426834812373113187537051495212550849659642577870890603641148359054813310396227631, 761.542683481237311318753705149521255084965964257787089060364114835905481517176162979]",
"[779.3207892400802278387908693901780526495811184322523948018915094372112562034689455628, 779.3207892400802278387908693901780526495811184322523948018915094372112564094623507005]",
"[793.7229654880039714888634085250207470070231821932044172458966196063228918018903012659, 793.7229654880039714888634085250207470070231821932044172458966196063228920381779153872]",
"[802.9815054200952085730361285513370197012190020338148127571865612613171858943390482687, 802.9815054200952085730361285513370197012190020338148127571865612613171861749917203471]",
"[806.8392273842726817053713046238412107334551912518243900488996919907178786041856073078, 806.8392273842726817053713046238412107334551912518243900488996919907178789478774379599]",
"[806.8392223202249830882222732359312894697252756668699170704809105220728140922314218739, 806.8392223202249830882222732359312894697252756668699170704809105220728145236034974967]",
"[806.8392172561772844710732418480213682059953600819154440920621290534277495639523355987, 806.8392172561772844710732418480213682059953600819154440920621290534277501156433452849]"
]
},
{
"lower_level": 32,
"upper_level": 33,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "683.6697988305937753055436368504125178426953828100184207102255917794510077353518478045426312227675963",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[683.6698089586891725398416996262323603701552139799273666670631547167411366715929635786, 683.6698089586891725398416996262323603701552139799273666670631547167411368421168882272]",
"[683.6698038946414739226926682383224391064252983949728936886443732480960722034724051518, 683.6698038946414739226926682383224391064252983949728936886443732480960723739973143236]",
"[683.6697988305937753055436368504125178426953828100184207102255917794510077353518478045, 683.6697988305937753055436368504125178426953828100184207102255917794510079058777393405]",
"[687.2118664586368374361699690681619582535646945027919706418746351720554661274288377318, 687.2118664586368374361699690681619582535646945027919706418746351720554662983923476779]",
"[695.7128357159704737361907167474314090195793633825979250318217639575268411763011837854, 695.7128357159704737361907167474314090195793633825979250318217639575268413488364148758]",
"[708.9365682602105940067043373451478430269937845198691776026763002172875124143493006032, 708.9365682602105940067043373451478430269937845198691776026763002172875125906077879872]",
"[725.6905234252690178017999794727920457684661820078781353018330817430965325239357867398, 725.6905234252690178017999794727920457684661820078781353018330817430965327074668855823]",
"[744.0737460892692431318012471386220033861549432636943239897960285632890365456697996845, 744.07374608926924313180124713862200338615494326369432398979602856328903674186537336]",
"[761.6351391455505036446555881076902229752211081053085527995845549958331477037226322625, 761.6351391455505036446555881076902229752211081053085527995845549958331479203364498835]",
"[775.8636829575833146943873819466672579835061652619823799349728224319723801961569218322, 775.8636829575833146943873819466672579835061652619823799349728224319723804439235951773]",
"[785.0106017306297227015300511797156055985038100300967403671476370942900038182139295288, 785.0106017306297227015300511797156055985038100300967403671476370942900041116199857955]",
"[788.8218144043009079862049700094903124636014763858090446306870108124284348382093706915, 788.8218144043009079862049700094903124636014763858090446306870108124284351965183106482]",
"[788.8218085428767719106445200538172875564429682864913542635489521999914167859687843842, 788.8218085428767719106445200538172875564429682864913542635489521999914172346825379941]",
"[788.8218026814526358350840700981442626492844601871736638964108935875543987167539728692, 788.821802681452635835084070098144262649284460187173663896410893587554399289817031944]"
]
},
{
"lower_level": 31,
"upper_level": 32,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "665.2548418477731465097779112027404259390172749129873401987349415707896390502071771633175711765397258",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[665.2548535706214186608988111140864757533342911116227209330110587956636750642300685256, 665.2548535706214186608988111140864757533342911116227209330110587956636752260767585581]",
"[665.2548477091972825853383611584134508461757830123050305658730001832266570572186223047, 665.2548477091972825853383611584134508461757830123050305658730001832266572190664512319]",
"[665.2548418477731465097779112027404259390172749129873401987349415707896390502071771633, 665.2548418477731465097779112027404259390172749129873401987349415707896392120561428262]",
"[668.7455980664247472337734770012898327675726306499399691651462140930656941775046649744, 668.745598066424747233773477001289832767572630649939969165146214093065694339737227654]",
"[677.1234210333907805620971450050989840479351775532902496875825017558841859382148507885, 677.1234210333907805620971450050989840479351775532902496875825017558841861018246459376]",
"[690.1555930855738794983175150779806739230165498425715789824830476447246622369574087937, 690.1555930855738794983175150779806739230165498425715789824830476447246624038301287029]",
"[706.6697690251607131868270731542878032380838240794666202580646969051133895707802200035, 706.6697690251607131868270731542878032380838240794666202580646969051133897440279328407]",
"[724.7954513349046262304928620590406105379964895360003822902618793088166538696753025888, 724.7954513349046262304928620590406105379964895360003822902618793088166540540279903726]",
"[742.1158815021524488005266499144891853795054530792697889426792879673953144305283600404, 742.1158815021524488005266499144891853795054530792697889426792879673953146327927237311]",
"[756.1513917612883510422247343229282482693522613877260803298548471768739792686843565414, 756.1513917612883510422247343229282482693522613877260803298548471768739794982937370278]",
"[765.1742171747683008978207215233463891328814045288204229470904456822710863005082341174, 765.1742171747683008978207215233463891328814045288204229470904456822710865702142235827]",
"[768.9337237252163374345190720090732167407070358174138900261512687625195933793568681193, 768.9337237252163374345190720090732167407070358174138900261512687625195937061606517305]",
"[768.9337169280671314549857281581167937292605702563043844547400587955756326221473324207, 768.933716928067131454985728158116793729260570256304384454740058795575633028646302342]",
"[768.933710130917925475452384307160370717814104695194878883328848828631671849801586757, 768.9337101309179254754523843071603707178141046951948788833288488286316723662468380594]"
]
},
{
"lower_level": 30,
"upper_level": 31,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "645.2539987793817476321078982973115969658474830252198215969474372323383781924010257459205293235729281",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[645.2540123736801595911745859992244429887404141474388327397698571662262996271027752535, 645.2540123736801595911745859992244429887404141474388327397698571662262997801955695606]",
"[645.2540055765309536116412421482680199772939485863293271683586471992823389097519004997, 645.2540055765309536116412421482680199772939485863293271683586471992823390628460150611]",
"[645.2539987793817476321078982973115969658474830252198215969474372323383781924010257459, 645.2539987793817476321078982973115969658474830252198215969474372323383783454964605616]",
"[648.6883974522290467917035953377166243310333824715985038372259654623415162258194873986, 648.6883974522290467917035953377166243310333824715985038372259654623415163792442106851]",
"[656.9309635902688949994947869415849626054607945328070273665633611145018728001023051353, 656.9309635902688949994947869415849626054607945328070273665633611145018729547094699504]",
"[669.7527366038964402506819052006199263172403824804486472385067361024454060561442682399, 669.7527366038964402506819052006199263172403824804486472385067361024454062135543317861]",
"[686.0035816086476930984766812547933534202046069266313055191083214007349741950695440901, 686.0035816086476930984766812547933534202046069266313055191083214007349743579586067128]",
"[703.846482739288240440743755551582575428150091326484908400634164834014084585596844822, 703.8464827392882404407437555515825754281500913264849084006341648340140847580347635651]",
"[720.9023854991854380421700288830118462418572795547121407772570159495851722110877231064, 720.9023854991854380421700288830118462418572795547121407772570159495851723989355579047]",
"[734.7260077073171729485011318246752329946045945478963610418820748110993925470979752224, 734.7260077073171729485011318246752329946045945478963610418820748110993927584871569984]",
"[743.6126189475527286599568268687227010792366306978784584157023074719911700652460652427, 743.6126189475527286599568268687227010792366306978784584157023074719911703111870665889]",
"[747.315368936521136362962772619407367540174565631645525572102367534753280818280572901, 747.3153689365211363629627726194073675401745656316455255721023675347532811134935067046]",
"[747.3153610373416566280068794569119958979646826171704303340234908203230218132089827214, 747.3153610373416566280068794569119958979646826171704303340234908203230221773422940099]",
"[747.3153531381621768930509862944166242557547996026953350959446141058927627949183763717, 747.3153531381621768930509862944166242557547996026953350959446141058927632544356627033]"
]
},
{
"lower_level": 29,
"upper_level": 30,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "623.8079601288776167031839055803137177376692457415931028959737846280675990469309255517868346296002158",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[623.8079759272365761730956919053044610220890117705432933721315380569281169882190599617, 623.8079759272365761730956919053044610220890117705432933721315380569281171595355657408]",
"[623.807968028057096438139798742809089379879128756068198134052661342497858017574992217, 623.8079680280570964381397987428090893798791287560681981340526613424978581888930319956]",
"[623.8079601288776167031839055803137177376692457415931028959737846280675990469309255518, 623.8079601288776167031839055803137177376692457415931028959737846280675992182504982503]",
"[627.1811040685613064880249941851806233228100217009701891939436891809443131077832359658, 627.1811040685613064880249941851806233228100217009701891939436891809443132794329251277]",
"[635.2766603548359629390119828930158205338704986938659447440881924698855788972823317394, 635.2766603548359629390119828930158205338704986938659447440881924698855790701188539217]",
"[647.8697519326549146839932504943246710246985697354820838917550342169784292930752740034, 647.8697519326549146839932504943246710246985697354820838917550342169784294687283659717]",
"[663.8344070903320119646851354682319122322241715316299013389622688275192442452734683909, 663.8344070903320119646851354682319122322241715316299013389622688275192444264375240546]",
"[681.3700238815862967694239779449517444143275414338527915584993908058512732816170734585, 681.3700238815862967694239779449517444143275414338527915584993908058512734723934783537]",
"[698.1385188881066998649469874092898596681241706132322664196217014355777405678352960528, 698.1385188881066998649469874092898596681241706132322664196217014355777407741359706701]",
"[711.7319439604911392140245597608376693503464745010626801359917047632124508680538840604, 711.7319439604911392140245597608376693503464745010626801359917047632124510980907764807]",
"[720.470570823006250638751560419678620494623851746315113452584089497209635063874280584, 720.470570823006250638751560419678620494623851746315113452584089497209635328787517119]",
"[724.1116598786895068279933733945139957188598970400073091525001308945175845021418057323, 724.1116598786895068279933733945139957188598970400073091525001308945175848168687572023]",
"[724.1116506765678006364050550710500309793229361837869301662059400946731739672833968257, 724.1116506765678006364050550710500309793229361837869301662059400946731743518523992792]",
"[724.1116414744460944448167367475860662397859753275665511799117492948287634188803137074, 724.1116414744460944448167367475860662397859753275665511799117492948287639004392256096]"
]
},
{
"lower_level": 28,
"upper_level": 29,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "601.0611621762272162962451048440773601119867224433354689551193889338089011109429036519955713554169207",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[601.0611805804706286794217414910052895910606441557762269277077705334977221109788753631, 601.0611805804706286794217414910052895910606441557762269277077705334977222736272522863]",
"[601.0611713783489224878334231675413248515236832995558479414135797336533116109608895075, 601.0611713783489224878334231675413248515236832995558479414135797336533117736110530381]",
"[601.061162176227216296245104844077360111986722443335468955119388933808901110942903652, 601.06116217622721629624510484407736011198672244333546895511938893380890127359485379]",
"[604.368302889664447929428724175288499715776963663093820445995569511196396779459545311, 604.3683028896644479294287241752884997157769636630938204459955695111963969425542750493]",
"[612.3054532145826355237719148236295684535623733719522712764057984145081496967765853077, 612.3054532145826355237719148236295684535623733719522712764057984145081498614625021143]",
"[624.6521361745906493730388832874620016149193491193823839338630430571866759754767073485, 624.6521361745906493730388832874620016149193491193823839338630430571866761439365326567]",
"[640.3084341700519492354487374230283894535769494260744333211429297615670826380799013511, 640.3084341700519492354487374230283894535769494260744333211429297615670828139199242673]",
"[657.512999775412088148686028744260457303348525328766182543620996896008401042215983298, 657.5129997754120881486860287442604573033485253287661825436209968960084012309232636823]",
"[673.9718895322829423278985402397128783350407170397093700370440236667757373826938319295, 673.9718895322829423278985402397128783350407170397093700370440236667757375921764920557]",
"[687.3173527103247364426406371110756955714855314954818512255640241122667562832419324704, 687.3173527103247364426406371110756955714855314954818512255640241122667565244885490052]",
"[695.8965748975170632349606741018666231122048536556554201643195725058622874960447920366, 695.8965748975170632349606741018666231122048536556554201643195725058622877839795429734]",
"[699.4712444168179647905235007853718031799491322950461722119199085765686772527927033562, 699.471244416817964790523500785371803179949132295046172211919908576568677607475001996]",
"[699.4712336677361184768560280484194889953064846260073793922815513768935004920896270869, 699.4712336677361184768560280484194889953064846260073793922815513768935009405252259004]",
"[699.47122291865427216318855531146717481066383695696858657264319417721832371294784085, 699.4712229186542721631885553114671748106638369569685865726431941772183242919613420451]"
]
},
{
"lower_level": 27,
"upper_level": 28,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "577.1610476409100556633559004467595048912993424736226623219741643587620547854982400216771075935213051",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[577.1610691390737482906908459206641332605846378117002479612508787581124082129703719233, 577.1610691390737482906908459206641332605846378117002479612508787581124083848929132742]",
"[577.1610583899919019770233731837118190759419901426614551416125215584372314992343059725, 577.1610583899919019770233731837118190759419901426614551416125215584372316711589340376]",
"[577.1610476409100556633559004467595048912993424736226623219741643587620547854982400217, 577.1610476409100556633559004467595048912993424736226623219741643587620549574249537214]",
"[580.3975851044590868098256899325644910692543458788129973081212103539959063321195756781, 580.3975851044590868098256899325644910692543458788129973081212103539959065045446124963]",
"[588.165289743552811554530265986524523129637588424963237053583557070731353763990921704, 588.165289743552811554530265986524523129637588424963237053583557070731353938207711969]",
"[600.2483913015188609498453023879851075166813566582172321115769026673381392035388124141, 600.2483913015188609498453023879851075166813566582172321115769026673381393820077767977]",
"[615.574855335051849186482347316217077968242552277640733971557951014652790893869236135, 615.574855335051849186482347316217077968242552277640733971557951014652791080658663137]",
"[632.4253379445683088282817919364388130725580405155411960077687717831828649040255226668, 632.425337944568308828281791936438813072558040515541196007768771783182865105330383202]",
"[648.5531065013911910690987877298655968535659359416426348858809920619415270924301626346, 648.5531065013911910690987877298655968535659359416426348858809920619415273171875849371]",
"[661.6333862576214974178958514105546762744816518660680198960910256200930703157746341184, 661.6333862576214974178958514105546762744816518660680198960910256200930705764207203389]",
"[670.0421326704245989669244352540523606219319880759049900040966033874485290848115048609, 670.0421326704245989669244352540523606219319880759049900040966033874485293982746718102]",
"[673.5457695172337880794775477343695410642723678072961773642693399725321918794146210665, 673.5457695172337880794775477343695410642723678072961773642693399725321922685303881433]",
"[673.5457569231243740921261541548308421897189829774950881606135684156667380347613007589, 673.5457569231243740921261541548308421897189829774950881606135684156667385304404648369]",
"[673.5457443290149601047747605752921433151655981476939989569577968588012841688596765627, 673.5457443290149601047747605752921433151655981476939989569577968588012848135695234677]"
]
},
{
"lower_level": 26,
"upper_level": 27,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "552.2573455894969310534893822276950190598697740358706161154136110589270559291137595172760985322341429",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[552.2573707777157590281921693867724168089765436954727945227251541726579635118004534996, 552.2573707777157590281921693867724168089765436954727945227251541726579636839687445833]",
"[552.2573581836063450408407758072337179344231588656717053190693826157925097204571059687, 552.2573581836063450408407758072337179344231588656717053190693826157925098926278421676]",
"[552.2573455894969310534893822276950190598697740358706161154136110589270559291137595173, 552.2573455894969310534893822276950190598697740358706161154136110589270561012869397519]",
"[555.4188280203865484084053905752883916610678702512425267410458455591577977377674513723, 555.418828020386548408405390575288391661067870251242526741045845559157797910496604389]",
"[563.006403100505624808519914090646008487798535852820584055694295447811025460164583513, 563.0064031005056248085199140906460084877985358528205840556942954478110256348938818032]",
"[574.8093040447881907864193498306729515932529812358601499438958560271761486077087672216, 574.8093040447881907864193498306729515932529812358601499438958560271761487871866034182]",
"[589.7851467101622293222317704154197407064938182274058522222556026191349116727751187366, 589.7851467101622293222317704154197407064938182274058522222556026191349118615467893142]",
"[606.2592481701368907298757676397564326893401649520018603265061220562548465431598764445, 606.2592481701368907298757676397564326893401649520018603265061220562548467481477508869]",
"[622.035059665930499982117308584473593882505238911699312561275899497786689195043235603, 622.0350596659304999821173085844735938825052389116993125612758994977866894262373325083]",
"[634.8334764611961566013573179180977175023237191406014176562670967843017418049867773357, 634.8334764611961566013573179180977175023237191406014176562670967843017420763005558237]",
"[643.061024394406397348654916734119250751512561944124684442078733712486570553590172777, 643.0610243944063973486549167341192507515125619441246844420787337124865708839984135472]",
"[646.4891605557749241329267316311808811903880610754508923791695416992388601913019266385, 646.489160555774924132926731631180881190388061075450892379169541699238860606487638518]",
"[646.4891457503177943806481830882423039221420387973469610053538381126001998175188431746, 646.4891457503177943806481830882423039221420387973469610053538381126002003524366279988]",
"[646.4891309448606646283696345453037266538960165192430296315381345259615394195693970218, 646.4891309448606646283696345453037266538960165192430296315381345259615401226118633612]"
]
},
{
"lower_level": 25,
"upper_level": 26,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "526.5013695101169262117822709872622042326497515811504943751345491821737045105209991934663213250542598",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[526.5013991210311857163393680731393587691417961373583571227659563554510251385285916438, 526.5013991210311857163393680731393587691417961373583571227659563554510253109356576748]",
"[526.5013843155740559640608195302007815008957738592544257489502527688123648245247948789, 526.5013843155740559640608195302007815008957738592544257489502527688123649969347356744]",
"[526.5013695101169262117822709872622042326497515811504943751345491821737045105209991935, 526.5013695101169262117822709872622042326497515811504943751345491821737046829338125946]",
"[529.5834930953514157745431755099641635672939508704999610256588440933902974828741265781, 529.5834930953514157745431755099641635672939508704999610256588440933902976559047228992]",
"[536.9806099631715330047392938986301633369563721583877205522612014114354695216021900621, 536.9806099631715330047392938986301633369563721583877205522612014114354696968506062852]",
"[548.4872436790828107030809032529492684362380555396472471811806095941751492227798479341, 548.4872436790828107030809032529492684362380555396472471811806095941751494032859884025]",
"[563.0923656187130040784916924649198626552633794562692510614882454465566238815907865072, 563.0923656187130040784916924649198626552633794562692510614882454465566240723768541955]",
"[579.1685197443400172811880387687496048478680764593966035572513594543866475393577008105, 579.1685197443400172811880387687496048478680764593966035572513594543866477480684720659]",
"[594.5722166002378173201531797552972567479771503464576164596488742188265610082968891422, 594.5722166002378173201531797552972567479771503464576164596488742188265612459658379129]",
"[607.0726313307349325564110150008194453840403716624640224411720596385281329230423988393, 607.0726313307349325564110150008194453840403716624640224411720596385281332050506611487]",
"[615.1086054671589519858649169843376298561108350265358011978339190630652195883788898652, 615.1086054671589519858649169843376298561108350265358011978339190630652199357501471759]",
"[618.4569176229954291116262988129666455713695265596376776450297156611689549320754952225, 618.4569176229954291116262988129666455713695265596376776450297156611689553733846097879]",
"[618.4569001530268910504392802414502299960138185077462706991290778085227758295517816705, 618.4569001530268910504392802414502299960138185077462706991290778085227764039461341956]",
"[618.4568826830583529892522616699338144206581104558548637532284399558765966996488790834, 618.4568826830583529892522616699338144206581104558548637532284399558765974618233048693]"
]
},
{
"lower_level": 24,
"upper_level": 25,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "500.0453322940386066741710807423374495095138310619800027328522783843546083407145628866509287700434686",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[500.045367233975682796545117885370280660225247165762816624653554089646966412478201658, 500.0453672339756827965451178853702806602252471657628166246535540896469665849693693971]",
"[500.0453497640071447353580993138538650848695391138714096787529162370007873765963820024, 500.0453497640071447353580993138538650848695391138714096787529162370007875490909405173]",
"[500.0453322940386066741710807423374495095138310619800027328522783843546083407145628867, 500.0453322940386066741710807423374495095138310619800027328522783843546085132125110976]",
"[503.0439408298718942806142011316777282208964477393304038936708965982141343232390973272, 503.0439408298718942806142011316777282208964477393304038936708965982141344963043975519]",
"[510.2406252116444593740093996481033923446689100466393494525222162753441508358386414766, 510.2406252116444593740093996481033923446689100466393494525222162753441510109380994452]",
"[521.4354763830871174202086514728288000209243157732107129239951939488767123482018295521, 521.4354763830871174202086514728288000209243157732107129239951939488767125281213226472]",
"[535.6504644998091993688677174857637397268746067215193582773148667796484256245851094808, 535.6504644998091993688677174857637397268746067215193582773148667796484258139264789509]",
"[551.30783483419886765065955105776169906386145825619703194801323551069092835237673577, 551.3078348341988676506595510577616990638614582561970319480132355106909285581457786462]",
"[566.3199353553404627780210878005330680759751950641357529047785752102527617069556284932, 566.3199353553404627780210878005330680759751950641357529047785752102527619392698440168]",
"[578.5067472928146512737142158373970699774388217580911372341206931694738112796598915807, 578.5067472928146512737142158373970699774388217580911372341206931694738115526445646547]",
"[586.3411183691473428699144604154591973797566619753592380375174190043851949000004507567, 586.3411183691473428699144604154591973797566619753592380375174190043851952330196406167]",
"[589.6054273215287306570381830518543816716246625636375307198387093121706685919847131724, 589.6054273215287306570381830518543816716246625636375307198387093121706690114921635082]",
"[589.6054066224856678699051132965255323483200131045780385288392627513262135470284105926, 589.6054066224856678699051132965255323483200131045780385288392627513262140895511126077]",
"[589.6053859234426050827720435411966830250153636455185463378398161904817584762821834189, 589.6053859234426050827720435411966830250153636455185463378398161904817591934024670405]"
]
},
{
"lower_level": 23,
"upper_level": 24,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "473.0416765732071022021708057063513798029030270225986958183471946365781571754051453197367365728751903",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[473.0417179712932277764369452170090784495123259407176802003460877582670671423738918465, 473.0417179712932277764369452170090784495123259407176802003460877582670673240382089087]",
"[473.0416972722501649893038754616802291262076764816581880093466411974226121588895185831, 473.0416972722501649893038754616802291262076764816581880093466411974226123405578525432]",
"[473.0416765732071022021708057063513798029030270225986958183471946365781571754051453197, 473.041676573207102202170805706351379802903027022598695818347194636578157357077495638]",
"[475.9527609558429852829589631514116879934424506009423623513807654423030912132724029346, 475.9527609558429852829589631514116879934424506009423623513807654423030913955114974962]",
"[482.9393917680620148431610863619550682677227391348626607702493263406575721052828004923, 482.9393917680620148431610863619550682677227391348626607702493263406575722895566033534]",
"[493.8074945388551279625533302316611585497268026532736025177476191692994223188433419831, 493.8074945388551279625533302316611585497268026532736025177476191692994225079454701529]",
"[507.6136194859482119936703729400778076447315298701735761068290467831183860120500090991, 507.6136194859482119936703729400778076447315298701735761068290467831183862106017821643]",
"[522.8320961944669697720607395898131191800860381046716118279570424339493298154083378116, 522.8320961944669697720607395898131191800860381046716118279570424339493300304541942601]",
"[537.4337912784940910005453375303110071617164275334186079487737206384107664264852256223, 537.433791278494091000545337530311007161716427533418607948773720638410766668213766271]",
"[549.291935255605166965003649289690105518421305470110200187230961072269690296350215858, 549.2919352556051669650036492896901055184213054701102001872309610722696905790182037196]",
"[556.9150182396784432749405112306462824533608408975151101210392527924289156976272465126, 556.915018239678443274940511230646282453360840897515110121039252792428916040851765448]",
"[560.0912881336027183310297426538445961866294027639243981543347393123877730166756180307, 560.0912881336027183310297426538445961866294027639243981543347393123877734474159622418]",
"[560.0912634967699960033951177534870210623381443558646615198584900232061416013013000783, 560.0912634967699960033951177534870210623381443558646615198584900232061421571095610217]",
"[560.0912388599372736757604928531294459380468859478049248853822407340245101591250918116, 560.0912388599372736757604928531294459380468859478049248853822407340245108936440748026]"
]
},
{
"lower_level": 22,
"upper_level": 23,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "445.6424184198634991832882582954561486382151181535798755805182145388421304722844695703552569258618055",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[445.6424676935289438385575080961712988867976349696993488494707131172053931780889304647, 445.6424676935289438385575080961712988867976349696993488494707131172053933420497804679]",
"[445.6424430566962215109228831958137237625063765616396122149944638280237618251866997476, 445.6424430566962215109228831958137237625063765616396122149944638280237619891523309497]",
"[445.6424184198634991832882582954561486382151181535798755805182145388421304722844695704, 445.6424184198634991832882582954561486382151181535798755805182145388421306362548808917]",
"[448.4621159092855534929845778239047069349760931864401380548341370604600807430361339494, 448.4621159092855534929845778239047069349760931864401380548341370604600809077068845645]",
"[455.2294235358031252281132113105688770661849008113320443388330648381612143613167297607, 455.2294235358031252281132113105688770661849008113320443388330648381612145285027563711]",
"[465.7563588447260540583965924198138197841101076512456666275939130345142303584078830501, 465.7563588447260540583965924198138197841101076512456666275939130345142305315633626866]",
"[479.1355714288065104952595856444110178547250017679671414508357516691957735221880491681, 479.1355714288065104952595856444110178547250017679671414508357516691957737070272020711]",
"[493.8957669212835117088096800915767890481354700000498494963745420911194537569496572136, 493.895766921283511708809680091576789048135470000049849496374542091119453962184593007]",
"[508.0689154778219759813138407790282724022105428167953053475409712479143380469456583106, 508.0689154778219759813138407790282724022105428167953053475409712479143382851859673567]",
"[519.5838579946678860527947414790493412080804621335360110330711947858525503160960379215, 519.583857994667886052794741479049341208080462133536011033071194785852550605017610374]",
"[526.9863095644432673620584391252613693542561868750623751619059402724417534262674129965, 526.9863095644432673620584391252613693542561868750623751619059402724417537902805584767]",
"[530.0706468107357662104315110336628862136987947365288730498494720300759451975298991214, 530.0706468107357662104315110336628862136987947365288730498494720300759456703944390105]",
"[530.0706173391003080418013952089871829671032925169569897121703242073553292593106124656, 530.070617339100308041801395208987182967103292516956989712170324207355329888503563857]",
"[530.0705878674648498731712793843114797205077902973851063744911763846347132866926697682, 530.0705878674648498731712793843114797205077902973851063744911763846347141408888493301]"
]
},
{
"lower_level": 21,
"upper_level": 22,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "417.9985017568843307201383202676308704529816424111196317312564514244251616509787544762490516265615136",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[417.9985607001552470573985519169822769461726468502633984066147470698663933707757304909, 417.9985607001552470573985519169822769461726468502633984066147470698663935261690635416]",
"[417.9985312285197888887684360923065736995771446306915150689355992471457775108772422137, 417.9985312285197888887684360923065736995771446306915150689355992471457776662762940273]",
"[417.9985017568843307201383202676308704529816424111196317312564514244251616509787544762, 417.998501756884330720138320267630870452981642411119631731256451424425161806383524513]",
"[420.7230949075760512118441004378941869862150822936902962185402003465185482114820862669, 420.7230949075760512118441004378941869862150822936902962185402003465185483677772900818]",
"[427.262158692426170397144580293265386167102471162675924070845348652529727394133456478, 427.2621586924261703971445802932653861671024711626759240708453486525297275536219246379]",
"[437.4340503933281913220801330543181083124953653745735620060759345558051446212891294829, 437.4340503933281913220801330543181083124953653745735620060759345558051447883467686524]",
"[450.3689763944707673925979528377906180157871043482480019383775008146174175477690676666, 450.3689763944707673925979528377906180157871043482480019383775008146174177296280650187]",
"[464.6522191242543833187375127596535594084213092923499859300612951755010500239380107668, 464.6522191242543833187375127596535594084213092923499859300612951755010502316210936172]",
"[478.3793416718442066134346124171403667238151798700573220183362133797999365209639269527, 478.3793416718442066134346124171403667238151798700573220183362133797999367704334886496]",
"[489.5370754872372017728478434356869802151891686671920796770305195965063327402833813665, 489.5370754872372017728478434356869802151891686671920796770305195965063330539591648482]",
"[496.709890529043211781665578979239389032566894920621864777431069057378310047089278323, 496.7098905290432117816655789792393890325668949206218647774310690573783104560635738636]",
"[499.6985423088834276881000011423434737997922554749238795973483536342374726270447339869, 499.6985423088834276881000011423434737997922554749238795973483536342374731746349351409]",
"[499.698506856954627659151126758137780174257320878960163270671737482413508133592859462, 499.6985068569546276591511267581377801742573208789601632706717374824135088813821849922]",
"[499.6984714050258276302022523739320865487223862829964469439951213305895435949514416837, 499.6984714050258276302022523739320865487223862829964469439951213305895446332594986451]"
]
},
{
"lower_level": 20,
"upper_level": 21,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "390.2591598584134849532461905864056814093048077732180953254385347866200688324048922166294093208240802",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[390.2592307622710850111439393548170686603746769651455279787917670902679976189951378546, 390.2592307622710850111439393548170686603746769651455279787917670902679977837599649526]",
"[390.2591953103422849821950649706113750348397423691818116521151509384440332257000147657, 390.2591953103422849821950649706113750348397423691818116521151509384440333904717211117]",
"[390.2591598584134849532461905864056814093048077732180953254385347866200688324048922166, 390.2591598584134849532461905864056814093048077732180953254385347866200689971834767311]",
"[392.8850749683996247721495726072760415513449763612934937848523875736373713514433992716, 392.8850749683996247721495726072760415513449763612934937848523875736373715172249203923]",
"[399.1873195738967503715577363535281179733794433309095657035916011411926270271394417259, 399.1873195738967503715577363535281179733794433309095657035916011411926271965190378769]",
"[408.9908287977439108030442379312887152604150095261808253822796432605607658881278497111, 408.9908287977439108030442379312887152604150095261808253822796432605607660660400910454]",
"[421.464761515680763530710030937469650392351370796522827629897681923484742091563063217, 421.4647615156807635307100309374696503923513707965228276298976819234847422861679906643]",
"[435.2530871899651234272141403984804964436898158844272624932762514035227410158359420294, 435.25308718996512342721414039848049644368981588442726249327625140352274123957973399]",
"[448.5173568915914396937429793990037517138730571082744003260615599027597680269301119003, 448.5173568915914396937429793990037517138730571082744003260615599027597682978617874287]",
"[459.3043934956920018137917352014054962902036347619167640183105177457845734840613677359, 459.3043934956920018137917352014054962902036347619167640183105177457845738276018419774]",
"[466.2389002309206829644377444116299755396985375254268190311590876897683140223720306386, 466.2389002309206829644377444116299755396985375254268190311590876897683144739559446988]",
"[469.1282524149952716479135403292776416304354231946992675413779393604334677291356938281, 469.1282524149952716479135403292776416304354231946992675413779393604334683385435900392]",
"[469.1282095057578862334722955645751224333397696756950214810189509828544177004434326516, 469.1282095057578862334722955645751224333397696756950214810189509828544185392945294949]",
"[469.1281665965205008190310507998726032362441161566907754206599626052753676183215208336, 469.128166596520500819031050799872603236244116156690775420659962605275368793207375697]"
]
},
{
"lower_level": 19,
"upper_level": 20,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "362.5712788900354023077973728728247752337102130327533807277697482249426706291219523241689900476154416",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[362.5713647085101731366798624022298136279015200707618728484877249801007704563541177628, 362.5713647085101731366798624022298136279015200707618728484877249801007706120393937928]",
"[362.5713217992727877222386176375272944308058665517576267881287366025217205427380350435, 362.5713217992727877222386176375272944308058665517576267881287366025217206984316368797]",
"[362.5712788900354023077973728728247752337102130327533807277697482249426706291219523242, 362.5712788900354023077973728728247752337102130327533807277697482249426707848238794269]",
"[365.0950837555528399749134023441833663195141005458068315320853690619628452593885465215, 365.0950837555528399749134023441833663195141005458068315320853690619628454159942346298]",
"[371.1522738842113744852943479150277663734066453726482615885376376510454961300416882722, 371.1522738842113744852943479150277663734066453726482615885376376510454962898803708792]",
"[380.5745908659241076904185694770556097638259379437312119371814436874469515164506643966, 380.5745908659241076904185694770556097638259379437312119371814436874469516839479676687]",
"[392.5714804056112227139466608162878696477194077500424243529697992893826458687471201169, 392.5714804056112227139466608162878696477194077500424243529697992893826460512205668279]",
"[405.8476195182500119178706166381271709789179735652915246116472088112726597938280283343, 405.847619518250011917870616638127170978917973565291524611647208811272660002445141961]",
"[418.6328496084140266581297065821099355730119697189000552650116295880740519215253602242, 418.6328496084140266581297065821099355730119697189000552650116295880740521725077686851]",
"[429.0362087230701909370532449663928941607149495689063363067498800870473716500111165979, 429.0362087230701909370532449663928941607149495689063363067498800870473719662859263989]",
"[435.7240619102102311202743650513703653123300002914962662232520601194529891256124324307, 435.7240619102102311202743650513703653123300002914962662232520601194529895393426659946]",
"[438.5106361557817636335447161791704418847018187645230337178741701534820168903609151294, 438.5106361557817636335447161791704418847018187645230337178741701534820174471967225208]",
"[438.5105838645588131773473656493931813417840355270997234298656159891467375618918145336, 438.5105838645588131773473656493931813417840355270997234298656159891467383284602877959]",
"[438.5105315733358627211500151196159207988662522896764131418570618248114581828993153746, 438.5105315733358627211500151196159207988662522896764131418570618248114592601009614159]"
]
},
{
"lower_level": 18,
"upper_level": 19,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "335.0787563111594810382977241729023258706767108017249645067261083605525426348118479826765950367686488",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[335.0788608936053819506924252324568469565122772765715850827432166892231010816287708318, 335.0788608936053819506924252324568469565122772765715850827432166892231012372853450953]",
"[335.0788086023824314944950747026795864135944940391482747947346625248878218582203091373, 335.0788086023824314944950747026795864135944940391482747947346625248878220138870298194]",
"[335.0787563111594810382977241729023258706767108017249645067261083605525426348118479827, 335.0787563111594810382977241729023258706767108017249645067261083605525427904887140038]",
"[337.4971569760789334709785846307838111358223171754491725919880896849190716941602881047, 337.4971569760789334709785846307838111358223171754491725919880896849190718506401553335]",
"[343.3013897236772671790719549453425585961716993466226001244836489156976197763727958958, 343.3013897236772671790719549453425585961716993466226001244836489156976199357214407085]",
"[352.3302219583028410877786869717282663741478356062165734291396408062335244232901307929, 352.3302219583028410877786869717282663741478356062165734291396408062335245894379053448]",
"[363.8346598164229277216919031344691861011273757524858943339065523609931735356093391497, 363.8346598164229277216919031344691861011273757524858943339065523609931737150635079264]",
"[376.5820199220442104848416724840827754092311167807171288031091798356994493570854572921, 376.5820199220442104848416724840827754092311167807171288031091798356994495597938004708]",
"[388.8726460101467181194370657398445885414898214380264636100026219579914066733114033722, 388.8726460101467181194370657398445885414898214380264636100026219579914069137628230969]",
"[398.8798408837063621351360065095083237922944517794333855404075636540545584518169229635, 398.8798408837063621351360065095083237922944517794333855404075636540545587505861025151]",
"[405.3130122962689908725513916897770788109420967053575147284505129567786114735711072777, 405.3130122962689908725513916897770788109420967053575147284505129567786118597520818981]",
"[407.9934619795451303413756791362503068555591516512454597825029910730750766552431954066, 407.9934619795451303413756791362503068555591516512454597825029910730750771706409955118]",
"[407.9933977692181546666448302531754699878074784231913242468453857359053445338532790034, 407.9933977692181546666448302531754699878074784231913242468453857359053452405053134943]",
"[407.9933335588911789919139813701006331200558051951371887111877803987356123645138958097, 407.9933335588911789919139813701006331200558051951371887111877803987356133582085871558]"
]
},
{
"lower_level": 17,
"upper_level": 18,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "307.9218437641446991577032228592744535653393407695980151042641305561906829562343465074484415643766141",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[307.9219721847986505071649206254241273008426872257062861755793412305301470074192372833, 307.9219721847986505071649206254241273008426872257062861755793412305301471727107152122]",
"[307.9219079744716748324340717423492904330910139976521506399217358933604149818267918954, 307.9219079744716748324340717423492904330910139976521506399217358933604151471307285769]",
"[307.9218437641446991577032228592744535653393407695980151042641305561906829562343465074, 307.9218437641446991577032228592744535653393407695980151042641305561906831215507414018]",
"[310.2316798008391933560700800751468479025675758636149407189539288362044626926627358342, 310.2316798008391933560700800751468479025675758636149407189539288362044628590111291214]",
"[315.775373549068262671611560101849429742547386088828379792623870868386124663781447678, 315.7753735490682626716115601018494297425473860888283797926238708683861248338297704278]",
"[324.3989285856842252861749326491810842691005235890942484547944584290968311736441783325, 324.398928585684225286174932649181084269100523589094248454794458429096831352478540627]",
"[335.3961253996447682962083172223221840325433444328155500311700861316041725097635415219, 335.3961253996447682962083172223221840325433444328155500311700861316041727058118388367]",
"[347.5987657869696356732630861168868300437639729846242609745485348923190275943378473164, 347.5987657869696356732630861168868300437639729846242609745485348923190278204918476457]",
"[359.3798208002334907921932387200296987992915108465916804637673622715014935330982012169, 359.3798208002334907921932387200296987992915108465916804637673622715014938081605189218]",
"[368.9788374793155137262716899298631883284103888361480833654925641203008515601041941799, 368.9788374793155137262716899298631883284103888361480833654925641203008519108663874784]",
"[375.1496024808766733938536117888763807458056033121254620705350058451152771174086517356, 375.1496024808766733938536117888763807458056033121254620705350058451152775820186310689]",
"[377.7207069587520877728719998338722306396699641605308533084262899639725258617129875968, 377.7207069587520877728719998338722306396699641605308533084262899639725264956166817824]",
"[377.7206274422354793255542620912570618283843876036485572816221680007812856692517872743, 377.7206274422354793255542620912570618283843876036485572816221680007812865560291239328]",
"[377.7205479257188708782365243486418930170988110467662612548180460375900454109964765752, 377.7205479257188708782365243486418930170988110467662612548180460375900466820224624123]"
]
},
{
"lower_level": 16,
"upper_level": 17,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "281.2364591941302873450667538745431893986340345715247796134396593465076223466449061719050721877454156",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[281.2366182271635042397022293597735270212051876852893716670479032728901024781347763153, 281.2366182271635042397022293597735270212051876852893716670479032728901026352682514503]",
"[281.2365387106468957923844916171583582099196111284070756402437813096988624123898409737, 281.2365387106468957923844916171583582099196111284070756402437813096988625695387446238]",
"[281.2364591941302873450667538745431893986340345715247796134396593465076223466449061719, 281.2364591941302873450667538745431893986340345715247796134396593465076225038092372576]",
"[283.4346968119639290277000986595343331923903934968304055631275310420018413832020896371, 283.4346968119639290277000986595343331923903934968304055631275310420018415417221987905]",
"[288.7105750029313458097395191184864907456946774459742567272802995429585705879433008086, 288.7105750029313458097395191184864907456946774459742567272802995429585707513142567789]",
"[296.9175353072917290295811701847440538778981351428507499709339346694624889933996528314, 296.9175353072917290295811701847440538778981351428507499709339346694624891682721749603]",
"[307.3932885255118858940603036838700912631138581772503100283789979787726943812447861078, 307.3932885255118858940603036838700912631138581772503100283789979787726945786317165366]",
"[319.0358837520804413946997769914104201928100922679474837311892982555378838852984242424, 319.0358837520804413946997769914104201928100922679474837311892982555378841220549742198]",
"[330.2929621500591977433994027381498752659377512249884015043319713186498420751012283826, 330.2929621500591977433994027381498752659377512249884015043319713186498423758731440583]",
"[339.4722299957623145835890361078631605074148751465985166501526461845181538861371585843, 339.4722299957623145835890361078631605074148751465985166501526461845181542862473484743]",
"[345.3731484389802287023016083251997706489205703959103498868721806309142886255333693636, 345.3731484389802287023016083251997706489205703959103498868721806309142891758182272903]",
"[347.8318048779377501962692943643681868039330145397333481163841328634632829747753287643, 347.8318048779377501962692943643681868039330145397333481163841328634632837503436612299]",
"[347.8317054697891330944062552759257113210181586090192659610332935384870249561359064586, 347.8317054697891330944062552759257113210181586090192659610332935384870260726095245099]",
"[347.8316060616405159925432161874832358381033026783051838056824542135107668446840497433, 347.8316060616405159925432161874832358381033026783051838056824542135107684879431559205]"
]
},
{
"lower_level": 15,
"upper_level": 16,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "255.1534453652903443739987645720935335331399435230355587337481956346982790671315245562668985802505534",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[255.1536441815875785777248427489784844989696553844637230444498742846507947637373193303, 255.1536441815875785777248427489784844989696553844637230444498742846507949216124394737]",
"[255.1535447734389614758618036605360090160547994537496408890990349596745369154344219433, 255.15354477343896147586180366053600901605479945374964088909903495967453707332882908]",
"[255.1534453652903443739987645720935335331399435230355587337481956346982790671315245563, 255.1534453652903443739987645720935335331399435230355587337481956346982792250452184164]",
"[257.2371672561506616386767634015354860512544144640735553617703096658336503689640881605, 257.2371672561506616386767634015354860512544144640735553617703096658336505283955662441]",
"[262.2382344808989486160882575114094166863912634884049916271223495690878866566277334857, 262.2382344808989486160882575114094166863912634884049916271223495690878868214850372163]",
"[270.0177203874212626405007477126491333684261885091816257233388538405333049428559369329, 270.0177203874212626405007477126491333684261885091816257233388538405333051205787762956]",
"[279.9583668492413433643026883776935107066140961788890230889168640814677182393083757145, 279.9583668492413433643026883776935107066140961788890230889168640814677184422261314071]",
"[291.0261536843802273380733628354357384039726284687154739152273399362256752388480167126, 291.0261536843802273380733628354357384039726284687154739152273399362256754858633746994]",
"[301.745359768850231764649655570982531859417543232978919867301375447927949514563912896, 301.7453597688502317646496555709825318594175432329789198673013754479279498334181324993]",
"[310.4937090235006985818187776222410256927328388974850021032391888624151110399443060135, 310.4937090235006985818187776222410256927328388974850021032391888624151114706856919624]",
"[316.1175977501190838703007196832518659556950725933095210956347494418102169062887129966, 316.1175977501190838703007196832518659556950725933095210956347494418102175072818180383]",
"[318.4608093497852769811346098694019723339331987085814553527013932252612216653479856594, 318.4608093497852769811346098694019723339331987085814553527013932252612225244360316798]",
"[318.4606837453147718588766606039036858602954105112794031497097432615618670760717372971, 318.4606837453147718588766606039036858602954105112794031497097432615618683316094208952]",
"[318.460558140844266736618711338405399386657622313977350946718093297862512372771983858, 318.4605581408442667366187113384053993866576223139773509467180932978625142525184630532]"
]
},
{
"lower_level": 14,
"upper_level": 15,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "229.7977399365870219396936442607001885346978947906869301741046376878404473629673280779584128079550994",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[229.7979911455280321842095427916967614819734711852910345800879376152391561447228497015, 229.7979911455280321842095427916967614819734711852910345800879376152391563026817706366]",
"[229.7978655410575270619515935261984750083356829879889823770962876515398017538450888897, 229.7978655410575270619515935261984750083356829879889823770962876515398019118283792034]",
"[229.797739936587021939693644260700188534697894790686930174104637687840447362967328078, 229.7977399365870219396936442607001885346978947906869301741046376878404475209749875002]",
"[231.7641301315717537070283498657694645099691541868911144196616357650248387707679391177, 231.7641301315717537070283498657694645099691541868911144196616357650248389301507259433]",
"[236.483636470223578649640969021790777586382836948445358670945463645817828011229095097, 236.4836364702235786496409690217907775863828369484453586709454636458178281755001390024]",
"[243.8251509277455551186132091768594501440812178735600706528420821106263588976605521282, 243.8251509277455551186132091768594501440812178735600706528420821106263590734966536841]",
"[253.2174964371458045374373567348666255708050461046494323858458899168173491007563695237, 253.2174964371458045374373567348666255708050461046494323858458899168173492992156052332]",
"[263.6961956244048843910458553112974820197067512882937209448622382462999889788610621085, 263.6961956244048843910458553112974820197067512882937209448622382462999892169125963848]",
"[273.8640678135872344734393150429077907337981238465016649183811922450170526055346454515, 273.8640678135872344734393150429077907337981238465016649183811922450170529081741088278]",
"[282.1706676378228695914109920435843768183016487690805592593716459732253990652151441288, 282.1706676378228695914109920435843768183016487690805592593716459732253994688298782641]",
"[287.5105603045701574574825246207562581670143861854909316178190378866378362736917407669, 287.5105603045701574574825246207562581670143861854909316178190378866378368321081159778]",
"[289.7354190716411961285088365532743882917129878524091810885000930310653217822104867093, 289.7354190716411961285088365532743882917129878524091810885000930310653225782289170883]",
"[289.7352584513721327351722839567029453307760806120800160119483248492487632744039037834, 289.7352584513721327351722839567029453307760806120800160119483248492487644419060542147]",
"[289.7350978311030693418357313601315023698391733717508509353965566674322046535083366597, 289.7350978311030693418357313601315023698391733717508509353965566674322064187837381042]"
]
},
{
"lower_level": 13,
"upper_level": 14,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "205.2874028207388817895879591343908187533150021414029488645429152310052993598484490769431009131308039",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[205.2877240612770085762610643275337046751888166220612790176464515946384160046139856641, 205.2877240612770085762610643275337046751888166220612790176464515946384161725060986685]",
"[205.2875634410079451829245117309622617142519093817321139410946834128218576822312172356, 205.2875634410079451829245117309622617142519093817321139410946834128218578501544930446]",
"[205.2874028207388817895879591343908187533150021414029488645429152310052993598484490769, 205.2874028207388817895879591343908187533150021414029488645429152310052995278028874207]",
"[207.1337237630158151826905237592961307734083790368709065111787494088462423950488788742, 207.1337237630158151826905237592961307734083790368709065111787494088462425645937955806]",
"[211.5651108000697520516933644828472325795695734901340951955188809016904248096848930054, 211.5651108000697520516933644828472325795695734901340951955188809016904249848903262079]",
"[218.4584557194777612583831868382903326886099661193357854836120764833003981390437695106, 218.4584557194777612583831868382903326886099661193357854836120764833003983276623596825]",
"[227.2896688162152211077149025832444296906536249588253194891526548097023005092632940543, 227.2896688162152211077149025832444296906536249588253194891526548097023007241591129971]",
"[237.1653678061509916210380654162579427007775928404044296831286065084660104373835247651, 237.1653678061509916210380654162579427007775928404044296831286065084660106983512267604]",
"[246.7687657928833941670746975848005453289636648265328137438653907005052972475185584236, 246.7687657928833941670746975848005453289636648265328137438653907005052975838748768931]",
"[254.6230321980232705220796404006120757098595444693972559544026987461416920482325871063, 254.6230321980232705220796404006120757098595444693972559544026987461416925031115476159]",
"[259.6721195529186747709903578149745629072159648064315249009040848928956647808242323394, 259.6721195529186747709903578149745629072159648064315249009040848928956654191878204685]",
"[261.7757806531084444258914398330479043748454475085377771537033241276050454159463559264, 261.7757806531084444258914398330479043748454475085377771537033241276050463402549179789]",
"[261.7755724386203846778677704370505797127721513794941669704176845872330216321081038486, 261.7755724386203846778677704370505797127721513794941669704176845872330230128011049036]",
"[261.7753642241323249298441010410532550506988552504505567871320450468609977002637083858, 261.7753642241323249298441010410532550506988552504505567871320450468609998332133490026]"
]
},
{
"lower_level": 12,
"upper_level": 13,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "181.7324142689074338151428390807681413669710453365247699080096915681206861673550947816147089836342896",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[181.7328306978835533111901778727627906911176375946119902745809706488647332777234210425, 181.7328306978835533111901778727627906911176375946119902745809706488647334562953520348]",
"[181.7326224833954935631665084767654660290443414655683800912953311084927097225392577771, 181.7326224833954935631665084767654660290443414655683800912953311084927099011515855274]",
"[181.7324142689074338151428390807681413669710453365247699080096915681206861673550947816, 181.7324142689074338151428390807681413669710453365247699080096915681206863460078187501]",
"[183.45597145914393790828421649444912284276273136991973266639953569553408690625150109, 183.4559714591439379082842164944491228427627313699197326663995356955340870869590753321]",
"[187.5927890518789570584886842824961168855951019076202492684590398275410479273109087816, 187.5927890518789570584886842824961168855951019076202492684590398275410481153352412265]",
"[194.0279363286611689789983122113835151532716336073676769902956075412653555509720826146, 194.027936328661168978998312211383515153271633607367676990295607541265355756338950996]",
"[202.2853850313439691682803335641772872052796293595380610209258491056682222819518018644, 202.2853850313439691682803335641772872052796293595380610209258491056682225213060015019]",
"[211.5443587643131857524252188828887330594701908065120667842320018036602987787461474723, 211.5443587643131857524252188828887330594701908065120667842320018036602990777514844024]",
"[220.5702919541688196814295554292371063247354295582367570208055498661754927047865163685, 220.5702919541688196814295554292371063247354295582367570208055498661754931016648487653]",
"[227.9617481774089213450316587954726607072736026610257469141616971572660706854835394393, 227.9617481774089213450316587954726607072736026610257469141616971572660712371420301725]",
"[232.7132874301078501074375235323961125361355301805623484608517677258718391930251950577, 232.7132874301078501074375235323961125361355301805623484608517677258718399868986667298]",
"[234.6929301969074923026794421817529381202412353347646628957466470536230770596419851302, 234.6929301969074923026794421817529381202412353347646628957466470536230782373738326661]",
"[234.6926560525845193653767437706280458758089108241595028264652820226322522776996637552, 234.6926560525845193653767437706280458758089108241595028264652820226322540817506620869]",
"[234.6923819082615464280740453595031536313765863135543427571839169916414272803560304099, 234.6923819082615464280740453595031536313765863135543427571839169916414301423843762824]"
]
},
{
"lower_level": 11,
"upper_level": 12,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "159.2331019933004402172955802406699746692827875613466087948922960229184324554079743394633868422964234",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[159.2336502819463860919009770629197591581474365825569289334550260849000813950365338816, 159.2336502819463860919009770629197591581474365825569289334550260849000815561871716683]",
"[159.2333761376234131545982786517948669137151120719517688641736610539092569252222539756, 159.2333761376234131545982786517948669137151120719517688641736610539092570864260794955]",
"[159.2331019933004402172955802406699746692827875613466087948922960229184324554079743395, 159.2331019933004402172955802406699746692827875613466087948922960229184326166649873227]",
"[160.8311882677482686777702975668878203273277574872847157740900036465200303671664938109, 160.8311882677482686777702975668878203273277574872847157740900036465200305305113777281]",
"[164.6669634001675230892471190087475275067869279662129437441952998345971558924275215693, 164.6669634001675230892471190087475275067869279662129437441952998345971560631835831901]",
"[170.6338516796134183856561407591138521062296702539356749503826612295365305350385344358, 170.6338516796134183856561407591138521062296702539356749503826612295365307233627160024]",
"[178.3048469613354195891757941048624770966055859457576239575666717998624670342613267884, 178.3048469613354195891757941048624770966055859457576239575666717998624672570497285688]",
"[186.9332776430923304958146232502687151821674928645577866853895470280038564866514255112, 186.9332776430923304958146232502687151821674928645577866853895470280038567700638260034]",
"[195.368638121725779528900122855679364801273658050853229683697692621294253621137856189, 195.3686381217257795289001228556793648012736580508532296836976926212942540044871755261]",
"[202.2866977721396728979674233888314219148302051107278586559636869841383791711067766626, 202.286697772139672897967423388831421914830205110727858655963686984138379713935450573]",
"[206.733871731990057534023651239910558362521624931174053482142449578691076214335000722, 206.7338717319900575340236512399105583625216249311740534821424495786910770106170908982]",
"[208.5866389343611856393566806915172492513620283496219684230441829699173471044424723374, 208.5866389343611856393566806915172492513620283496219684230441829699173483116434760024]",
"[208.586271459883706089370012399795892623553165535697456859328302921037134032239677603, 208.5862714598837060893700123997958926235531655356974568593283029210371359292753352467]",
"[208.5859039854062265393833441080745359957443027217729452956124228721569207045157605827, 208.5859039854062265393833441080745359957443027217729452956124228721569238025422521294]"
]
},
{
"lower_level": 10,
"upper_level": 11,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "137.8779584717804654640559992004708005637331752470856124257225482533715663581874267677808997751908148",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[137.8786934207354245640293357839135138193509008749346355531543083511319918121835143197, 137.8786934207354245640293357839135138193509008749346355531543083511319919851346319816]",
"[137.8783259462579450140426674921921571915420380610101239894384283022517790851854704088, 137.8783259462579450140426674921921571915420380610101239894384283022517792582078828807]",
"[137.8779584717804654640559992004708005637331752470856124257225482533715663581874267678, 137.8779584717804654640559992004708005637331752470856124257225482533715665312811335099]",
"[139.3477638864067547690483560480905887221317847900642651685993821194194439855991805584, 139.3477638864067547690483560480905887221317847900642651685993821194194441613204345665]",
"[142.8757886448082082375058667665021190629889055380852953346097725191436255111833276867, 142.8757886448082082375058667665021190629889055380852953346097725191436256962017855309]",
"[148.3639947365784381703793976503873743452565994600859654805512473506231676766756648817, 148.3639947365784381703793976503873743452565994600859654805512473506231678836957466433]",
"[155.4353767960994042910432583940569998292482825018420034335482491717192353251487799474, 155.4353767960994042910432583940569998292482825018420034335482491717192355753017956093]",
"[163.4189038711083464344599793702055378261935804962931716916561207032498900003967075385, 163.4189038711083464344599793702055378261935804962931716916561207032498903265094662336]",
"[171.250039258821350416497722226525612660122042600792785710541438918620612130082274762, 171.2500392588213504164977222265256126601220426007927857105414389186206125819963959655]",
"[177.683660059006195836316127511487161193589399038536929345884338950004665208466485059, 177.6836600590061958363161275114871611935893990385369293458843389500046658632769712452]",
"[181.8193520189723561114092604512202796642075900941789567604759360007081591362122722061, 181.8193520189723561114092604512202796642075900941789567604759360007081601196258861027]",
"[183.5422525575914727527837414507995336291020335464352962112232807424672732963677592573, 183.5422525575914727527837414507995336291020335464352962112232807424672748273514954858]",
"[183.5417496220727966335847940581471073283948254505164211879755182814638423155367943756, 183.5417496220727966335847940581471073283948254505164211879755182814638447963554349091]",
"[183.5412466865541205143858466654946810276876173545975461647277558204604109554333004247, 183.541246686554120514385846665494681027687617354597546164727755820460415144738168757]"
]
},
{
"lower_level": 9,
"upper_level": 10,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "117.7404320950698786748379823761043741226215339902275030515757957796940959682846217220708091617211105",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[117.7414379661072309132358771614092267240359501820652530980713207017009569803728642912, 117.7414379661072309132358771614092267240359501820652530980713207017009571582004045133]",
"[117.7409350305885547940369297687568004233287420861463780748235582406975264743287430066, 117.7409350305885547940369297687568004233287420861463780748235582406975266522538587093]",
"[117.7404320950698786748379823761043741226215339902275030515757957796940959682846217221, 117.7404320950698786748379823761043741226215339902275030515757957796940961463073127703]",
"[119.0788936910063624524451804299452687585792163898989865075174544747741704064065110269, 119.078893691006362452445180429945268758579216389898986507517454474774170588026599706]",
"[122.2918719321229962901350335848970812554856916370458867910535557360728911881573389333, 122.291871932122996290135033584897081255485691637045886791053555736072891382547391625]",
"[127.2900632009885946999962518132561283519642956351309602157871790596518954395701817667, 127.2900632009885946999962518132561283519642956351309602157871790596518956642455028485]",
"[133.7475134002953794216159559487088738803876771523147768569320395130872881950601703413, 133.747513400295379421615955948708873880387677152314776856932039513087288479229545311]",
"[141.0704878641216392407254596472806563795771509569744902144398338742027922916871663756, 141.0704878641216392407254596472806563795771509569744902144398338742027926809952568779]",
"[148.2824959216414710501574901917646766781837797592831049292029138574981659139315222254, 148.282495921641471050157490191764676678183779759283104929202913857498166478656780494]",
"[154.2196086947157333991482412568482830270037599323298917344468732997223615453730064542, 154.2196086947157333991482412568482830270037599323298917344468732997223623971282525887]",
"[158.0360308025126670217251453903358102868838133629844542013377030437050238881446484454, 158.0360308025126670217251453903358102868838133629844542013377030437050252159912524878]",
"[159.6257785949283103133672201581733609611630831460633027498588141997921786713067194444, 159.6257785949283103133672201581733609611630831460633027498588141997921808186866039989]",
"[159.6250732394715683605386906416116594117527750713494895456188150124024816051867903096, 159.6250732394715683605386906416116594117527750713494895456188150124024852264999069864]",
"[159.6243678840148264077101611250499578623424669966356763413788158250127839048288843841, 159.6243678840148264077101611250499578623424669966356763413788158250127902677427145442]"
]
},
{
"lower_level": 8,
"upper_level": 9,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "98.87393815109264219869961624368659756298090484447581989870554395112101915936208475600110099697549742",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[98.87534886200612610435667527681000066180152099390344630718554232590041181804267103545, 98.8753488620061261043566752768100006618015209939034463071855423259004119867890642526]",
"[98.87464350654938415152814576024829911239121291918963310294554313851071548870237789573, 98.87464350654938415152814576024829911239121291918963310294554313851071565758561822052]",
"[98.873938151092642198699616243686597562980904844475819898705543951121019159362084756, 98.87393815109264219869961624368659756298090484447581989870554395112101932838217218843]",
"[100.0774803285627246372850705286933839041111831803896538205864655254034801136888249069, 100.0774803285627246372850705286933839041111831803896538205864655254034802859674083642]",
"[102.9669173456005230407369686618869042996219610626221736694043593800401091039433975883, 102.9669173456005230407369686618869042996219610626221736694043593800401092876321263432]",
"[107.4619057090586023156298443274226897825170219222109906958113314559799671596301371024, 107.46190570905860231562984432742268978251702192221099069581133145597996737028440185]",
"[113.2887600320950570731190448101165013544018581490275350246422283724711759505190529309, 113.2887600320950570731190448101165013544018581490275350246422283724711762141521225382]",
"[119.9329624852447349463740266983367512583506166165254034265685485137729915981524323973, 119.9329624852447349463740266983367512583506166165254034265685485137729919557957034987]",
"[126.5084817902351171027559404683975277492109469605130800812506591262503234882827211709, 126.5084817902351171027559404683975277492109469605130800812506591262503240044546589242]",
"[131.9350124838605157810998363846911664224183256354901871068218916685355509836851518988, 131.9350124838605157810998363846911664224183256354901871068218916685355517646702636249]",
"[135.4230684354752018508804696501493645153157831094914765991251817655490193137303615531, 135.4230684354752018508804696501493645153157831094914765991251817655490205484975656254]",
"[136.8758051239566759915020813265377090807055942731170865383578398360470472094330606528, 136.875805123956675991502081326537709080705594273117086538357839836047049258528077908]",
"[136.8747867174702594052753522329305647397252294477749933747491954628641653349979593969, 136.8747867174702594052753522329305647397252294477749933747491954628641689137044758949]",
"[136.87376831098384281904862313932342039874486462243290021114055108968128274787082851, 136.8737683109838428190486231393234203987448646224329002111405510896812892830462881141]"
]
},
{
"lower_level": 7,
"upper_level": 8,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "81.30366231146665459930756672848678438241399102843576360464293758504186016724810695134329231243495019",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[81.30569912443948777176102491570107306437472067911994993186022633140762239047525665014, 81.30569912443948777176102491570107306437472067911994993186022633140762256997771955611]",
"[81.30468071795307118553429582209392872339435585377785676825158195822474127886168173327, 81.30468071795307118553429582209392872339435585377785676825158195822474145856172708658]",
"[81.30366231146665459930756672848678438241399102843576360464293758504186016724810695134, 81.30366231146665459930756672848678438241399102843576360464293758504186034714573461706]",
"[82.36772849704114585482362063342781407869653285681870277088554632776621955499144087758, 82.36772849704114585482362063342781407869653285681870277088554632776621973832013667145]",
"[84.92283058201702744921080770302383420250965807704126549038849110092027404396464174467, 84.92283058201702744921080770302383420250965807704126549038849110092027423918547495976]",
"[88.89786664252496614708387526886187905797066371261733161314088677756131470940439719795, 88.89786664252496614708387526886187905797066371261733161314088677756131493268047950344]",
"[94.07297917316625390415420858072261461386042013348236170342604149212872311728066657214, 94.07297917316625390415420858072261461386042013348236170342604149212872339572516035613]",
"[100.0153173302411390711204998695314430463604781982112783349774188564183480202832074885, 100.0153173302411390711204998695314430463604781982112783349774188564183483971055454275]",
"[105.9323598851916992192611250897993374284274639560051977807733155728719758653138585097, 105.9323598851916992192611250897993374284274639560051977807733155728719764101532986966]",
"[110.8304777121544248614973869538394358668593847926270921097829995463358329422612452072, 110.8304777121544248614973869538394358668593847926270921097829995463358337748324514203]",
"[113.978619325940516469331164523195276102824873590648525379059683503414212070257057357, 113.9786193259405164693311645231952761028248735906485253790596835034142134150621581202]",
"[115.2894145909882778208188229928485963844933227507828163216544131187071503833491307805, 115.2894145909882778208188229928485963844933227507828163216544131187071526906998722077]",
"[115.2878916938259461595478118461813144199084849650412211444680928568794253243756235406, 115.2878916938259461595478118461813144199084849650412211444680928568794295224819813881]",
"[115.2863687966636144982768006995140324553236471792996259672817725950516993132873549865, 115.2863687966636144982768006995140324553236471792996259672817725950517073031256464554]"
]
},
{
"lower_level": 6,
"upper_level": 7,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "65.01231084409231141146124959369926048180242476103233505611272600086394288994298112811843969216724443",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[65.01535663841697473400327188703382441097210033251552541048536652451939111805472339112, 65.0153566384169747340032718870338244109721003325155254104853665245193912880302698232]",
"[65.01383374125464307273226074036654244638726254677393023329904626269166700399885219215, 65.01383374125464307273226074036654244638726254677393023329904626269166717426985773849]",
"[65.01231084409231141146124959369926048180242476103233505611272600086394288994298112812, 65.01231084409231141146124959369926048180242476103233505611272600086394306050944565379]",
"[65.93047371258539247125495614066684559444194160272920253616868891888388993669177477973, 65.93047371258539247125495614066684559444194160272920253616868891888389011185434316928]",
"[68.13605846321149538994598517795607930941847916825920333982375953208563843810674239118, 68.13605846321149538994598517795607930941847916825920333982375953208563862916255743079]",
"[71.56759149017762760766651194992546314343735880521271810628227363094465970287251145524, 71.56759149017762760766651194992546314343735880521271810628227363094465993144764072318]",
"[76.06128105277532721456269555001211836545612797732152246699772179168770605392089608784, 76.06128105277532721456269555001211836545612797732152246699772179168770635648561963253]",
"[81.26943005811519448459837181398309292094228420276112935236738342444312370623025076162, 81.26943005811519448459837181398309292094228420276112935236738342444312414190233920937]",
"[86.49728349603270896889245971215023480822985380042707444125015348245457493921711071474, 86.49728349603270896889245971215023480822985380042707444125015348245457560700389112487]",
"[90.84208864002983343126069052865717444175540044689434332178007012139563370013966205769, 90.84208864002983343126069052865717444175540044689434332178007012139563478082464893133]",
"[93.63414961643500641589045342124243735293955568112256409603944965214772058960802817822, 93.63414961643500641589045342124243735293955568112256409603944965214772244556160041062]",
"[94.79604937577365531341634577837230215735645139287655211042829726893125205850633973813, 94.79604937577365531341634577837230215735645139287655211042829726893125545758324990247]",
"[94.79367160410083537348046153285737793134582277123913081045372646263799719221661283539, 94.7936716041008353734804615328573779313458227712391308104537264626380037774626351238]",
"[94.79129383242801543354457728734245370533519414960170951047915565634474061010059671456, 94.79129383242801543354457728734245370533519414960170951047915565634475382546311589997]"
]
},
{
"lower_level": 5,
"upper_level": 6,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "49.91377254577268551017034720247531041606348161312407034075621642272567954117571285114495473540774583",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[49.91852808911832539004211569350515886808473885639891294070535803531218609635866591465, 49.91852808911832539004211569350515886808473885639891294070535803531218624558075970196]",
"[49.9161503174455054501062314479902346420741102347614916407307872290189328187671893829, 49.91615031744550545010623144799023464207411023476149164073078722901893296845059713531]",
"[49.91377254577268551017034720247531041606348161312407034075621642272567954117571285114, 49.91377254577268551017034720247531041606348161312407034075621642272567969132043456865]",
"[50.67593209863304558083143188072556437116624778368466677133864149907869765353715333321, 50.67593209863304558083143188072556437116624778368466677133864149907869780948149917161]",
"[52.50819834710448461776369398452476319234415721096190930545305214185229950494089727291, 52.50819834710448461776369398452476319234415721096190930545305214185229968067544092756]",
"[55.35931565102630916602122369886627967694174809554230848351239460214237215497709875138, 55.35931565102630916602122369886627967694174809554230848351239460214237237727624761687]",
"[59.12516509156435654477255793316216660232789127958898687262971386578604787435712203797, 59.12516509156435654477255793316216660232789127958898687262971386578604818870640326423]",
"[63.54875916483206731257619705079203366723482672712032459179257560428228374406197671126, 63.54875916483206731257619705079203366723482672712032459179257560428228422618562751143]",
"[68.03971359220813170321116285092332903041559555406195481228889121333732435772109770073, 68.03971359220813170321116285092332903041559555406195481228889121333732514189157640052]",
"[71.7925450156394019207043527491543269617994807521913677975717170739251898530494176623, 71.79254501563940192070435274915432696179948075219136779757171707392519120492585102169]",
"[74.20335289877177229159474789565934918926894383602648043679672283437242879515867282489, 74.20335289877177229159474789565934918926894383602648043679672283437243129006867323232]",
"[75.20543806896672660745328436435223168565384425071735607016171113984282996287777932401, 75.20543806896672660745328436435223168565384425071735607016171113984283489101121180724]",
"[75.20151794245616626852821645335641104217435868503220215492868381154323639017856756487, 75.20151794245616626852821645335641104217435868503220215492868381154324661285392434372]",
"[75.1975978159456059296031485423605903986948731193470482396956564832436397561040403277, 75.19759781594560592960314854236059039869487311934704823969565648324366140141100299803]"
]
},
{
"lower_level": 4,
"upper_level": 5,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "35.80089861283602603970797279249562840012840102226753630961886147263102501334288766941125667125973001",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[35.80873886585714671755810861448726968708737215363784414008491612923020686162186240591, 35.80873886585714671755810861448726968708737215363784414008491612923020703210339230542]",
"[35.80481873934658637863304070349144904360788658795269022485188880093061593748237500393, 35.80481873934658637863304070349144904360788658795269022485188880093061610872445252821]",
"[35.80089861283602603970797279249562840012840102226753630961886147263102501334288766941, 35.800898612836026039707972792495628400128401022267536309618861472631025185345512751]",
"[36.38932682706069213474190000576184550942080026304106122178724884654695032012737800292, 36.38932682706069213474190000576184550942080026304106122178724884654695050060936405245]",
"[37.80657199313461753874554544517543876010913727237988543108766104478249182619535247468, 37.80657199313461753874554544517543876010913727237988543108766104478249203543092763535]",
"[40.0125950422982907585990289853211454310355637556310811203085563380988393304431099877, 40.01259504229829075859902898532114543103556375563108112030855633809883960729386262406]",
"[42.96945591183149984671666954540746975623389837390884454501359153741116593477549954567, 42.96945591183149984671666954540746975623389837390884454501359153741116634609877160292]",
"[46.52077407737052886422424363310366917922023158196651776006806308799604096511533935411, 46.52077407737052886422424363310366917922023158196651776006806308799604162714116030972]",
"[50.19197815170827880561023606703538674220250083997265373467162799534559650947521126207, 50.19197815170827880561023606703538674220250083997265373467162799534559764652420058657]",
"[53.2857123950546210745433186018654486126262295699638757096569996834846308894648371217, 53.28571239505462107454331860186544861262622956996387570965699968348463299308237881881]",
"[55.27141567111912142107779103335426876141089031392781370020181842285425380389739213818, 55.27141567111912142107779103335426876141089031392781370020181842285425803098315850934]",
"[56.09448479461982559265821032513430814466157143621342122370279507083617172056128378799, 56.09448479461982559265821032513430814466157143621342122370279507083618080690824673693]",
"[56.08754821423417686227712101945071969654507909451071395968580451338570559131609449699, 56.08754821423417686227712101945071969654507909451071395968580451338572579064890533831]",
"[56.08061163384852813189603171376713124842858675280800669566881395593523267011722474149, 56.08061163384852813189603171376713124842858675280800669566881395593527760205159625531]"
]
},
{
"lower_level": 3,
"upper_level": 4,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "22.23279092609037758133547758234223011196028885590727660142954302897011885468358717836757794088895615",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[22.24666408686167504209765619370940700819327353931269112946352414387104002414608640229, 22.24666408686167504209765619370940700819327353931269112946352414387104020701282021481]",
"[22.23972750647602631171656688802581856007678119760998386544653358642057943941483677346, 22.23972750647602631171656688802581856007678119760998386544653358642057962362734307891]",
"[22.23279092609037758133547758234223011196028885590727660142954302897011885468358717837, 22.23279092609037758133547758234223011196028885590727660142954302897011904024186590927]",
"[22.61248543515127540300648056404844137092095671128207364576553921748787016369069967646, 22.61248543515127540300648056404844137092095671128207364576553921748787036182086622662]",
"[23.53246579292568091292622253336796868202025731581308327709012917726952400669412013313, 23.53246579292568091292622253336796868202025731581308327709012917726952424704360540613]",
"[24.96579263751993788108594176790215237481468341970288874179726445508999266607468642774, 24.96579263751993788108594176790215237481468341970288874179726445508999300570909267774]",
"[26.95387082782685512641456717773367545611236519838059915350391213193501256857196114551, 26.95387082782685512641456717773367545611236519838059915350391213193501310826336705422]",
"[29.46070515977772398773524453552196843087466824900385556170543795976438663253014540675, 29.4607051597777239877352445355219684308746682490038555617054379597643875625214522388]",
"[32.14982864755526187604604290328295321031617779051393729741062432822285441235022728301, 32.14982864755526187604604290328295321031617779051393729741062432822285615309186986691]",
"[34.45284551648952959580606166605149178762232046928189892362050986260042093854292382104, 34.45284551648952959580606166605149178762232046928189892362050986260042453851876821771]",
"[35.92708971617191231678632679763064496812397028190185873283630298314278071399769017809, 35.92708971617191231678632679763064496812397028190185873283630298314278885950867619632]",
"[36.53289777739532264494501032754933514021027504091700929072120832797278922153307843711, 36.5328977773953226449450103275493351402102750409170092907212083279728085645118275232]",
"[36.51938880092688134159067263118726840392687114437203612379800130375742637292714158105, 36.51938880092688134159067263118726840392687114437203612379800130375747247770381804372]",
"[36.50587982445844003823633493482520166764346724782706295687479427954204636582724092418, 36.50587982445844003823633493482520166764346724782706295687479427954215352568227461289]"
]
},
{
"lower_level": 2,
"upper_level": 3,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "8.263662166930671150674808310311011703447063357305393222998702997597569311247068285535075329137132966",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[8.290680119867553757383483703035145176013871150395339556845117046028268216248434600424, 8.290680119867553757383483703035145176013871150395339556845117046028268430462234447303]",
"[8.27717114339911245402914600667307843973046725385036638992191002181291876374775144298, 8.277171143399112454029146006673078439730467253850366389921910021812918980582440238578]",
"[8.263662166930671150674808310311011703447063357305393222998702997597569311247068285535, 8.263662166930671150674808310311011703447063357305393222998702997597569530702646029853]",
"[8.355155378294392051864330325681473101498496187836919648180684160269202120328333553099, 8.355155378294392051864330325681473101498496187836919648180684160269202355860553177129]",
"[8.591218879480788321939143496060946766855496409241710164077274274586501436070593068371, 8.591218879480788321939143496060946766855496409241710164077274274586501723263049580482]",
"[8.962014289301551706653516519792913534075403963939416035628331952251508689551606718049, 8.962014289301551706653516519792913534075403963939416035628331952251509097115972647797]",
"[9.618816458658729682017061195075234018377917884892387884180112094120292976050785899986, 9.618816458658729682017061195075234018377917884892387884180112094120293631729933003868]",
"[10.69121438810019913319027842373768734239588048082409637223659982230575705995927779293, 10.69121438810019913319027842373768734239588048082409637223659982230575824176522284942]",
"[12.03068381502158239773661935612453848174095303519282931326631899036118146065852606779, 12.03068381502158239773661935612453848174095303519282931326631899036118390358382795862]",
"[13.24410725500675162565360965389478600521924680575821038779002904524398910691983480051, 13.24410725500675162565360965389478600521924680575821038779002904524399490041756830972]",
"[14.00961111966769304275454577649438695083692259405737701447185173537739964943858187075, 14.0096111196676930427545457764943869508369225940573770144718517353774145544715293921]",
"[14.30943733149330784717927201890735546588154696559665351547370794937906956167986445966, 14.30943733149330784717927201890735546588154696559665351547370794937910841047691609066]",
"[14.27923491244500183415394632545387485754946535242698210817324996230766264828641765605, 14.27923491244500183415394632545387485754946535242698210817324996230776091746450204594]",
"[14.2490324933966958211286206320003942492173837392573107008727919752362162774492753431, 14.24903249339669582112862063200039424921738373925731070087279197523645322836666003235]"
]
}
],
"pointwise_nonnegative_pair_energy_certified": true,
"second_is_unassigned_mathematical_control": false
},
{
"depth": 4,
"shell_levels": [
19,
71
],
"other_unsmoothed_chart_minimum_source_cost_lower_bound": "3.274338832282279419145460687730324734948352105043027097553147466050482861512657431409689040804272343",
"common_smoothing_width_interval": "[0.00000000002581063064296819424690279470796972440268404712337365137284454566576394061065317124291, 0.00000000002581063064296819424690279470796972440268404712337365137284454566576394561819719427741]",
"smoothing_bands": [
{
"lower_level": 70,
"upper_level": 71,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "16.40416415668200570167777105387383249314526802164309688423352174919914416593363977391704769333079888",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[16.49946169595074446985196019351729748426599315905729255078675401634607034503314601853, 16.49946169595074446985196019351729748426599315905729255078675401634607034505208375304]",
"[16.49946173060497132266893978409204445900838635281762860525960329717056258133058319454, 16.49946173060497132266893978409204445900838635281762860525960329717056258134952767605]",
"[16.49946176525919817548591937466679143375077954657796465973245257799505481762802037055, 16.49946176525919817548591937466679143375077954657796465973245257799505481764697159907]",
"[16.48610230757554521580183452293117986119904506576143214375717522762628500373988117747, 16.48610230757554521580183452293117986119904506576143214375717522762628500375899831489]",
"[16.45403956049120409829816702220372853192886600318307017532004835063521150712389568268, 16.45403956049120409829816702220372853192886600318307017532004835063521150714359316387]",
"[16.40416415668200570167777105387383249314526802164309688423352174919914416593363977392, 16.40416415668200570167777105387383249314526802164309688423352174919914416595470504204]",
"[16.61421401454996280918773956673699914417105669095121498940010175492977062355368057031, 16.61421401454996280918773956673699914417105669095121498940010175492977062357743296878]",
"[17.36459895075260878787544713412035319659697696127808037488810354171518096563003077392, 17.36459895075260878787544713412035319659697696127808037488810354171518096565860083878]",
"[18.55526764469880944990492036373348289428462023512104870089344575020213546786046051052, 18.5552676446988094499049203637334828942846202351210487008934457502021354678974186565]",
"[19.72571790313994513474051350425658352695761473602571549015820686552248188000028846531, 19.72571790313994513474051350425658352695761473602571549015820686552248188005217925516]",
"[20.47815022391055252291629534346642723982077758853555940902490138386288287905929864792, 20.4781502239105525229162953434664272398207775885355594090249013838628828791392732796]",
"[20.7916637104779439016086474812837313094713291556683621646473276164960957190689980448, 20.79166371047794390160864748128373130947132915566836216464732761649609571920485607499]",
"[20.79166374424090292201048778815390166689520885316568529410032259337290940854515361472, 20.7916637442409029220104877881539016668952088531656852941003225933729094087959283495]",
"[20.79166377800386194241232809502407202431908855066300842355331757024972309796013785336, 20.7916637780038619424123280950240720243190885506630084235533175702497230984481516468]"
]
},
{
"lower_level": 69,
"upper_level": 70,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "51.26046798854631962146737837874770280796901046092915147769376164020295553599625701634814057509613388",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[51.26046798854631962146737837874770280796901046092915147769376164020295553599625701635, 51.26046798854631962146737837874770280796901046092915147769376164020295553604269544889]",
"[51.26046802230927864186921868561787316539289015842647460714675661707976922552986709277, 51.26046802230927864186921868561787316539289015842647460714675661707976922557631233979]",
"[51.26046805607223766227105899248804352281676985592379773659975159395658291506347723666, 51.26046805607223766227105899248804352281676985592379773659975159395658291510992916322]",
"[51.53431966474149723045289876642929999487894312607748114631616239175672109772131939577, 51.53431966474149723045289876642929999487894312607748114631616239175672109776823355976]",
"[52.19156347800898141477659461770602867729778854722311147992440922129818132340126418914, 52.19156347800898141477659461770602867729778854722311147992440922129818132344982684926]",
"[53.21394272390050844125275643491579065703339824078397921320089292148562858177099032232, 53.2139427239005084412527564349157906570333982407839792132008929214856285818234552487]",
"[54.76041610081354249886603978429329544958828246127292339371806854538282563725786614628, 54.76041610081354249886603978429329544958828246127292339371806854538282563731797408183]",
"[56.93517199203571171550399410280670064288356552215236754065104108368888517751213376246, 56.93517199203571171550399410280670064288356552215236754065104108368888517758569678115]",
"[59.44824294944031881783802566715954772038344537356458575263766398065098343761849881895, 59.4482429494403188178380256671595477203834453735645857526376639806509834377143878177]",
"[61.67349918362000464359079486546210247577617631477813327774741395808163974607145234145, 61.67349918362000464359079486546210247577617631477813327774741395808163974620357020222]",
"[63.10402105944191639093795949558423060707982295615598077648519688311713899316342743338, 63.10402105944191639093795949558423060707982295615598077648519688311713899335491031681]",
"[63.70007185953581230561480431284037059362200310530002218366712956408940461541936200557, 63.70007185953581230561480431284037059362200310530002218366712956408940461571141948147]",
"[63.70007189156049658063124658977239738701049517495779401816031557696222346558905824058, 63.70007189156049658063124658977239738701049517495779401816031557696222346605876676392]",
"[63.70007192358518085564768886670442418039898724461556585265350158983504231568529306682, 63.70007192358518085564768886670442418039898724461556585265350158983504231647956385029]"
]
},
{
"lower_level": 68,
"upper_level": 69,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "90.56402009005353334308763069155029539563851001850449109342173973814985994382821765423418330216559171",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[90.56402009005353334308763069155029539563851001850449109342173973814985994382821765423, 90.56402009005353334308763069155029539563851001850449109342173973814985994389692026425]",
"[90.56402012207821761810407296848232218902700208816226292791492575102267879408676913353, 90.56402012207821761810407296848232218902700208816226292791492575102267879415547876043]",
"[90.56402015410290189312051524541434898241549415782003476240811176389549764434532074776, 90.56402015410290189312051524541434898241549415782003476240811176389549764441403725662]",
"[91.10885431352563280399905553634949482584657386900388123948213787433453148002940018146, 91.10885431352563280399905553634949482584657386900388123948213787433453148009881851395]",
"[92.41645625087398869844152846282251596282873022794743834661056358110674600122758486883, 92.41645625087398869844152846282251596282873022794743834661056358110674600129951416733]",
"[94.45050369048616669083604184370939552002832747581924371908229520400596751615600530753, 94.45050369048616669083604184370939552002832747581924371908229520400596751623388128277]",
"[97.25798006714181127260010421178243841838055337303717718550539038246385909253302596186, 97.25798006714181127260010421178243841838055337303717718550539038246385909262253890435]",
"[100.7769019901070596852950417950649854307447044993073680076567596629349250865440228103, 100.7769019901070596852950417950649854307447044993073680076567596629349250866539420745]",
"[104.538079873367661539444859443024884636865178773232150215553470054698160335521733554, 104.5380798733676615394448594430248846368651787732321502155534700546981603356651676293]",
"[107.7589558533791794094527004625861800860312818699017957004670203920293053032269784899, 107.7589558533791794094527004625861800860312818699017957004670203920293053034236488768]",
"[109.8295189932395693705236116430489881791110795798007922751534581505885524898549050983, 109.8295189932395693705236116430489881791110795798007922751534581505885524901356728754]",
"[110.6922536517102674106755363329248515455074215528505885781769184829748856466245021289, 110.692253651710267410675536332924851545507421552850588578176918482974885647040551978]",
"[110.6922536810486768202555456636722882128551760005293888799980885344399383844564225304, 110.6922536810486768202555456636722882128551760005293888799980885344399383850974044931]",
"[110.6922537103870862298355549944197248802029304482081891818192585859049911222071320462, 110.6922537103870862298355549944197248802029304482081891818192585859049911232354757205]"
]
},
{
"lower_level": 67,
"upper_level": 68,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "133.5525933929568817734684756374860475367005658011887652938668922242327047291755017915131847625773713",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[133.5525933929568817734684756374860475367005658011887652938668922242327047291755017915, 133.5525933929568817734684756374860475367005658011887652938668922242327047292724222726]",
"[133.5525934222952911830484849682334842040483202488675655956880622756977574671199095029, 133.5525934222952911830484849682334842040483202488675655956880622756977574672168375407]",
"[133.5525934516337005926284942989809208713960746965463658975092323271628102050643174842, 133.5525934516337005926284942989809208713960746965463658975092323271628102051612525389]",
"[134.3529493663331039740455214805741133637437424935484797224224675319006824456798125348, 134.3529493663331039740455214805741133637437424935484797224224675319006824457778697516]",
"[136.273803519924957364137630407169410295920332245283435091414137573083652045197788352, 136.273803519924957364137630407169410295920332245283435091414137573083652045299866245]",
"[139.2617988526714733483116660042338223984881766886694628647261643147635750187223956067, 139.261798852671473348311666004233822398488176688669462864726164314763575018834000813]",
"[143.258414011462035551060276876990667923312360637240335657740392395862176051917800672, 143.2584140114620355510602768769906679233123606372403356577403923958621760520480429999]",
"[148.0450564661871393057469786541336899948219908082696222841160776966441367018776250477, 148.0450564661871393057469786541336899948219908082696222841160776966441367020404950903]",
"[152.9835072261393139526680709103464004666946808759649251268760339559026493839156798495, 152.9835072261393139526680709103464004666946808759649251268760339559026493841319025221]",
"[157.1435646387450786815693029631763327378619413499855289727951996009222228090886588923, 157.1435646387450786815693029631763327378619413499855289727951996009222228093888394269]",
"[159.8178872694470084974166971717820215249450272829525371874374160480845959990492892377, 159.8178872694470084974166971717820215249450272829525371874374160480845959994798999368]",
"[160.9321883801677044701284429003230702708618309680048851489731642329156554577505417053, 160.9321883801677044701284429003230702708618309680048851489731642329156554583857337917]",
"[160.9321884057585213723823765658126857106211181972074375983881149134071821673320688525, 160.9321884057585213723823765658126857106211181972074375983881149134071821682966476461]",
"[160.9321884313493382746363102313023011503804054264099900478030655938987088768043544048, 160.9321884313493382746363102313023011503804054264099900478030655938987088783168767727]"
]
},
{
"lower_level": 66,
"upper_level": 67,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "179.4403109526759227554302133537825052647167380502675743875685262060055869566344739751763850986157592",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[179.4403109526759227554302133537825052647167380502675743875685262060055869566344739752, 179.440310952675922755430213353782505264716738050267574387568526206005586956759795846]",
"[179.4403109782667396576841470192721207044760252794701268369834768864971136663805541382, 179.4403109782667396576841470192721207044760252794701268369834768864971136665058841055]",
"[179.4403110038575565599380806847617361442353125086726792863984275669886403761266343013, 179.4403110038575565599380806847617361442353125086726792863984275669886403762519720951]",
"[180.4814280633778973633544410216190960235988406567841144150117300983054322948131717614, 180.4814280633778973633544410216190960235988406567841144150117300983054322949399960557]",
"[182.9801089695826347761298440464270190134091494811415616433299890958985143977788005445, 182.9801089695826347761298440464270190134091494811415616433299890958985143979109592921]",
"[186.8669459192578305249413182412922367142948840791664010070036824860296001046019798938, 186.8669459192578305249413182412922367142948840791664010070036824860296001047467801031]",
"[191.9840793363393826401806629425370170566431511958538449287964472841599204684111925955, 191.9840793363393826401806629425370170566431511958538449287964472841599204685807195047]",
"[197.9654262381718407660184342390052823814219395175355246496686841804845250861685052014, 197.9654262381718407660184342390052823814219395175355246496686841804845250863812850114]",
"[204.0134737071550460893049665816880033768057929494005094952336162776281875386281120873, 204.013473707155046089304966581688003376805792949400509495233616277628187538911445886]",
"[209.0587814749023057915683714801001825239744539977318819201467450551616191588528692127, 209.0587814749023057915683714801001825239744539977318819201467450551616191592466444939]",
"[212.302193617633816645324764200209688655754510975633556007380920174853103493633815538, 212.3021936176338166453247642002096886557545109756335560073809201748531034941975071657]",
"[213.653615355396142963129008785265999888840979540499555668114979376164587266397260383, 213.6536153553961429631290087852659998888409795404995556681149793761645872672234437659]",
"[213.6536153760508057524419906909468778191277001554949414336562371221946907878241882968, 213.6536153760508057524419906909468778191277001554949414336562371221946907890645159042]",
"[213.6536153967054685417549725966277557494144207704903271991974948682247943091215672052, 213.6536153967054685417549725966277557494144207704903271991974948682247943110351729421]"
]
},
{
"lower_level": 65,
"upper_level": 66,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "227.5077485665706807289454860175283566327928681957666528322625461486392955762712376073653817807879209",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[227.5077485665706807289454860175283566327928681957666528322625461486392955762712376074, 227.5077485665706807289454860175283566327928681957666528322625461486392955764117289083]",
"[227.5077485872253435182584679232092345630795888107620385978038038946693990979051264428, 227.5077485872253435182584679232092345630795888107620385978038038946693990980456266497]",
"[227.5077486078800063075714498288901124933663094257574243633450616406995026195390152782, 227.5077486078800063075714498288901124933663094257574243633450616406995026196795241214]",
"[228.7755053783570737158470988536082587402567082115055569508186573311384539971054996687, 228.7755053783570737158470988536082587402567082115055569508186573311384539972477586853]",
"[231.8181215975391200321971353424044340914907582441427548408826036242668391898786856137, 231.8181215975391200321971353424044340914907582441427548408826036242668391900272279827]",
"[236.5510801475514160827189144881661765941874111549222604500009834676436148988771637999, 236.5510801475514160827189144881661765941874111549222604500009834676436148990406003211]",
"[242.7230725345406425960599700242977895472480261957567260557446991412395412754270212599, 242.7230725345406425960599700242977895472480261957567260557446991412395412756195951343]",
"[249.8292389150205457366717592717338318818394109661967431498448167133655844951448588458, 249.8292389150205457366717592717338318818394109661967431498448167133655844953883836857]",
"[256.9220904401214025682687578846259957859459917631258588976067201700970639686293240235, 256.9220904401214025682687578846259957859459917631258588976067201700970639689558526987]",
"[262.8010070260549108821289978948462358845469069201724503280315925559803462024261370577, 262.8010070260549108821289978948462358845469069201724503280315925559803462028822039431]",
"[266.5803105494126129081007959445827702445602781622238281419646233934148663353421782443, 266.5803105494126129081007959445827702445602781622238281419646233934148663359963944607]",
"[268.1550203586771313921970742137536662840995563279022111857404138824362416402610501706, 268.1550203586771313921970742137536662840995563279022111857404138824362416412185421783]",
"[268.1550203730640764837202253748576872954712553778523503592075795936270083793571076959, 268.1550203730640764837202253748576872954712553778523503592075795936270083807869970441]",
"[268.1550203874510215752433765359617083068429544278024895326747453048177751183111785138, 268.1550203874510215752433765359617083068429544278024895326747453048177751204975120247]"
]
},
{
"lower_level": 64,
"upper_level": 65,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "277.0972067873500087743939497600403480313104039794618514711232838534442038861808981540410001640798468",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[277.097206787350008774393949760040348031310403979461851471123283853444203886180898154, 277.0972067873500087743939497600403480313104039794618514711232838534442038863569842333]",
"[277.0972068017369538659171009211443690426821030294119906445904495646349706255130253468, 277.0972068017369538659171009211443690426821030294119906445904495646349706256891216815]",
"[277.0972068161238989574402520822483900540538020793621298180576152758257373648451530794, 277.09720681612389895744025208224839005405380207936212981805761527582573736502125859]",
"[278.5780658560559464365127764407372745232444205183670612480389213234030675813955788741, 278.5780658560559464365127764407372745232444205183670612480389213234030675815739335668]",
"[282.1321275304467113311560432774096273866275207068820382634271853417557660609372633574, 282.1321275304467113311560432774096273866275207068820382634271853417557660611236901689]",
"[287.6606679027386806457503032712502110523747227200662177892394096119978816498544471778, 287.6606679027386806457503032712502110523747227200662177892394096119978816500600106593]",
"[294.8245656636032441292548890667971080299471806931243162336855079786706559802677368927, 294.8245656636032441292548890667971080299471806931243162336855079786706559805107262902]",
"[302.9885276990889857226993308594026786366340248692898975906387698575880088523145855225, 302.9885276990889857226993308594026786366340248692898975906387698575880088526229879594]",
"[311.064025738683278957383426942155144937264195699811909377973002148391319896803667075, 311.0640257386832789573834269421551449372641956998119093779730021483913198972185200051]",
"[317.7270020101643104061934558066086417308345063299672953887951592833582544318629182237, 317.7270020101643104061934558066086417308345063299672953887951592833582544324435278357]",
"[322.0103438997445348728341618301227363114157072964203200857665029875689564294413981059, 322.0103438997445348728341618301227363114157072964203200857665029875689564302745265876]",
"[323.7950696902931364092692697760239392142508162031168656829005193390617291446002166011, 323.7950696902931364092692697760239392142508162031168656829005193390617291458173037391]",
"[323.7950696969199426780534692020788891561411640184369008693704872962103202910085822648, 323.7950696969199426780534692020788891561411640184369008693704872962103202928182924651]",
"[323.7950697035467489468376686281338390980315118337569360558404552533589114372439746484, 323.795069703546748946837668628133839098031511833756936055840455253358911439992241517]"
]
},
{
"lower_level": 63,
"upper_level": 64,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "327.6083957744427560539002311501572650239584935798588089870893624948133866740994789831645810057998607",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[327.6083957744427560539002311501572650239584935798588089870893624948133866740994789832, 327.6083957744427560539002311501572650239584935798588089870893624948133866742863214103]",
"[327.6083957810695623226844305762122149658488413951788441735593304519619778208041456527, 327.6083957810695623226844305762122149658488413951788441735593304519619778209909999546]",
"[327.608395787696368591468630002267164907739189210498879360029298409110568967508812862, 327.6083957876963685914686300022671649077391892104988793600292984091105689676956779591]",
"[329.289353666828731095935102860281707203768520885187129155031947881375988741556382651, 329.2893536668287310959351028602817072037685208851871291550319478813759887417454737206]",
"[333.3236525658742631367412081560548819602011304908660493591746847525383719138412081701, 333.3236525658742631367412081560548819602011304908660493591746847525383719140382828378]",
"[339.5992286248059948527459671607267118979741365822474816899612097292941224094512389116, 339.5992286248059948527459671607267118979741365822474816899612097292941224096672289474]",
"[347.6945523662892168726338602870603694629516081559785774283110867189091386087746243017, 347.6945523662892168726338602870603694629516081559785774283110867189091386090275987294]",
"[356.8519027391488644475748643717083698058246751899999018197840233943969919471828700911, 356.8519027391488644475748643717083698058246751899999018197840233943969919475004646499]",
"[365.85029969336481947746493601129248006962124194648402476905540692766110632853763599, 365.8502996933648194774649360112924800696212419464840247690554069276611063289603219249]",
"[373.2497001908904534091355917300269644841630857860772174260213907814705913347218307133, 373.2497001908904534091355917300269644841630857860772174260213907814705913353079394056]",
"[378.0064576506653724501075363390052188572179211807262582787624647594483615243856026574, 378.0064576506653724501075363390052188572179211807262582787624647594483615252200632681]",
"[379.9884399231626519161357031577214527700512570738968371189437558244408576340879687878, 379.9884399231626519161357031577214527700512570738968371189437558244408576352985361584]",
"[379.9884399203557786911828862146594684753631326353241804297600345771545707491018624426, 379.9884399203557786911828862146594684753631326353241804297600345771545707508896400133]",
"[379.9884399175489054662300692715974841806750081967515237405763133298682838639504792626, 379.9884399175489054662300692715974841806750081967515237405763133298682838666460568668]"
]
},
{
"lower_level": 62,
"upper_level": 63,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "378.4944857922303805882766263297629065846006278672424596896045944433927010359724376498955094138183996",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[378.4944857978441270381822602158868751739768767443877730679720369379652748053674390608, 378.4944857978441270381822602158868751739768767443877730679720369379652748055525666687]",
"[378.4944857950372538132294432728248908792887523058151163787883156906789879206699383553, 378.4944857950372538132294432728248908792887523058151163787883156906789879208550789175]",
"[378.4944857922303805882766263297629065846006278672424596896045944433927010359724376499, 378.4944857922303805882766263297629065846006278672424596896045944433927010361575911664]",
"[380.3630277615677059699165788079886850678621108775800251365208483678953034461680029514, 380.3630277615677059699165788079886850678621108775800251365208483678953034463552809653]",
"[384.8475284899859268692264905273115267415806928497973052397754382028871164012492630007, 384.847528489985926869226490527311526741580692849797305239775438202887116401444156496]",
"[391.8234185104345279794698721397172732804484211614157223710012084068960438098654814074, 391.8234185104345279794698721397172732804484211614157223710012084068960438100784207167]",
"[400.7919530610559723152902827338955848511155789090842359577729544388796669088155880514, 400.7919530610559723152902827338955848511155789090842359577729544388796669090638142056]",
"[410.8806789864215458427290526077079151442429103880389836487522227049327471245665632721, 410.8806789864215458427290526077079151442429103880389836487522227049327471248764457324]",
"[420.7444328280776079575207739933143049119776112911662962392808099642590319649961112713, 420.7444328280776079575207739933143049119776112911662962392808099642590319654062434557]",
"[428.8343735171231492520449483836242339343582534516340384806016010607293305097169509969, 428.8343735171231492520449483836242339343582534516340384806016010607293305102828731849]",
"[434.0350496670449972786898576186344969856631530819127655661753056045383205556121240173, 434.0350496670449972786898576186344969856631530819127655661753056045383205564144543026]",
"[436.2019980536930292907682074365535872897760113504199345763281905438019820588305904337, 436.2019980536930292907682074365535872897760113504199345763281905438019820599900608335]",
"[436.2019980395747884342576060477653383221792440309173472725906532933803267923840976618, 436.2019980395747884342576060477653383221792440309173472725906532933803267940897199008]",
"[436.2019980254565475777470046589770893545824767114147599688531160429586715257830676706, 436.201998025456547577747004658977089354582476711414759968853116042958671528343874626]"
]
},
{
"lower_level": 61,
"upper_level": 62,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "429.2584820389322763865341697210622843276776751725375908692862398210223914037519698750764934245082714",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[429.2584820671687580995553724986387822628712098115427654767613143218657019360987900856, 429.2584820671687580995553724986387822628712098115427654767613143218657019362990201933]",
"[429.2584820530505172430447711098505332952744424920401781730237770714440466699253799803, 429.2584820530505172430447711098505332952744424920401781730237770714440466701256252013]",
"[429.2584820389322763865341697210622843276776751725375908692862398210223914037519698751, 429.2584820389322763865341697210622843276776751725375908692862398210223914039522296696]",
"[431.3025408586529946240795442451245600971067222646736471112205308490705943370079472089, 431.3025408586529946240795442451245600971067222646736471112205308490705943372104950484]",
"[436.2082820434601031045953732835260447994665048279643019111767427161477152142346928363, 436.2082820434601031045953732835260447994665048279643019111767427161477152144454461154]",
"[443.8394350017615489453474536606061844039456029368031400702701941236320501601138443276, 443.8394350017615489453474536606061844039456029368031400702701941236320501603440500366]",
"[453.6250386638873498993716353794034296472894904644916251836625469086787669284239861746, 453.6250386638873498993716353794034296472894904644916251836625469086787669286922450013]",
"[464.585320194479501951857515249533954187163154943780891729396737686022522963593987703, 464.5853201944795019518575152495339541871631549437808917293967376860225229639287444878]",
"[475.2589087193500458170237439719348866132922812297745777654850455712666042869607684862, 475.2589087193500458170237439719348866132922812297745777654850455712666042874036355278]",
"[483.995109501286028984421916582378233405030290927648792845747228699649657513279955116, 483.9951095012860289844219165823782334050302909276487928457472286996496575138907405804]",
"[489.6112385628666229363279273011981016710519321202889275421724222854417500188087289963, 489.6112385628666229363279273011981016710519321202889275421724222854417500196740536541]",
"[491.9512923213808880132264743043398654536120913432965876000583519487430410297062575357, 491.9512923213808880132264743043398654536120913432965876000583519487430410309554048303]",
"[491.9512922938432309018295514751774493426162944123151456251571154398479044081423303282, 491.9512922938432309018295514751774493426162944123151456251571154398479044099768587178]",
"[491.9512922663055737904326286460150332316204974813337036502558789309527677864144082172, 491.9512922663055737904326286460150332316204974813337036502558789309527677891624948058]"
]
},
{
"lower_level": 60,
"upper_level": 61,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "479.4498874881108769270232218899926245038495546850451320117056412649652237488417675186015768085088032",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[479.449887543186191149817067548317456725841148547008015961508114282755496991384559837, 479.4498875431861911498170675483174567258411485470080159615081142827554969915989214153]",
"[479.4498875156485340384201447191550406148453516160265739866068777738603603701131634079, 479.4498875156485340384201447191550406148453516160265739866068777738603603703275427983]",
"[479.4498874881108769270232218899926245038495546850451320117056412649652237488417675186, 479.4498874881108769270232218899926245038495546850451320117056412649652237490561641813]",
"[481.6578059701456397129326176567126098523051415145593924336967444363276773280641367068, 481.6578059701456397129326176567126098523051415145593924336967444363276773282809855016]",
"[486.9568103628804175386571568073846585534551128381367182813311934111472922863412901809, 486.9568103628804175386571568073846585534551128381367182813311934111472922865669230387]",
"[495.1997060958586590796852492927810009322057845611496606112930518313392223661155704258, 495.1997060958586590796852492927810009322057845611496606112930518313392223663620142908]",
"[505.7481370846559630285336231431890657881287969574915894836400983395036094742327794541, 505.7481370846559630285336231431890657881287969574915894836400983395036094745199147862]",
"[517.5221635442637507328547669419169151680142391867322588207000751954929554060120024954, 517.5221635442637507328547669419169151680142391867322588207000751954929554063702221309]",
"[528.9519152746163770864512414072166952991722102972177721748234162159960344556043160152, 528.9519152746163770864512414072166952991722102972177721748234162159960344560780519618]",
"[538.2915657016614809726716938385822456587148524023883149045602777951431248073921287332, 538.2915657016614809726716938385822456587148524023883149045602777951431248080451893222]",
"[544.295626671859132415830825840567634175270976219456034713296354174528687015090985253, 544.295626671859132415830825840567634175270976219456034713296354174528687016015646866]",
"[546.7973187162370076628794080358715517062455732980604802306340272130885093143114287753, 546.79731871623700766287940803587155170624557329806048023063402721308850931564512416]",
"[546.7973186729116372074822972004883228034460278977504564077099677067171722213671714055, 546.79731867291163720748229720048832280344602789775045640770996770671717222332360903]",
"[546.7973186295862667520851863651050939006464824974404325847859082003458351282493864214, 546.7973186295862667520851863651050939006464824974404325847859082003458351311755923672]"
]
},
{
"lower_level": 59,
"upper_level": 60,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "528.6616215574683535079297039365073885824575947948251521014724218953485978629122736266787959105467474",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[528.6616216441190944187239256072738463880566855954451997473205409080912720481783321995, 528.6616216441190944187239256072738463880566855954451997473205409080912720484071906662]",
"[528.6616216007937239633268147718906174852571401951351759243964814017199349555453029131, 528.6616216007937239633268147718906174852571401951351759243964814017199349557741818907]",
"[528.6616215574683535079297039365073885824575947948251521014724218953485978629122736267, 528.6616215574683535079297039365073885824575947948251521014724218953485978631411731152]",
"[531.0221184219793734513412721446393701111741522094934826116836499854118589672921232173, 531.0221184219793734513412721446393701111741522094934826116836499854118589675239924683]",
"[536.6873109542946949630042920645252831868539537773763172739194082130647494215643595948, 536.6873109542946949630042920645252831868539537773763172739194082130647494218068675259]",
"[545.4998326901971845717406147191828439328302853883435992502747922201980852539773162919, 545.4998326901971845717406147191828439328302853883435992502747922201980852542450288809]",
"[556.7585909082107255125467884390681634767781464829321234028085479868995381274058613723, 556.7585909082107255125467884390681634767781464829321234028085479868995381277228476211]",
"[569.2903935069048776849649102759739638502482038786771935867331671993665378171927506089, 569.2903935069048776849649102759739638502482038786771935867331671993665378175958005953]",
"[581.4243334653175560921849036392823783047009395999197357128889653070287145393475042482, 581.4243334653175560921849036392823783047009395999197357128889653070287145398903867579]",
"[591.3259702483050746175739929691267927318890037817979008098633541702958343024647804047, 591.3259702483050746175739929691267927318890037817979008098633541702958343032246725578]",
"[597.6913081545043015842552443478397574779056401871465499336349684823999740789740523689, 597.6913081545043015842552443478397574779056401871465499336349684823999740800624805666]",
"[600.3435322445796945776027262412429351080300717711886792756956367838335293669101062484, 600.3435322445796945776027262412429351080300717711886792756956367838335293684929820839]",
"[600.3435321828039285475504553265868288089864528799260281759635379051123050567510078262, 600.3435321828039285475504553265868288089864528799260281759635379051123050590859870702]",
"[600.3435321210281625174981844119307225099428339886633770762314390263910807463831343472, 600.343532121028162517498184411930722509942833988663377076231439026391080749888006767]"
]
},
{
"lower_level": 58,
"upper_level": 59,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "576.5271662773085266950887319442330995318258693406022098792672698148671312612529454145430400464289444",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[576.5271664008600587551932737735453121299131071231275120787314675723095798808198096285, 576.527166400860058755193273773545312129913107123127512078731467572309579881062645734]",
"[576.5271663390842927251410028588892058308694882318648609789993686935883555710363769818, 576.5271663390842927251410028588892058308694882318648609789993686935883555712792379163]",
"[576.5271662773085266950887319442330995318258693406022098792672698148671312612529454145, 576.527166277308526695088731944233099531825869340602209879267269814867131261495829019]",
"[579.0293049582826496370101867574803358267904671281437884539733306551326655933773989778, 579.0293049582826496370101867574803358267904671281437884539733306551326655936237888667]",
"[585.0344378754157809451392777251973294403349443619596604351266237380879539808177021445, 585.0344378754157809451392777251973294403349443619596604351266237380879539810766468634]",
"[594.3757557748848412450115679467194778334060252862765532028205544522997564918790859777, 594.3757557748848412450115679467194778334060252862765532028205544522997564921677715021]",
"[606.2939382361044561849344055818553506104505687311189614837469057870822416309747761698, 606.293938236104456184934405581855350610450568731118961483746905787082241631321604699]",
"[619.5292370918711942683627184554464968790364970932797344620557551067250146595156484435, 619.5292370918711942683627184554464968790364970932797344620557551067250146599640296787]",
"[632.3169458175428693542690045424563837620314833286682719177443036061343233071931485286, 632.3169458175428693542690045424563837620314833286682719177443036061343233078065313207]",
"[642.7403408372369981872007603802313579981505577053438838207707228254955741360191804353, 642.7403408372369981872007603802313579981505577053438838207707228254955741368886267046]",
"[649.4410947445083723532801175071508114258507331558908973053429622475551730590852830172, 649.4410947445083723532801175071508114258507331558908973053429622475551730603423723483]",
"[652.2330754889534873233397361067783328900654225551652223838826008839234295199510177912, 652.2330754889534873233397361067783328900654225551652223838826008839234295217914867853]",
"[652.2330754057311994655729316614861542712205448696051334126645483211208344222223922446, 652.2330754057311994655729316614861542712205448696051334126645483211208344249501422756]",
"[652.2330753225089116078061272161939756523756671840450444414464957583182393242474599322, 652.233075322508911607806127216193975652375667184045044441446495758318239328355202768]"
]
},
{
"lower_level": 57,
"upper_level": 58,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "622.7179145717923567458417850040019190184013267333129843793110283122771647198990370805369326251238001",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[622.7179147382369324613753938945862762560910821044331623217471334378823549144692198025, 622.7179147382369324613753938945862762560910821044331623217471334378823549147365556387]",
"[622.7179146550146446036085894492940976372462044188730733505290808750797598171841284415, 622.7179146550146446036085894492940976372462044188730733505290808750797598174514923453]",
"[622.7179145717923567458417850040019190184013267333129843793110283122771647198990370805, 622.7179145717923567458417850040019190184013267333129843793110283122771647201664290518]",
"[625.3510746372435133387605279176946497708738471761976962005825352039088777001701215021, 625.351074637243513338760527917694649770873847176197696200582535203908877700441181686]",
"[631.6706589065556740358626675747208718022115499949027153234600883342978091117569399549, 631.6706589065556740358626675747208718022115499949027153234600883342978091120411281945]",
"[641.5011233648212304992789311587259899988563037966563269235817663628290748701134279266, 641.501123364821230499278931158725989998856303796656326923581766362829074870428704214]",
"[654.0292917211121829023358770667250598101659498214257636742334566578730094003702395552, 654.029291721112182902335877066725059810165949821425763674233456657873009400746276686]",
"[667.9153556570578594985242033364403830978723608955155159320770180006232784062446733104, 667.9153556570578594985242033364403830978723608955155159320770180006232784067268230441]",
"[681.3078399674877101623069104548328793593081535730663209484414869302537668228629594314, 681.3078399674877101623069104548328793593081535730663209484414869302537668235175194752]",
"[692.2138976028614760471758068834456950732171132515611780385359360147560963307295636364, 692.2138976028614760471758068834456950732171132515611780385359360147560963316517024086]",
"[699.2249346106946160950190252828489883418930447482732052705877932195701158524822196352, 699.2249346106946160950190252828489883418930447482732052705877932195701158538095220961]",
"[702.146199965632135257733158648157855779927572917439205275205635553022351528817480658, 702.1461999656321352577331586481578557799275729174392052752056355530223515307547449087]",
"[702.1461998575889816905866489625707424461261062346255115965929854632455511974122009613, 702.1461998575889816905866489625707424461261062346255115965929854632455512002776795288]",
"[702.1461997495458281234401392769836291123246395518118179179803353734687508657486415307, 702.1461997495458281234401392769836291123246395518118179179803353734687508700587664994]"
]
},
{
"lower_level": 56,
"upper_level": 57,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "666.9406980237713431776925172879531360931900664469666804347294936405532670429980711417117874101654561",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[666.9406982398576503119855366591273627607929998125940677919547938201068677048797836189, 666.9406982398576503119855366591273627607929998125940677919547938201068677051328438685]",
"[666.9406981318144967448390269735402494269915331297803741133421437303300673739389268406, 666.9406981318144967448390269735402494269915331297803741133421437303300673741920205553]",
"[666.9406980237713431776925172879531360931900664469666804347294936405532670429980711417, 666.9406980237713431776925172879531360931900664469666804347294936405532670432511961625]",
"[669.6945489012697808423045283713302448824065954968760604737497980480411828226510922138, 669.694548901269780842304528371330244882406595496876060473749798048041182822908025785]",
"[676.3037911535778155514021593621735970823372431117816635929013037989269078196517319916, 676.3037911535778155514021593621735970823372431117816635929013037989269078199222891186]",
"[686.5848347092185444124182644472176997061629270094919111835718641962147104067068303658, 686.5848347092185444124182644472176997061629270094919111835718641962147104070096457414]",
"[699.6748934477333601492900745902307923975287821579297226346597786614496978755962762234, 699.6748934477333601492900745902307923975287821579297226346597786614496978759621377885]",
"[714.1604110542540967769312905417533840756429552740446603745849851882483540547119748825, 714.1604110542540967769312905417533840756429552740446603745849851882483540551879389606]",
"[728.109985163873096766860975691938776775249241702211720965077520803663059690823783727, 728.1099851638730967668609756919387767752492417022117209650775208036630596914786535933]",
"[739.4606478361624079121522296773040046809843358402674311402981452878046590796483860926, 739.460647836162407912152229677304004680984335840267431140298145287804659080580989742]",
"[746.7575023567667791731592869754846661461710287692439625872242870598315159955700086966, 746.757502356766779173159286975484666146171028769243962587224287059831515996923360001]",
"[749.7978583250313443720117134154133571699723874938060578515869701190224939371292564818, 749.7978583250313443720117134154133571699723874938060578515869701190224939391165910788]",
"[749.7978581883633403938367194463816227213657297933779946539728566592533227370888406271, 749.7978581883633403938367194463816227213657297933779946539728566592533227400422030049]",
"[749.7978580516953364156617254773498882727590720929499314563587431994841515367785563798, 749.7978580516953364156617254773498882727590720929499314563587431994841515412379154206]"
]
},
{
"lower_level": 55,
"upper_level": 56,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "708.9354737802999761210719154424175230871657821556103815321017068742258292575740159336622289684572203",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[708.9354740536359840774219033804809919843790975564665079273299337937641716566891318439, 708.9354740536359840774219033804809919843790975564665079273299337937641716569659232051]",
"[708.9354739169679800992469094114492575357724398560384447297158203339950004571315738888, 708.9354739169679800992469094114492575357724398560384447297158203339950004574084030332]",
"[708.9354737802999761210719154424175230871657821556103815321017068742258292575740159337, 708.9354737802999761210719154424175230871657821556103815321017068742258292578508828614]",
"[711.7999504991881129422112883991054430695105791378581869996589676242231546896031284764, 711.7999504991881129422112883991054430695105791378581869996589676242231546898839324174]",
"[718.6746948101531714310523243109500483319385461956991414139427358691541750045081306564, 718.6746948101531714310523243109500483319385461956991414139427358691541750048030126317]",
"[729.3687415828385989259794444973577821098082665506431287457597505835767345600435752589, 729.3687415828385989259794444973577821098082665506431287457597505835767345603717863677]",
"[742.9738255577049312931481554573454686345205775358203902913832146375556836935684455267, 742.9738255577049312931481554573454686345205775358203902913832146375556836939618057321]",
"[758.0087861072599577517479573364931750692989609293789113470791712950639184685382542289, 758.0087861072599577517479573364931750692989609293789113470791712950639184690454089092]",
"[772.46896180331232410821214583006291916711814168782719096673743434055969645720850388, 772.468961803312324108212145830062919167118141687827190966737434340559696457900610746]",
"[784.2271227043068717433483746853909281689157875142495794958590707852346606348619215031, 784.2271227043068717433483746853909281689157875142495794958590707852346606358412770511]",
"[791.7859403593475760555224556430775640840170245853592675427801931013311265885591290768, 791.7859403593475760555224556430775640840170245853592675427801931013311265899740001278]",
"[794.9354476140905723179706483524317092352563484140731830880137104214806810561991619861, 794.9354476140905723179706483524317092352563484140731830880137104214806810582710878541]",
"[794.9354474445049140510340029974717717189319260806224416586899913094813425746158624092, 794.9354474445049140510340029974717717189319260806224416586899913094813425776907874955]",
"[794.9354472749192557840973576425118342026075037471717002293662721974820040927505606228, 794.9354472749192557840973576425118342026075037471717002293662721974820040973926577517]"
]
},
{
"lower_level": 54,
"upper_level": 55,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "748.4731522243859351612725137683064569687862013058811030693223946314286484516397573294279391860641514",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[748.4731525635572516951458044782263320014350459727825859279698328554273254138040373632, 748.4731525635572516951458044782263320014350459727825859279698328554273254140812292267]",
"[748.4731523939715934282091591232663944851106236393318444986461137434279869327218968065, 748.47315239397159342820915912326639448511062363933184449864611374342798693299913401]",
"[748.4731522243859351612725137683064569687862013058811030693223946314286484516397573294, 748.4731522243859351612725137683064569687862013058811030693223946314286484519170377137]",
"[751.4384329024521702107120172769043872635688037582371065740905893225224573450136463548, 751.4384329024521702107120172769043872635688037582371065740905893225224573452958612298]",
"[758.5551067606781108025305455849668091395450031281132988621569720584580638516997528879, 758.5551067606781108025305455849668091395450031281132988621569720584580638519996157735]",
"[769.6254884015742208825059988120027011044057455313199361204564320861146313119967599313, 769.6254884015742208825059988120027011044057455313199361204564320861146313123384132364]",
"[783.6998584383327463145888880178421760817480917631605452365248692880818582039602678013, 783.6998584383327463145888880178421760817480917631605452365248692880818582043836117044]",
"[799.2354413182940224734678607654031742393286972209314455177173594727934160664247402805, 799.2354413182940224734678607654031742393286972209314455177173594727934160669907860737]",
"[814.160825964376533469554682605288044905466434409466606379246340138643667586230406573, 814.1608259643765334695546826052880449054664344094666063792463401386436675870284500802]",
"[826.2902479923700806648849442441568706672077062030732079388917686563733043072472829831, 826.2902479923700806648849442441568706672077062030732079388917686563733043084058239152]",
"[834.087733500338329803939257771606566446598372837130648553158822847247839996283532383, 834.0877335003383298039392577716065664465983728371306485531588228472478399979891443665]",
"[837.3366856713917288181289969532358347145762352864658912296643510784529935373013384734, 837.3366856713917288181289969532358347145762352864658912296643510784529935398335494554]",
"[837.3366854640385487557559462079998671034216179936873837406367427633348656690139662594, 837.3366854640385487557559462079998671034216179936873837406367427633348656728106256677]",
"[837.3366852566853686933828954627638994922670007009088762516091344482167378003684294656, 837.3366852566853686933828954627638994922670007009088762516091344482167378061458124838]"
]
},
{
"lower_level": 53,
"upper_level": 54,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "785.35354871554023650391899477594036354514432086587207726578978795469113709122957420851721329789416",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[785.3535491302465966286650962664122987674535554514290922438450045849273928265396165227, 785.3535491302465966286650962664122987674535554514290922438450045849273928268432534139]",
"[785.3535489228934165662920455211763311562989381586505847548173962698092649588845953656, 785.3535489228934165662920455211763311562989381586505847548173962698092649591882840738]",
"[785.3535487155402365039189947759403635451443208658720772657897879546911370912295742085, 785.3535487155402365039189947759403635451443208658720772657897879546911370915333136542]",
"[788.4100335303284873698357445564491965645148928077503440605326747834295234038934842897, 788.4100335303284873698357445564491965645148928077503440605326747834295234042027444061]",
"[795.7455973685984456012152039020966922906747322915068028865065232427274661142689337796, 795.7455973685984456012152039020966922906747322915068028865065232427274661145979426545]",
"[807.1564745534372533609156274776626550584317638682183100233408023168921958247866749557, 807.1564745534372533609156274776626550584317638682183100233408023168921958251624594785]",
"[821.6554199213993728044963842182802921083950698837054714046524216997206495272386300115, 821.6554199213993728044963842182802921083950698837054714046524216997206495277058694003]",
"[837.6438913088780964019343874973116056300819970036366558392468722547746307464933437001, 837.6438913088780964019343874973116056300819970036366558392468722547746307471203802747]",
"[852.9900924989150981034220438933618246773040460334510791323354136194604909838319989606, 852.9900924989150981034220438933618246773040460334510791323354136194604909847189021651]",
"[865.4553324666721876513349718421100638736708170119160448790692814242225922338334629636, 865.4553324666721876513349718421100638736708170119160448790692814242225922351244222682]",
"[873.4687009194050898343327091157274504038208577765548874338215626838969416147663567557, 873.4687009194050898343327091157274504038208577765548874338215626838969416166711565693]",
"[876.8076042917845202043094645045543786332605389735189229620546288858380988268510879681, 876.8076042917845202043094645045543786332605389735189229620546288858380988296850110553]",
"[876.8076040411780179769669620731910538210064999268918924841042433607988579926304247007, 876.8076040411780179769669620731910538210064999268918924841042433607988579968891687846]",
"[876.8076037905715157496244596418277290087524608802648620061538578357596171580026686404, 876.8076037905715157496244596418277290087524608802648620061538578357596171645002357882]"
]
},
{
"lower_level": 52,
"upper_level": 53,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "819.4034441183271349974711375079553135941552814984234590744310660472617227857272492529966957908922413",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[819.4034446195401394521561423706819632186633595916775200303318370973402044527429170827, 819.4034446195401394521561423706819632186633595916775200303318370973402044530366310163]",
"[819.4034443689336372248136399393186384064093205450504895523814515723009636192350831679, 819.4034443689336372248136399393186384064093205450504895523814515723009636195288575546]",
"[819.403444118327134997471137507955313594155281498423459074431066047261722785727249253, 819.4034441183271349974711375079553135941552814984234590744310660472617227860210830134]",
"[822.541735511770111780341668964039024864692267160925248737790282256315983463232233833, 822.5417355117701117803416689640390248646922671609252487377902822563159834635307775438]",
"[830.0736351982745864083891367831680717581798052077046052908326152878338376652986111371, 830.073635198274586408389136783168071758179805207704605290832615287833837665613969468]",
"[841.7899237248603399872006531908568461905908032052281480900100478841752614271767898247, 841.7899237248603399872006531908568461905908032052281480900100478841752614275319565747]",
"[856.6696703112415522445698378919892774742189831702346731667743066974647798412838280727, 856.6696703112415522445698378919892774742189831702346731667743066974647798417168315303]",
"[873.0642858532566317300983855220575304614903218114828244080187772203861062603904820845, 873.0642858532566317300983855220575304614903218114828244080187772203861062609595105944]",
"[888.7878215736694434773983637698117085997987888805243224642243303591771271680414329937, 888.7878215736694434773983637698117085997987888805243224642243303591771271688317687204]",
"[901.5541587799268248220539976772221743835363534687754895572762036729629369152050286384, 901.554158779926824822053997677222174383536353468775489557276203672962936916339763972]",
"[909.7610897242518117259557988603470977644348957525812314450381292157478563465965621573, 909.7610897242518117259557988603470977644348957525812314450381292157478563482553196878]",
"[913.1806441054541346511880804243454281423244883989258213496908090964852314023564670359, 913.1806441054541346511880804243454281423244883989258213496908090964852314048103490486]",
"[913.1806438053812244924021137164847796354555664601781442606552290055369099115262635945, 913.18064380538122449240211371648477963545556646017814426065522900553690991520375899]",
"[913.1806435053083143336161470086241311285866445214304671716196489145885884203422816674, 913.1806435053083143336161470086241311285866445214304671716196489145885884259508006023]"
]
},
{
"lower_level": 51,
"upper_level": 52,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "850.4747400179967895973084405045133473170187414392662708803768652886328448278566867561260988122756614",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[850.4747406181426099148803739202346443307565853167616250584480254705294878082931196961, 850.4747406181426099148803739202346443307565853167616250584480254705294878085954276968]",
"[850.4747403180696997560944072123739958238876633780139479694124453795811663180749032261, 850.4747403180696997560944072123739958238876633780139479694124453795811663183772813957]",
"[850.4747400179967895973084405045133473170187414392662708803768652886328448278566867561, 850.4747400179967895973084405045133473170187414392662708803768652886328448281591340151]",
"[853.685623887667082292459374507756179834021188047019345917155465695513935363064025967, 853.6856238876670822924593745077561798340211880470193459171554656955139353633712814128]",
"[861.3917455851318617551559931800118601124159447623037604240834126495458415781499849071, 861.3917455851318617551559931800118601124159447623037604240834126495458415784743885451]",
"[873.3790461542533056327158334220106613337399484342286517255041584181948762099138104548, 873.3790461542533056327158334220106613337399484342286517255041584181948762102788138007]",
"[888.5966691945494072095163939552266199009302369751126068480059975952199566672479247724, 888.5966691945494072095163939552266199009302369751126068480059975952199566676923204159]",
"[905.3515814772802365432660057636798660652284501048642531999585115985110066418560815449, 905.3515814772802365432660057636798660652284501048642531999585115985110066424392593375]",
"[921.4097946525358789548378794643469676005137674346776970428297539584610248697647892358, 921.4097946525358789548378794643469676005137674346776970428297539584610248705738654483]",
"[934.4431629217900489370030766873277448669250597572013854015428746991242542624088196728, 934.4431629217900489370030766873277448669250597572013854015428746991242542635697625393]",
"[942.8217566707761175362351207833855643468618469352378768333700636957371540098311328184, 942.8217566707761175362351207833855643468618469352378768333700636957371540115283331737]",
"[946.3128371870710886543799798572375772644125694349674371353628476493370561386380275526, 946.3128371870710886543799798572375772644125694349674371353628476493370561411510446501]",
"[946.3128368304853410141462626559706855828642281113044602450973134235681879906984624782, 946.3128368304853410141462626559706855828642281113044602450973134235681879944715127607]",
"[946.3128364738995933739125454547037939013158867876414833548317791977993198423904935666, 946.3128364738995933739125454547037939013158867876414833548317791977993198481608888449]"
]
},
{
"lower_level": 50,
"upper_level": 51,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "878.4426954823051053362867274748829878958559001429376882334789169586370505128203915420944256883728688",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[878.4426961954766006167541618774167712589525827902636420140099854101747868074410861971, 878.4426961954766006167541618774167712589525827902636420140099854101747868078037307894]",
"[878.4426958388908529765204446761498795774042414666006651237444511844059186601307383298, 878.4426958388908529765204446761498795774042414666006651237444511844059186604934638863]",
"[878.4426954823051053362867274748829878958559001429376882334789169586370505128203915421, 878.4426954823051053362867274748829878958559001429376882334789169586370505131831959036]",
"[881.7171231131500897878718625406237173789158474304999095025988846543768064249515801955, 881.7171231131500897878718625406237173789158474304999095025988846543768064253202355612]",
"[889.5757499151454659165856996968129029792192202207221281391558464019495893480555517395, 889.5757499151454659165856996968129029792192202207221281391558464019495893484450861222]",
"[901.8002806759997487464029257600272321772372628257849271290067922660358977758926766303, 901.8002806759997487464029257600272321772372628257849271290067922660358977763316422828]",
"[917.3136208969799466628974762039811721704443253822929665471221109929877404505144482176, 917.3136208969799466628974762039811721704443253822929665471221109929877404510500720275]",
"[934.3837904884168369528617173222868502422050991242202757046263574273817510337738979669, 934.383790488416836952861717322286850242205099124220275704626357427381751034478505687]",
"[950.7347667842999176532206476148318314581101962260295617741584046403933228294839409236, 950.7347667842999176532206476148318314581101962260295617741584046403933228304636969738]",
"[964.0016890783485285459361257803297516785624320516665095441274540204097582422545363022, 964.001689078348528545936125780329751678562432051666509544127454020409758243663222777]",
"[972.5304246758211000943185308226578760251553894295720880298279406066821512701742080647, 972.5304246758211000943185308226578760251553894295720880298279406066821512722376251477]",
"[976.0840642573925282672404038184155988668699029002313486258444410996293520403471536349, 976.0840642573925282672404038184155988668699029002313486258444410996293520434091849216]",
"[976.084063836290739570108656620132860362130433715202412573425956576970961218218536412, 976.084063836290739570108656620132860362130433715202412573425956576970961222828513471]",
"[976.0840634151889508729769094218501218573909645301734765210074720543125703956316732904, 976.0840634151889508729769094218501218573909645301734765210074720543125704027061159867]"
]
},
{
"lower_level": 49,
"upper_level": 50,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "903.2042329794163118664921122319163187989057570681257828839739928209445881554134244981435816354260848",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[903.2042338216198892607556066284817958083846954381836549888109618662613697981232572502, 903.2042338216198892607556066284817958083846954381836549888109618662613697984955182163]",
"[903.2042334005181005636238594301990573036452262531547189363924773436029789767683403344, 903.2042334005181005636238594301990573036452262531547189363924773436029789771406952188]",
"[903.2042329794163118664921122319163187989057570681257828839739928209445881554134244981, 903.2042329794163118664921122319163187989057570681257828839739928209445881557858711418]",
"[906.5333034661177093085714007432070129206068304851657720514231736787427311602342083646, 906.5333034661177093085714007432070129206068304851657720514231736787427311606126085669]",
"[914.5230732108906204110117846256938528135823858946422748790996151914341773412061495474, 914.5230732108906204110117846256938528135823858946422748790996151914341773416057720545]",
"[926.951604138218286501642576281843195091565609723957857916333416796245885950989481469, 926.9516041382182865016425762818431950915656097239578579163334167962458859514393481252]",
"[942.7191861518656522301546617318799677739309397399692692892799737374976152074013562231, 942.7191861518656522301546617318799677739309397399692692892799737374976152079494852051]",
"[960.0602949815638823612765206787445097147733527247978868462566205161081859087921353731, 960.0602949815638823612765206787445097147733527247978868462566205161081859095120917237]",
"[976.6627827200919305570144811700561254008509689524241742245448904016028056513208132739, 976.6627827200919305570144811700561254008509689524241742245448904016028056523207142668]",
"[990.1303074079289983550037332494052391627260218389285171387217112397305036805301574524, 990.1303074079289983550037332494052391627260218389285171387217112397305036819669470992]",
"[998.7880016590613849214707631196937960140448307822885885595900972268317518268511717435, 998.7880016590613849214707631196937960140448307822885885595900972268317518289561590237]",
"[1002.395373969334619764314890565147527643826385915208660283985255494761750022888360535, 1002.395373969334619764314890565147527643826385915208660283985255494761750026015697448]",
"[1002.395373474612802248973670305356968068067352738852709227182032585759211251264738785, 1002.395373474612802248973670305356968068067352738852709227182032585759211255983699974]",
"[1002.395372979890984733632450045566408492308319562496758170378809676756672479163343681, 1002.395372979890984733632450045566408492308319562496758170378809676756672486429474775]"
]
},
{
"lower_level": 48,
"upper_level": 49,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "924.6763016078903979105100447014183250833288769485693484819302099582877486399775521255473588112124143",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[924.6763025973340329411924852209994442348469433012812505955366557762928261816333537884, 924.6763025973340329411924852209994442348469433012812505955366557762928261819907788963]",
"[924.6763021026122154258512649612088846590879101249252995387334328672902874108054524172, 924.6763021026122154258512649612088846590879101249252995387334328672902874111629854773]",
"[924.6763016078903979105100447014183250833288769485693484819302099582877486399775521255, 924.6763016078903979105100447014183250833288769485693484819302099582877486403351909787]",
"[928.051244509553420598161008232590371982613747438252586174276198112172551855097270518, 928.051244509553420598161008232590371982613747438252586174276198112172551855461611038]",
"[936.1511081514787375787220617808956472734330599125347224021876242347494789850330759999, 936.1511081514787375787220617808956472734330599125347224021876242347494789854212793331]",
"[948.7508962901166192494319327147881311563454617992905076602220855384676610676185122875, 948.7508962901166192494319327147881311563454617992905076602220855384676610680631810498]",
"[964.7318480369058727231594889309875173003068323032665323827647543773174133757358024848, 964.7318480369058727231594889309875173003068323032665323827647543773174133762908749463]",
"[982.3002138326475244014661389895318294735715153134794806524323903863017618611528397452, 982.3002138326475244014661389895318294735715153134794806524323903863017618619009726752]",
"[999.1135448305403990718924149901005232833151847635766301215717578858289168910427497844, 999.1135448305403990718924149901005232833151847635766301215717578858289168921055803785]",
"[1012.749182669137533993481740260574815877337803191003083023750079276573846862599060246, 1012.749182669137533993481740260574815877337803191003083023750079276573846864153661265]",
"[1021.514949628031069884493901144303274913032191247636034542800959994323868098007679368, 1021.514949628031069884493901144303274913032191247636034542800959994323868100316344206]",
"[1025.167352183397863407979072987611464214319299632636320704466967432505526006203235399, 1025.167352183397863407979072987611464214319299632636320704466967432505526009670432533]",
"[1025.167351604682782010819331360534161812782605741611490006646056729755851084875494243, 1025.167351604682782010819331360534161812782605741611490006646056729755851090156774718]",
"[1025.167351025967700613659589733456859411245911850586659308825146027006176162993084366, 1025.16735102596770061365958973345685941124591185058665930882514602700617617119754165]"
]
},
{
"lower_level": 47,
"upper_level": 48,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "942.7942861345310910259937730163191993684729161117332510998984088249653542047540011943985237663558147",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[942.7942872919612538203132562704738041715463038937829124955402302304647040455956041959, 942.7942872919612538203132562704738041715463038937829124955402302304647040459625755088]",
"[942.7942867132461724231535146433965017700096100027580817977193195277150291251748021554, 942.7942867132461724231535146433965017700096100027580817977193195277150291255418976131]",
"[942.7942861345310910259937730163191993684729161117332510998984088249653542047540011944, 942.794286134531091025993773016319199368472916111733251099898408824965354205121218638]",
"[946.206444089671460497760148455555313127836432645301654446320944875911052866766997197, 946.2064440896714604977601484555553131278364326453016544463209448759110528671426500182]",
"[954.3956239754515836968373839729991074126209938682439517610751330734002365412344715821, 954.3956239754515836968373839729991074126209938682439517610751330734002365416401858266]",
"[967.1343485367286667095900784639692731560222451491184413332227109697747432497516934083, 967.1343485367286667095900784639692731560222451491184413332227109697747432502285437732]",
"[983.2883205120273675919617837808232417972516282255334264044395571802054813885356286124, 983.2883205120273675919617837808232417972516282255334264044395571802054813891515655513]",
"[1001.040810943008774701385917601055930389343409267076797326464956766563005765462892344, 1001.040810943008774701385917601055930389343409267076797326464956766563005766322079925]",
"[1018.024821019212085250663235077533188574438168016396162116660680597426019959937743638, 1018.024821019212085250663235077533188574438168016396162116660680597426019961193649814]",
"[1031.796481844187727611067228018801873124556211425595714816071495302605927857182424149, 1031.796481844187727611067228018801873124556211425595714816071495302605927859059087325]",
"[1040.649692114940003873375647488675024428889536576509868945581434157888435528750447229, 1040.649692114940003873375647488675024428889536576509868945581434157888435531581318511]",
"[1044.338529326752710463851940377071295749600331106168518269268938877578529219617254206, 1044.338529326752710463851940377071295749600331106168518269268938877578529223920097806]",
"[1044.33852865220427491170312645404977029796482098952850575102374249953966826308470023, 1044.338528652204274911703126454049770297964820989528505751023742499539668269705193522]",
"[1044.338527977655839359554312531028244846329310872888493232778546121500807305831883319, 1044.338527977655839359554312531028244846329310872888493232778546121500807316211221475]"
]
},
{
"lower_level": 46,
"upper_level": 47,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "957.5104504610571158216309448871655631417053716716680934878280625828196614159882032754096160095375308",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[957.5104518101539869259285727332086140449763919049481185243184553388973833267379544385, 957.5104518101539869259285727332086140449763919049481185243184553388973833271505473912]",
"[957.510451135605551373779758810187088593340881788308106006073258960858522371363078857, 957.5104511356055513737797588101870885933408817883081060060732589608585223717758132269]",
"[957.5104504610571158216309448871655631417053716716680934878280625828196614159882032754, 957.5104504610571158216309448871655631417053716716680934878280625828196614164010790626]",
"[960.951261471014821736561904769374336185209288930061419800894202529841425785130170562, 960.9512614710148217365619047693743361852092889300614198008942025298414257855500664748]",
"[969.2092088201432643992353645828126471392088723329180714321753977582550070080490650139, 969.2092088201432643992353645828126471392088723329180714321753977582550070084938989429]",
"[982.0549050404795680171674112529957241444128106022663529687162898980212616394042834304, 982.0549050404795680171674112529957241444128106022663529687162898980212616399081045496]",
"[998.3419879448374072760492864862921355604972433195758887220059622660455041012608770599, 998.3419879448374072760492864862921355604972433195758887220059622660455041018800525621]",
"[1016.23593302048523518274174059478272362760922785353907001591605698286762340958770258, 1016.23593302048523518274174059478272362760922785353907001591605698286762341040873017]",
"[1033.350880823641314813135094350547257855540570939238361489170320123641769945767424257, 1033.350880823641314813135094350547257855540570939238361489170320123641769946917997244]",
"[1047.226808872782386302631457645000991233558993204398251073141731329005205776107697518, 1047.226808872782386302631457645000991233558993204398251073141731329005205777774862359]",
"[1056.147048031661329867973193323827809195438028921550728352365325250040154890831122407, 1056.147048031661329867973193323827809195438028921550728352365325250040154893294861526]",
"[1059.863813882000429488515920217222202286543031990911009951446968775560973426455742644, 1059.863813882000429488515920217222202286543031990911009951446968775560973430154095466]",
"[1059.863813098079237661831051258037924741536748763029460532821333110294809874662987022, 1059.863813098079237661831051258037924741536748763029460532821333110294809880317598268]",
"[1059.863812314158045835146182298853647196530465535147911114195697445028646322250474035, 1059.863812314158045835146182298853647196530465535147911114195697445028646331101026838]"
]
},
{
"lower_level": 45,
"upper_level": 46,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "968.7924040355469455202976779212838668968980267642977946582692487068582204846648418420733943286203833",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[968.7924056033893291736674158396524219869105932200608934955205200373905475862947294222, 968.7924056033893291736674158396524219869105932200608934955205200373905475866514625572]",
"[968.7924048194681373469825468804681444419043099921793440768948843721243840354797856322, 968.7924048194681373469825468804681444419043099921793440768948843721243840358366806953]",
"[968.7924040355469455202976779212838668968980267642977946582692487068582204846648418421, 968.7924040355469455202976779212838668968980267642977946582692487068582204850218988334]",
"[972.2533830974511026430075616361087769443519171971436088423257331466197870082832118224, 972.2533830974511026430075616361087769443519171971436088423257331466197870086473623466]",
"[980.5597339216462868014636606223744621172104719186691550980732917073683163279288381378, 980.559733921646286801463660622374462117210471918669155098073291707368316328318120992]",
"[993.4807244929005941449411451493115332681373729911239003169051501969236977167936650045, 993.4807244929005941449411451493115332681373729911239003169051501969236977172423420285]",
"[1009.861363820585654519998558899472206476386646811976735047960023264053689909032539827, 1009.861363820585654519998558899472206476386646811976735047960023264053689909597322581]",
"[1027.854464957921041327327143434079345126770400356095129426649275865036828144678210732, 1027.854464957921041327327143434079345126770400356095129426649275865036828145446162589]",
"[1045.060947636877321047602243563044752479317232474662171920241529971604829100474419531, 1045.060947636877321047602243563044752479317232474662171920241529971604829101574244232]",
"[1059.009654326923825598380644708769764851483268316162690732958762733853796023998344381, 1059.009654326923825598380644708769764851483268316162690732958762733853796025619212881]",
"[1067.976679707337376216041783434834158036385471064269583253858770577350376448691722118, 1067.976679707337376216041783434834158036385471064269583253858770577350376451118431506]",
"[1071.71293974258555843485080193478147726554063724330420453383395166053108190500400226, 1071.712939742585558434850801934781477265540637243304204533833951660531081908685652732]",
"[1071.712938833778630981479286815713168109083941945520440258711420686072461641767979866, 1071.71293883377863098147928681571316810908394194552044025871142068607246164745099547]",
"[1071.712937924971703528107771696644858952627246647736675983588889711613841377885481962, 1071.712937924971703528107771696644858952627246647736675983588889711613841386862612929]"
]
},
{
"lower_level": 44,
"upper_level": 45,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "976.6215793652593732670276895189447189938619822569616347158298329174162633019605512949755105675540553",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[976.6215811828732281737707197570813373067753728525291632660748948663335038264309740239, 976.6215811828732281737707197570813373067753728525291632660748948663335038268565698079]",
"[976.6215802740663007203992046380130281503186775547453989909523638918748835641957626594, 976.6215802740663007203992046380130281503186775547453989909523638918748835646215452006]",
"[976.621579365259373267027689518944718993861982256961634715829832917416263301960551295, 976.6215793652593732670276895189447189938619822569616347158298329174162633023865195137]",
"[980.0942991001116982861877547375658546403903858292108117506223359418769634491241223992, 980.0942991001116982861877547375658546403903858292108117506223359418769634495582690696]",
"[988.4288277110924877900164030112094389905901428640681557119507870284703582608699040005, 988.4288277110924877900164030112094389905901428640681557119507870284703582613330228574]",
"[1001.393650459462505598051235918667496801802674415586277476945740829899876479227208856, 1001.393650459462505598051235918667496801802674415586277476945740829899876479758802814]",
"[1017.828556373331258685937527687899997233973705397777379272689199815572478624257066771, 1017.828556373331258685937527687899997233973705397777379272689199815572478624922519183]",
"[1035.878790366988360831016034153655336849966848549955151297444676787435253772258931491, 1035.878790366988360831016034153655336849966848549955151297444676787435253773158664803]",
"[1053.13765443992045860869859532874777222752469977388178328119679087965601307217144285, 1053.137654439920458608698595328747772227524699773881783281196790879656013073454138421]",
"[1067.127847282737532984076238506540042755845110020442822835917786444801500469059094577, 1067.127847282737532984076238506540042755845110020442822835917786444801500470943996658]",
"[1076.121542278361314685462928270005141731394498598954741243448437979043631429967479082, 1076.121542278361314685462928270005141731394498598954741243448437979043631432786561993]",
"[1079.868914568646691551846662338128065081743347695932785856668198133759484346418093874, 1079.868914568646691551846662338128065081743347695932785856668198133759484350698926038]",
"[1079.868913517142872333372767403804986426407533597712909985678781290593248619514172339, 1079.868913517142872333372767403804986426407533597712909985678781290593248626140972193]",
"[1079.868912465639053114898872469481907771071719499493034114689364447427012891838989136, 1079.868912465639053114898872469481907771071719499493034114689364447427012902354647054]"
]
},
{
"lower_level": 43,
"upper_level": 44,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "980.9917081394207449160970974613155497206542496833300543325746520741578157088569506612685678421541264",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[980.99171024242838335304488732996170703132587787976980607455348576049028716032065367, 980.9917102424283833530448873299617070313258778797698060745534857604902871607235341717]",
"[980.9917091909245641345709923956386283759900637815499302035640689173240514345888016259, 980.9917091909245641345709923956386283759900637815499302035640689173240514349918969522]",
"[980.9917081394207449160970974613155497206542496833300543325746520741578157088569506613, 980.9917081394207449160970974613155497206542496833300543325746520741578157092602586533]",
"[984.4677780149577697036610535743146669989237388087325514441080556069112845244305626294, 984.4677780149577697036610535743146669989237388087325514441080556069112845248420998106]",
"[992.810347159756616506783593248342843217920947582790655135839340459976139257434174068, 992.8103471597566165067835932483428432179209475827906551358393404599761392578748043419]",
"[1005.787677478651561223063470382253261853816658040048428377519881315812545945102167816, 1005.787677478651561223063470382253261853816658040048428377519881315812545945611532276]",
"[1022.23772810490224869309920229643229409290133432753192370973399251589624823837036169, 1022.237728104902248693099202296432294092901334327531923709733992515896248239014099535]",
"[1040.303244003452474343240927931055092594959145046421577347947363016679629315245285963, 1040.303244003452474343240927931055092594959145046421577347947363016679629316124320538]",
"[1057.575489565533406604667493992495473826346818943251127249259410750055014936862022507, 1057.575489565533406604667493992495473826346818943251127249259410750055014938126089862]",
"[1071.575995737031751547938353618315192479980929363373143658339233948696665285310616937, 1071.575995737031751547938353618315192479980929363373143658339233948696665287181465813]",
"[1080.576320667394063091554189231807343249857725001703604540370349162384994971322080704, 1080.576320667394063091554189231807343249857725001703604540370349162384994974137795509]",
"[1084.326455333687624412309345043877466673020420124234864223245114182935602085635869711, 1084.326455333687624412309345043877466673020420124234864223245114182935602089938635585]",
"[1084.326454118992161972333059029782932087158078060568172465691602319124852221342249755, 1084.326454118992161972333059029782932087158078060568172465691602319124852228049620743]",
"[1084.326452904296699532356773015688397501295735996901480708138090455314102356241173948, 1084.326452904296699532356773015688397501295735996901480708138090455314102366968050958]"
]
},
{
"lower_level": 42,
"upper_level": 43,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "981.9072824870586941976557919812265332286173539766997410462989184236554871611005691789120730954985792",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[981.9072849164496190776083640094156024003420381040331245614059421512769868872830312534, 981.9072849164496190776083640094156024003420381040331245614059421512769868877077213193]",
"[981.9072837017541566376320779953210678144796960403664328038524302874662370241918002162, 981.9072837017541566376320779953210678144796960403664328038524302874662370246167353333]",
"[981.9072824870586941976557919812265332286173539766997410462989184236554871611005691789, 981.9072824870586941976557919812265332286173539766997410462989184236554871615257493473]",
"[985.378326176471003418457503264067646412007502716408813217435711335056957614500730142, 985.3783261764710034184575032640676464120075027164088132174357113350569576149351801578]",
"[993.708832698886850560689347566779578958131106947080977765957428512870606908133154755, 993.7088326988868505606893475667795789581311069470809777659574285128706069086003563605]",
"[1006.667399022492044203016357421225849639461331576786169399809435751383890951340692671, 1006.667399022492044203016357421225849639461331576786169399809435751383890951885249517]",
"[1023.09353502519828301285200560767616077225202640123094522378544850736302169672130481, 1023.09353502519828301285200560767616077225202640123094522378544850736302169741705506]",
"[1041.132541623696600794936798092097519495653564198240327976911279091786562645859239237, 1041.132541623696600794936798092097519495653564198240327976911279091786562646819779812]",
"[1058.379217758590876513144656039137056837332520946335489761861968864310991704230198523, 1058.379217758590876513144656039137056837332520946335489761861968864310991705624402143]",
"[1072.358900613811632490440749738237929759949990952983166004362925061633355412128473115, 1072.358900613811632490440749738237929759949990952983166004362925061633355414207531379]",
"[1081.345839055240972801664486371319337152271845764750062141489038879054299448126460107, 1081.345839055240972801664486371319337152271845764750062141489038879054299451276200321]",
"[1085.090395906977708183674943577924014127127243242436672749234422950869996170277742744, 1085.09039590697770818367494357792401412712724324243667274923442295086999617512304784]",
"[1085.090394505453069730442408802572995675114202123487945322854918461217165151218789281, 1085.090394505453069730442408802572995675114202123487945322854918461217165158828143304]",
"[1085.09039310392843127720987402722197722310116100453921789647541397156433413121102316, 1085.09039310392843127720987402722197722310116100453921789647541397156433414348181609]"
]
},
{
"lower_level": 41,
"upper_level": 42,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "979.3819865134516256792853129603519476235326409529894918710617986582846610677416709075115525397543519",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[979.381989316500902585750382511053984527558723190886946723820807637590323103094833695, 979.381989316500902585750382511053984527558723190886946723820807637590323103514203881]",
"[979.3819879149762641325178477357029660755456820719382192974413031479374920854182523012, 979.3819879149762641325178477357029660755456820719382192974413031479374920858379042422]",
"[979.3819865134516256792853129603519476235326409529894918710617986582846610677416709075, 979.381986513451625679285312960351947623532640952989491871061798658284661068161603524]",
"[982.8396168567798887924790501437611578736155893098791014844647096855399181560991969905, 982.8396168567798887924790501437611578736155893098791014844647096855399181565284307605]",
"[991.137931605355868066482027316464776357600020834777992687091461591918829992023215643, 991.137931605355868066482027316464776357600020834777992687091461591918829992485238786]",
"[1004.04642193238350756092013985414282208433284531868588664159479858938058925355442476, 1004.046421932383507560920139854142822084332845318685886641594798589380589254093865756]",
"[1020.409529880920625026822768258126148332707491331294039958717302120759597311610944313, 1020.409529880920625026822768258126148332707491331294039958717302120759597312301746038]",
"[1038.380171167547756173735365704732971671073310977603547087464415884558203198191444741, 1038.380171167547756173735365704732971671073310977603547087464415884558203199147477236]",
"[1055.562260080313567312108633863470586952413519410745296061715417686223356716780758946, 1055.562260080313567312108633863470586952413519410745296061715417686223356718171769343]",
"[1069.489926629734057135219452031077695246089146794546609941785053211982023140640852108, 1069.489926629734057135219452031077695246089146794546609941785053211982023142720616379]",
"[1078.443425935627677552775432090168094849026499527746978503523709278217071632369108109, 1078.44342593562767755277543209016809484902649952774697850352370927821707163553062158]",
"[1082.174049687157787134231236538925419683471915351195975187749723324629053062896314311, 1082.174049687157787134231236538925419683471915351195975187749723324629053067782697342]",
"[1082.174048071474644046677391208292588105859120633111131504243554528828525437615326211, 1082.174048071474644046677391208292588105859120633111131504243554528828525445338073127]",
"[1082.174046455791500959123545877659756528246325915026287820737385733027997811338151751, 1082.174046455791500959123545877659756528246325915026287820737385733027997823889209941]"
]
},
{
"lower_level": 40,
"upper_level": 41,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "973.437081396818343224182662349783769861849916368343963230338811252523261870449149736209360406758302",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[973.437084628184629399290353011049433017075505804513650597351148844124317118174074396, 973.4370846281846293992903530110494330170755058045136505973511488441243171186047493267]",
"[973.4370830125014863117365076804166014394627110864288069138449800483237894943116115264, 973.4370830125014863117365076804166014394627110864288069138449800483237894947426092338]",
"[973.4370813968183432241826623497837698618499163683439632303388112525232618704491497362, 973.4370813968183432241826623497837698618499163683439632303388112525232618708804691409]",
"[976.8728723380256120374324522073591518490871723456511926097726236060610886953271053176, 976.8728723380256120374324522073591518490871723456511926097726236060610886957677874086]",
"[985.1187728157720701361290874483653852837638749414925789631579441217506593310420852313, 985.1187728157720701361290874483653852837638749414925789631579441217506593315156419774]",
"[997.9457299426379349607359962320471054927629939761272553804460063317419100062700297184, 997.945729942637934960735996232047105492762993976127255380446006331741910006821110111]",
"[1014.206511547063584701459648577373992115165344296292725341760400197635845714464861706, 1014.206511547063584701459648577373992115165344296292725341760400197635845715167423733]",
"[1032.066726971947225864715035133461911324594150936979914181737929561197696864135225483, 1032.066726971947225864715035133461911324594150936979914181737929561197696865103247139]",
"[1049.145013922037829209863028952764711449798134570739735577090154977513432175181290736, 1049.145013922037829209863028952764711449798134570739735577090154977513432176585119366]",
"[1062.989310932853061740577301978620675222753800140596474757465466434513042050311649849, 1062.989310932853061740577301978620675222753800140596474757465466434513042052407345692]",
"[1071.889215441386762464578109430121775257950740780170474321715318852119533829608211451, 1071.889215441386762464578109430121775257950740780170474321715318852119533832795812629]",
"[1075.597507881461725173130167355383100716601563373323254208265464378283248791583944366, 1075.597507881461725173130167355383100716601563373323254208265464378283248796525449902]",
"[1075.597506019940097457693373820133054524398985143077021907939615021059686789331642486, 1075.597506019940097457693373820133054524398985143077021907939615021059686797184100335]",
"[1075.597504158418469742256580284883008332196406912830789607613765663836124786032453458, 1075.597504158418469742256580284883008332196406912830789607613765663836124798889078723]"
]
},
{
"lower_level": 39,
"upper_level": 40,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "964.099724876359386822449605532545973914312006427431513695780865764991332513449370003278921152789733",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[964.0997285994026422533231926030460662987171628879239782964325644794384565150432708206, 964.0997285994026422533231926030460662987171628879239782964325644794384565155051449897]",
"[964.0997267378810145378863990677960201065145846576777459961067151222148945142463198722, 964.0997267378810145378863990677960201065145846576777459961067151222148945147085653965]",
"[964.0997248763593868224496055325459739143120064274315136957808657649913325134493700033, 964.0997248763593868224496055325459739143120064274315136957808657649913325139119847238]",
"[967.5051796306544360252568182655070801252713230624806287311939452214200052688355141401, 967.5051796306544360252568182655070801252713230624806287311939452214200052693065188984]",
"[975.678273597523902689666573760590886083416544277312865525006637131223022654266068144, 975.6782735975239026896665737605908860834165442773128655250066371312230226547663581498]",
"[988.3919762780811162195003952882887406430424067230275853989101655743610226687376660131, 988.3919762780811162195003952882887406430424067230275853989101655743610226693069665623]",
"[1004.510800014677764988296242472740187562667483041237835017406282611397665338357794562, 1004.510800014677764988296242472740187562667483041237835017406282611397665339061987746]",
"[1022.218165856210377754326045154727464590415575858029147848367691603325368007334408186, 1022.218165856210377754326045154727464590415575858029147848367691603325368008275218354]",
"[1039.153091415623269537938126549807036074989969200173396446940113390753414680328530936, 1039.153091415623269537938126549807036074989969200173396446940113390753414681658516007]",
"[1052.882387358667712233967695355194215383679174824679946068003081122580535192061854078, 1052.882387358667712233967695355194215383679174824679946068003081122580535194011743328]",
"[1061.708362501221262726519729700198905744870186635465797393759787907536657531563867827, 1061.708362501221262726519729700198905744870186635465797393759787907536657534497544059]",
"[1065.385850871030736352122201702416495957636273665599742737757721872478603485009975576, 1065.385850871030736352122201702416495957636273665599742737757721872478603489536595256]",
"[1065.385848726846240635766439396493263608122657599486108368477565696642898445090129466, 1065.385848726846240635766439396493263608122657599486108368477565696642898452286551566]",
"[1065.385846582661744919410677090570031258609041533372473999197409520807193404186241607, 1065.385846582661744919410677090570031258609041533372473999197409520807193416019159201]"
]
},
{
"lower_level": 38,
"upper_level": 39,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "951.4012027820583990941658848298234481562857823909558987765998056067088450622954264398108813421062318",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[951.4012070704273905268774094416699128553130145231831675151601179583802551394637574119, 951.4012070704273905268774094416699128553130145231831675151601179583802551398423346558]",
"[951.4012049262428948105216471357466805057993984570695331458799617825445501008795919259, 951.4012049262428948105216471357466805057993984570695331458799617825445501012585934215]",
"[951.4012027820583990941658848298234481562857823909558987765998056067088450622954264398, 951.4012027820583990941658848298234481562857823909558987765998056067088450626748521872]",
"[954.7677173384445534213965863110328011066028286967933756187584280124962083433438345311, 954.7677173384445534213965863110328011066028286967933756187584280124962083437316654295]",
"[962.8473552185312790238966127707035689362896631165337009489662607889598683970802739147, 962.8473552185312790238966127707035689362896631165337009489662607889598683974973317666]",
"[975.4156819089973341334101607582305796661887198621134768588408255375236683498034624034, 975.4156819089973341334101607582305796661887198621134768588408255375236683502893591549]",
"[991.352412859857622251314651607872543732403597919119377429669286677615438641621977139, 991.3524128598576222513146516078725437324035979191193774296692866776154386422424534641]",
"[1008.863960215218473299178359635614552939534087953860481776390703110893173731728536491, 1008.863960215218473299178359635614552939534087953860481776390703110893173732585269241]",
"[1025.615450677761657214327431003042136759961096213572309096835847276558877189802063083, 1025.615450677761657214327431003042136759961096213572309096835847276558877191048078687]",
"[1039.197700181303579152706915246002129602089108895300802504609589773190440153332534889, 1039.197700181303579152706915246002129602089108895300802504609589773190440155200857686]",
"[1047.929145345238557918706239172901130710603360608007548946795755801675759883247180807, 1047.929145345238557918706239172901130710603360608007548946795755801675759886109194112]",
"[1051.567246030661203295324711173971022669714164334281438239471620658861814146334780693, 1051.567246030661203295324711173971022669714164334281438239471620658861814150820100057]",
"[1051.56724356088487866066995171541083201373663028757031021695194872814139758475733832, 1051.567243560884878660669951715410832013736630287570310216951948728141397591992554089]",
"[1051.56724109110855402601519225685064135775909624085918219443227679742098102214078351, 1051.56724109110855402601519225685064135775909624085918219443227679742098103420357648]"
]
},
{
"lower_level": 37,
"upper_level": 38,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "935.3750461600871600549353348365616622182868300303730410378637528108333826390489446050997622753390107",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[935.3750510996398093242448537536820435302418981237952970829030966722742157594535097739, 935.3750510996398093242448537536820435302418981237952970829030966722742157598348765002]",
"[935.3750486298634846895900942951218528742643640770841690603834247415537991992512271895, 935.3750486298634846895900942951218528742643640770841690603834247415537991996330818593]",
"[935.3750461600871600549353348365616622182868300303730410378637528108333826390489446051, 935.3750461600871600549353348365616622182868300303730410378637528108333826394312861389]",
"[938.6938670347308397960314070307285986586643354705556547833469643653681796213688350748, 938.6938670347308397960314070307285986586643354705556547833469643653681796217596357357]",
"[946.6590405256637575196896675779391469907193204683782197573813531788608129354640586426, 946.6590405256637575196896675779391469907193204683782197573813531788608129358840765412]",
"[959.0493116663742248056853302571878640158920804668055337058901696075594120377566413827, 959.0493116663742248056853302571878640158920804668055337058901696075594120382453319347]",
"[974.7631145129543670847856545312145331441047786920098170146256076797846721506285550998, 974.7631145129543670847856545312145331441047786920098170146256076797846721512513696675]",
"[992.0351184920555082187200266672186209683984465093882068374895909044892994265384990782, 992.0351184920555082187200266672186209683984465093882068374895909044892994273967787815]",
"[1008.562389375010663468929841189412475580723395299499700460129854219778014816037443656, 1008.562389375010663468929841189412475580723395299499700460129854219778014817284253787]",
"[1021.964976138734783512943655050013278718287613607653693547295157056246297776801096071, 1021.964976138734783512943655050013278718287613607653693547295157056246297778671270247]",
"[1030.580923683069055371443041524502217074422400198644588024792095207944198368488518382, 1030.580923683069055371443041524502217074422400198644588024792095207944198371360627368]",
"[1034.170900137173449161419596079903304709818482282877558273591556354176507116397253082, 1034.170900137173449161419596079903304709818482282877558273591556354176507120921970646]",
"[1034.170897291605286329940885991575981301763645053020623898040183092381027785482544878, 1034.170897291605286329940885991575981301763645053020623898040183092381027792839409717]",
"[1034.170894446037123498462175903248657893708807823163689522488809830585548453468635935, 1034.170894446037123498462175903248657893708807823163689522488809830585548465855676013]"
]
},
{
"lower_level": 36,
"upper_level": 37,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "916.055002291129992061317967747267078223197797466415673735356397446144557142689893456517893490627673",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[916.0550079822663177242753879239217250393074719261295424864591439697355158016869553212, 916.0550079822663177242753879239217250393074719261295424864591439697355158020538823737]",
"[916.0550051366981548927966778355944016312526346962726081109077707079400364721884243889, 916.0550051366981548927966778355944016312526346962726081109077707079400364725559117128]",
"[916.0550022911299920613179677472670782231977974664156737353563974461445571426898934565, 916.0550022911299920613179677472670782231977974664156737353563974461445571430579399723]",
"[919.3171772066559615164670751707271444252748032845898996305607963813330661183617912615, 919.3171772066559615164670751707271444252748032845898996305607963813330661187373609597]",
"[927.1464009114957986224906999999723888438203020071657245645387239135046818275534763789, 927.1464009114957986224906999999723888438203020071657245645387239135046818279547062929]",
"[939.3251947993205510421402880612370441712486359074173385102670922902693697820461532847, 939.3251947993205510421402880612370441712486359074173385102670922902693697825075449078]",
"[954.7743037874385230908787781311180739186710157010614376918224810158126324459878462721, 954.7743037874385230908787781311180739186710157010614376918224810158126324465666962648]",
"[971.7620372864997463975229758816977681183922810045280152446714536748372875937211343564, 971.7620372864997463975229758816977681183922810045280152446714536748372875945063628689]",
"[988.0233637427817761562351051958387948672013091678834836239983009978897421922314505114, 988.0233637427817761562351051958387948672013091678834836239983009978897421933580160295]",
"[1001.212916966566521828470625206513326093854287178866395765309157007284991332017820843, 1001.212916966566521828470625206513326093854287178866395765309157007284991333694607455]",
"[1009.691914211343428813796725832324687693342382006592676341255878178852361841294390669, 1009.691914211343428813796725832324687693342382006592676341255878178852361843862494647]",
"[1013.224827782441149346578686966275191745906882090000998667087281411234887014094495337, 1013.224827782441149346578686966275191745906882090000998667087281411234887018148780289]",
"[1013.224824502186612035147177934303456302722832316088436142918298840053405620574803745, 1013.224824502186612035147177934303456302722832316088436142918298840053405627208150894]",
"[1013.224821221932074723715668902331720859538782542175873618749316268871924226025501661, 1013.224821221932074723715668902331720859538782542175873618749316268871924237295763158]"
]
},
{
"lower_level": 35,
"upper_level": 36,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "893.4728211602201449943215675859029045199882855120368485980021748116773027874210837891123179058360894",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[893.4728277207292196171845856498463754063563850598619736463401399540402655718792953921, 893.4728277207292196171845856498463754063563850598619736463401399540402655722755584296]",
"[893.4728244404746823057530766178746399631723352859494111221711573828587841796501895906, 893.4728244404746823057530766178746399631723352859494111221711573828587841800470971022]",
"[893.4728211602201449943215675859029045199882855120368485980021748116773027874210837891, 893.4728211602201449943215675859029045199882855120368485980021748116773027878186346953]",
"[896.6691410194457335285938371697682276377658787240979330148726735983128748718376492308, 896.6691410194457335285938371697682276377658787240979330148726735983128748722437413076]",
"[904.3403131855842846276714384026932322541955114091591963743253187543822957268425554361, 904.34031318558428462767143840269323225419551140915919637432531875438229572727777623]",
"[916.2732493462496278053951213403340742563841153071391950948009985866890502713477397622, 916.2732493462496278053951213403340742563841153071391950948009985866890502718512618541]",
"[931.4146976090587891634642329729656852984310121531536415338657253594211137310170646846, 931.4146976090587891634642329729656852984310121531536415338657253594211137316539972288]",
"[948.0721415064599850784390330907854847382430604843601773871986553016748541502520668079, 948.0721415064599850784390330907854847382430604843601773871986553016748541511236235409]",
"[964.0245880336776956385385467792387776980503651404186632287411855894668259052767750668, 964.0245880336776956385385467792387776980503651404186632287411855894668259065372681278]",
"[976.96676627024792332654495158490209988524412679137144446752873579600611532873738773, 976.9667662702479233265449515849020998852441267913714444675287357960061153306276852576]",
"[985.2867365439833275482917993543033387305954756605044965414203003098446973020949259043, 985.2867365439833275482917993543033387305954756605044965414203003098446973050132448691]",
"[988.7533885776882181965841243421971992716811655808801459891056885718810221179723772322, 988.753388577688218196584124342197199271681165580880145989105688571881022122622918375]",
"[988.7533847934128918945103559856366207653412844395997886768147585765894666608341653387, 988.753384793412891894510355985636620765341284439599788676814758576589466668526593905]",
"[988.7533810091375655924365876290760422590014032983194313645238285812979112024515614409, 988.7533810091375655924365876290760422590014032983194313645238285812979112156745405329]"
]
},
{
"lower_level": 34,
"upper_level": 35,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "867.6558102882436888982259247794678435200616684518766959563201228485901091736690865147432502950031138",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[867.6558178567943415023734614925890005327414307344374105809019828391732200849028369869, 867.6558178567943415023734614925890005327414307344374105809019828391732200853636942472]",
"[867.6558140725190152002996931360284220264015495931570532686110528438816646292859617508, 867.655814072519015200299693136028422026401549593157053268611052843881664629747560642]",
"[867.6558102882436888982259247794678435200616684518766959563201228485901091736690865147, 867.6558102882436888982259247794678435200616684518766959563201228485901091741314270369]",
"[870.7767404181695451358523341185752933469300853165497369697792805213765148755125597202, 870.7767404181695451358523341185752933469300853165497369697792805213765148759863107801]",
"[878.2669779252808733433086589533266937719673547237031790172104533254444127601257271046, 878.2669779252808733433086589533266937719673547237031790172104533254444127606386928468]",
"[889.9184604288170026584467751385123447943675942743816622568971917444890664279360322933, 889.9184604288170026584467751385123447943675942743816622568971917444890664285410725466]",
"[904.7077592215407247419345598078610248093574670642356112364152253156599480056431384366, 904.7077592215407247419345598078610248093574670642356112364152253156599480064281057051]",
"[920.9872588745249528537875074235377461483505069819741650719729394263748014997399522433, 920.9872588745249528537875074235377461483505069819741650719729394263748015008416348007]",
"[936.5863588738167441365298640954995071483027459745686388330820230477244805295628075949, 936.5863588738167441365298640954995071483027459745686388330820230477244805311908149678]",
"[949.2455937473490916727320618083087949904995378442384928674879630327126215699939526977, 949.2455937473490916727320618083087949904995378442384928674879630327126215724788277604]",
"[957.383671633858079345531894985856623370545835399719029188376340715560443878392272501, 957.3836716338580793455318949858566233705458353997190291883763407155604438822886170438]",
"[960.7745348246439282164245764631461553447314024012263439796903835184374375662122534254, 960.7745348246439282164245764631461553447314024012263439796903835184374375725166705044]",
"[960.7745304544228249018812780243691368621735661563365309500955822494380771322565051711, 960.7745304544228249018812780243691368621735661563365309500955822494380771428478677424]",
"[960.7745260842017215873379795855921183796157299114467179205007809804387166964974698669, 960.7745260842017215873379795855921183796157299114467179205007809804387167149805772976]"
]
},
{
"lower_level": 33,
"upper_level": 34,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "838.6240997066059074531822448462089702266743486560324276808816638892326334093146280597391370590901521",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[838.6241084470481140822688417237630071917900211458120537400712664272313542729384978983, 838.6241084470481140822688417237630071917900211458120537400712664272313542735586384923]",
"[838.624104076827010767725543284985988709232184900922240710476465158231993841126562979, 838.6241040768270107677255432849859887092321849009222407104764651582319938417475585537]",
"[838.6240997066059074531822448462089702266743486560324276808816638892326334093146280597, 838.6240997066059074531822448462089702266743486560324276808816638892326334099364786151]",
"[841.6596978428570015063694028055150599585670051780372213336900835430843272676254053261, 841.6596978428570015063694028055150599585670051780372213336900835430843272682627901896]",
"[848.9451393684781266993926367016087207034225453853239578689489719661558620197421455186, 848.9451393684781266993926367016087207034225453853239578689489719661558620204333121218]",
"[860.2780506433965829051227015956641362232313516494644753932254522524875474995970750097, 860.2780506433965829051227015956641362232313516494644753932254522524875475004147334147]",
"[874.6688066838600982611411260143101470304239321898709871318644952609324482216572655959, 874.668806683860098261141126014310147030423932189870987131864495260932448222722298413]",
"[890.5206620759061998568056709019884454822059017184328566452626981803506977676676304612, 890.5206620759061998568056709019884454822059017184328566452626981803506977691686872358]",
"[905.7200354528291210596098678967355034797900428438041507469343688486542407890265018091, 905.7200354528291210596098678967355034797900428438041507469343688486542407912543947222]",
"[918.0592257969169018137028378679661102002427869001194759949851693676489255955363893035, 918.0592257969169018137028378679661102002427869001194759949851693676489255989550198646]",
"[925.9915605086667879673665738169274191033084335292532446952975039421888168931228538037, 925.9915605086667879673665738169274191033084335292532446952975039421888168985232184064]",
"[929.2966969705028233347816528900953508266723476721649179323371539383071917196196241873, 929.2966969705028233347816528900953508266723476721649179323371539383071917284472673945]",
"[929.2966919171562412318285743611642218998771160618513709674012098998301184910844974543, 929.2966919171562412318285743611642218998771160618513709674012098998301185061024933853]",
"[929.2966868638096591288754958322330929730818844515378240024652658613530452598723398288, 929.2966868638096591288754958322330929730818844515378240024652658613530452864322414616]"
]
},
{
"lower_level": 32,
"upper_level": 33,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "806.3875444814233429811245993587809146583755135177186254022668148702379791006677809987085146958446418",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[806.387554588116507187030756416643172511965976738345719332138702947192125551545405031, 806.3875545881165071870307564166431725119659767383457193321387029471921255522046523553]",
"[806.3875495347699250840776778877120435851707451280321723672027589087150523261065930149, 806.3875495347699250840776778877120435851707451280321723672027589087150523267668281009]",
"[806.3875444814233429811245993587809146583755135177186254022668148702379791006677809987, 806.387544481423342981124599358780914658375513517718625402266814870237979101329002767]",
"[809.327362308513992267617424901097796538304353569337874117603166082754548929345426163, 809.3273623085139922676174249010977965383043535693378741176031660827545489300226885349]",
"[816.3829320282978556156118012043707503018486043200345283276322358324967940380097250564, 816.3829320282978556156118012043707503018486043200345283276322358324967940387421390801]",
"[827.3582652855054410293289362833272763424180698244760044864382728230150119693018689911, 827.3582652855054410293289362833272763424180698244760044864382728230150119701636560583]",
"[841.3017213384994616011143557802567314210702549687190054443477975846371460277365510505, 841.3017213384994616011143557802567314210702549687190054443477975846371460288510216145]",
"[856.6736949523976066356535689105274353241844633252034391770169718258663886776616917407, 856.6736949523976066356535689105274353241844633252034391770169718258663886792216029245]",
"[871.4245888952127372908548510410147129059863961482779251179125137177723521905861519068, 871.4245888952127372908548510410147129059863961482779251179125137177723521928904705935]",
"[883.4047334178337071443142800293303575119926599297998254596550441450893763633622878263, 883.4047334178337071443142800293303575119926599297998254596550441450893763668936765221]",
"[891.1062526506800220902754113109758958347940909895678564815295579978040076486921412174, 891.1062526506800220902754113109758958347940909895678564815295579978040076542873388623]",
"[894.3152155211829897477484277493742037044539651743807837017839283764102835911321482881, 894.3152155211829897477484277493742037044539651743807837017839283764102836003466130415]",
"[894.3152096689579892165831752602086848066726721601790009971239009243061557020518440046, 894.3152096689579892165831752602086848066726721601790009971239009243061557179003802655]",
"[894.3152038167329886854179227710431659088913791459772182924638734722020278100223885551, 894.3152038167329886854179227710431659088913791459772182924638734722020278384014246071]"
]
},
{
"lower_level": 31,
"upper_level": 32,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "770.9421735356169688487510427118924946309549910502567450318306449601213099490985923157735726706878049",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[770.9421852400669699110815476902235324265175770786603104411506998643295657206255514679, 770.9421852400669699110815476902235324265175770786603104411506998643295657212375632682]",
"[770.9421793878419693799162952010580135287362840644585277364906724122254378348620713521, 770.9421793878419693799162952010580135287362840644585277364906724122254378354752252857]",
"[770.9421735356169688487510427118924946309549910502567450318306449601213099490985923158, 770.9421735356169688487510427118924946309549910502567450318306449601213099497128873032]",
"[773.7751377449924384357539561827764726981346823337485955156448630828466199431367700503, 773.7751377449924384357539561827764726981346823337485955156448630828466199437651948889]",
"[780.5742598765090504747088695631296880132059745590160225491649987829001877058551148151, 780.5742598765090504747088695631296880132059745590160225491649987829001877065314747074]",
"[791.1506750679424523332151680690826168481672008756650723511655551633855099752677072605, 791.1506750679424523332151680690826168481672008756650723511655551633855099760562272328]",
"[804.5951549286398976880090278219793433747093400617046409333252556941138263811473052611, 804.5951549286398976880090278219793433747093400617046409333252556941138263821548838079]",
"[819.4318771524421558845791767907429895022087819595109271214116710317601125631719337977, 819.4318771524421558845791767907429895022087819595109271214116710317601125645663144593]",
"[833.682611239272329797670173184317977031689577317051225178073990102587516169971619877, 833.6826112392723297976701731843179770316895773170512251780739901025875161720150992853]",
"[845.2623646350644556963201362061477042317328033404704208764396785784446334288043176492, 845.262364635064455696320136206147704231732803340470420876439678578444633431926323888]",
"[852.7064892102054442346730650904114265362853574789375904976706511817329400647868118567, 852.7064892102054442346730650904114265362853574789375904976706511817329400697454234836]",
"[855.8082037489615746566303346293253915871489628522408861616779413668251089576434366626, 855.8082037489615746566303346293253915871489628522408861616779413668251089658732313859]",
"[855.8081969593740139916144794653422010522152961135703019787993481846825993387042425366, 855.8081969593740139916144794653422010522152961135703019787993481846825993530254324462]",
"[855.8081901697864533265986243013590105172816293748997177959207550025400897169795925809, 855.8081901697864533265986243013590105172816293748997177959207550025400897429630591097]"
]
},
{
"lower_level": 30,
"upper_level": 31,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "732.2660691640704750658525699745559318740113309143056430848226737752471365541772611583365822220818593",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[732.2660827432455963958842803025223129438786643916468114505798601395321557859632750984, 732.2660827432455963958842803025223129438786643916468114505798601395321557865490124354]",
"[732.2660759536580357308684251385391224089449976529762272677012669573896461700702681284, 732.2660759536580357308684251385391224089449976529762272677012669573896461706573289582]",
"[732.2660691640704750658525699745559318740113309143056430848226737752471365541772611583, 732.2660691640704750658525699745559318740113309143056430848226737752471365547656444015]",
"[734.9803368719989506499231777304469328117690209177106722405323691006369693874132196303, 734.9803368719989506499231777304469328117690209177106722405323691006369693880139666283]",
"[741.4945886833107369709073188653384791110984255899204489875262993560114574028726287444, 741.4945886833107369709073188653384791110984255899204489875262993560114574035144839047]",
"[751.6278727395076209030992058924133621603252492331444447805095965281536510927873082992, 751.6278727395076209030992058924133621603252492331444447805095965281536510935249169784]",
"[764.5181065448669136464416200606342581025987983264232161649385205115933781344206455169, 764.5181065448669136464416200606342581025987983264232161649385205115933781353450804304]",
"[778.7603528176449626162422637900165469363404658539533414257644037066675199343055665206, 778.7603528176449626162422637900165469363404658539533414257644037066675199355602690306]",
"[792.4556443764796867041849889535513860091394351101569067883907943954208894002151614129, 792.4556443764796867041849889535513860091394351101569067883907943954208894020263203304]",
"[803.5907776243452260671717775758223657904345946752300999386010465894092171993272462946, 803.590777624345226067171777575822365790434594675230099938601046589409217202070518759]",
"[810.749074534694239311103788186163804645663979948493808180661629964422009866038120053, 810.7490745346942393111037881861638046456639799484938081806616299644220098703888673995]",
"[813.7316935561032313687353961408249813548917095770000890028287701446055803819488473926, 813.7316935561032313687353961408249813548917095770000890028287701446055803892077564903]",
"[813.7316856626955564794059562657247030031300907208446118369793572166413261025277307823, 813.7316856626955564794059562657247030031300907208446118369793572166413261152872973876]",
"[813.7316777692878815900765163906244246513684718646891346711299442886770718205209064437, 813.731677769287881590076516390624424651368471864689134671129944288677071843952025684]"
]
},
{
"lower_level": 29,
"upper_level": 30,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "690.3145296482566515097133644700110703431139795866608388678741503071249225473363181282070989439758396",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[690.3145454350720012883722442202116270466372172989717931995729761630534311006779262269, 690.314545435072001288372244220211627046637217298971793199572976163053431101262234278]",
"[690.3145375416643263990428043451113486948755984428163160337235632350891768240071216378, 690.3145375416643263990428043451113486948755984428163160337235632350891768245929669269]",
"[690.3145296482566515097133644700110703431139795866608388678741503071249225473363181282, 690.3145296482566515097133644700110703431139795866608388678741503071249225479236984963]",
"[692.8973115352995498244260246233851404332272054984585301444532199005786285783344042948, 692.8973115352995498244260246233851404332272054984585301444532199005786285789341440996]",
"[699.095998886786858211782016891871369842749383429990216808753408728162986292470756006, 699.0959988867868582117820168918713698427493834299902168087534087281629862931110631331]",
"[708.7384054511363498767899261114700980279982226826436320751207923499385529773892228904, 708.7384054511363498767899261114700980279982226826436320751207923499385529781237830021]",
"[721.0147043397519227725472061742663868763398969004571785538665207860772967017237320846, 721.0147043397519227725472061742663868763398969004571785538665207860772967026421637814]",
"[734.5985108414028974747137222887270819438067543003044838913322553222163060004176555401, 734.5985108414028974747137222887270819438067543003044838913322553222163060016617927774]",
"[747.6786495770307714174187651622207241583094936930366261921321384137427868745368135469, 747.6786495770307714174187651622207241583094936930366261921321384137427868763326864461]",
"[758.3213896328378039774203236777866680200138131989487830783073083559954350064179363177, 758.3213896328378039774203236777866680200138131989487830783073083559954350091476661902]",
"[765.1631475571036632663202957103393965035731887626733010461917389602470914047677436812, 765.1631475571036632663202957103393965035731887626733010461917389602470914091334164861]",
"[768.0138745572518907293275999555815267653065336727976219460174619355364003057206003644, 768.0138745572518907293275999555815267653065336727976219460174619355364003131016410783]",
"[768.0138653589402594979836904858334406218268933186958826108558230642887386817259553161, 768.0138653589402594979836904858334406218268933186958826108558230642887386949130068673]",
"[768.0138561606286282666397810160853544783472529645941432756941841930410770549217109493, 768.0138561606286282666397810160853544783472529645941432756941841930410770795361623231]"
]
},
{
"lower_level": 28,
"upper_level": 29,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "645.014325063812559913355077649035876513653097006249858133265566811354957781347497188529463710949231",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[645.0143434604358223760428965885320488006123777144533368035888445538502810235351852119, 645.014343460435822376042896588532048800612377714453336803588844553850281024267823776]",
"[645.0143342621241911446989871187839626571327373603515974684272056826026194024413406604, 645.0143342621241911446989871187839626571327373603515974684272056826026194031757690705]",
"[645.0143250638125599133550776490358765136530970062498581332655668113549577813474971885, 645.014325063812559913355077649035876513653097006249858133265566811354957782083714365]",
"[647.4516676253437658457883335676367912349544722596833059435680589015232016833446802386, 647.4516676253437658457883335676367912349544722596833059435680589015232016840966908084]",
"[653.3013023799478419398833748511215758318931324748538892537370065729580548706902415796, 653.30130237994784193988337485112157583189313247485388925373700657295805487149452148]",
"[662.4007388944756780374870882442241840212713201074760135602262248228722343031896687617, 662.400738894475678037487088244224184021271320107476013560226224822872234304115605289]",
"[673.9979788312748868151576940355133137293053644368761735768175091224642442357225475768, 673.9979788312748868151576940355133137293053644368761735768175091224642442368860866915]",
"[686.8535536582236758024186119419876434295759095472282349242565302188764876735099000179, 686.8535536582236758024186119419876434295759095472282349242565302188764876750954422705]",
"[699.2533853544196850025679402712743949596241011901842398025880347897512011425473265264, 699.2533853544196850025679402712743949596241011901842398025880347897512011448523458222]",
"[709.3516020835648594119976481952353520872133295211910998611486516834793052160582473303, 709.3516020835648594119976481952353520872133295211910998611486516834793052195960278704]",
"[715.8433086966375554002167572329329574316397617875856217456316801369235372431717334356, 715.8433086966375554002167572329329574316397617875856217456316801369235372489081335159]",
"[718.5481800608509482624653357413764170062072869297771463927090185652850642516221333423, 718.5481800608509482624653357413764170062072869297771463927090185652850642614942757964]",
"[718.5481693134227839590030520799836350419369976495601937567896729390567686773951938427, 718.5481693134227839590030520799836350419369976495601937567896729390567686953781235377]",
"[718.5481585659946196555407684185908530776667083693432411208703273128284730991292910332, 718.5481585659946196555407684185908530776667083693432411208703273128284731332992505361]"
]
},
{
"lower_level": 27,
"upper_level": 28,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "596.2567999778443347202825897592283938452673216563646124695922321492339716631167588864636034882241553",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[596.256821472700663327207157082013957773807900216798517741430923401690562803460093537, 596.2568214727006633272071570820139577738079002167985177414309234016905628042742888384]",
"[596.256810725272499023744873420621175809537610936581565105511577775462267233288425672, 596.2568107252724990237448734206211758095376109365815651055115777754622672341047109262]",
"[596.2567999778443347202825897592283938452673216563646124695922321492339716631167588865, 596.256799977844334720282589759228393845267321656364612469592232149233971663935133014]",
"[598.5333156253358063142250052717618526060929665675752175345716223649382614706333791, 598.5333156253358063142250052717618526060929665675752175345716223649382614714692285146]",
"[603.9969679031290485973788499077433724133229260224074690053483563965851590704771799248, 603.9969679031290485973788499077433724133229260224074690053483563965851590713706088341]",
"[612.4959880085448860153170606659675321972764618467297747171848397532710861501784298204, 612.495988008544886015317060665967532197276461846729774717184839753271086151205753887]",
"[623.3423502250291061689836187312738183811098208836698547939741852835782653582711866413, 623.3423502250291061689836187312738183811098208836698547939741852835782653595601283211]",
"[635.3927237436282910815298031801635218565995612006890258345615046354604331107618415691, 635.3927237436282910815298031801635218565995612006890258345615046354604331125166559639]",
"[647.0403904811830042417349161196192525283678845897883782420063989249077917662444333176, 647.0403904811830042417349161196192525283678845897883782420063989249077917687989947038]",
"[656.5365887810958998301205678422710029516900794483978294329139957527490142311458047454, 656.5365887810958998301205678422710029516900794483978294329139957527490142350885730123]",
"[662.6412828284023102826361495632904836616386266883223679870409371738066812707738626043, 662.6412828284023102826361495632904836616386266883223679870409371738066812772391876963]",
"[665.1848978556458570283929283759154861226403574872852827502671944653041698127538734108, 665.1848978556458570283929283759154861226403574872852827502671944653041698240635708921]",
"[665.1848852608123959963548438515248627395296998201078430253000829201489372289257058368, 665.1848852608123959963548438515248627395296998201078430253000829201489372499117854214]",
"[665.1848726659789349643167593271342393564190421529304033003329713749937046401443976487, 665.1848726659789349643167593271342393564190421529304033003329713749937046807110506121]"
]
},
{
"lower_level": 26,
"upper_level": 27,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "543.8895009437929456489089170332248455074566096428099016316235223651001269955271260510699888348771127",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[543.8895261334598677129850860820060922736779249771647810815577454554105921535058052609, 543.8895261334598677129850860820060922736779249771647810815577454554105921544093352489]",
"[543.889513538626406680947001557615468890567267309987341356590633910255359574516465656, 543.8895135386264066809470015576154688905672673099873413565906339102553595754224429182]",
"[543.8895009437929456489089170332248455074566096428099016316235223651001269955271260511, 543.8895009437929456489089170332248455074566096428099016316235223651001269964355505876]",
"[545.9880311045894754791580794310549597230356082038689357080357008221774576873611847901, 545.9880311045894754791580794310549597230356082038689357080357008221774576882886283288]",
"[551.0245207370040767595274322402589968110349770102132409284976678471734573090091947933, 551.0245207370040767595274322402589968110349770102132409284976678471734573099988586879]",
"[558.8590665400191113147840574980918605275970560341955769695874584563843126557921801196, 558.8590665400191113147840574980918605275970560341955769695874584563843126569262828537]",
"[568.8744652779414168009068786686659806348252423657841302737365726007876120980876727964, 568.8744652779414168009068786686659806348252423657841302737365726007876120995040702902]",
"[580.033805385905226501716112681833559524931793333246017409004290680497349429495312698, 580.0338053859052265017161126818335595249317933332460174090042906804973494314160170955]",
"[590.849172951791741498294887408658611392889112401970725561179554314943195158967913351, 590.8491729517917414982948874086586113928891124019707255611795543149431951617616534254]",
"[599.6792346016221553381205939066044177619982468052879843235007089254108727745773751393, 599.6792346016221553381205939066044177619982468052879843235007089254108727789102294241]",
"[605.3556970824856014364057594209726156688947295110724940188190798543618866386881131617, 605.3556970824856014364057594209726156688947295110724940188190798543618866458782751191]",
"[607.7208809698800256315837104919796196974910044702240947092906118335772789721808270375, 607.7208809698800256315837104919796196974910044702240947092906118335772789849834935216]",
"[607.7208661610683811352597908613246510585347696888145053805788804215620467660093532648, 607.7208661610683811352597908613246510585347696888145053805788804215620467902381263052]",
"[607.7208513522567366389358712306696824195785349074049160518671490095468145538338963653, 607.7208513522567366389358712306696824195785349074049160518671490095468146015039393825]"
]
},
{
"lower_level": 25,
"upper_level": 26,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "487.705903947413567662746369272748101636577332109413713257602820662975169805349446808229380569458749",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[487.7059335650368566553942085340580389144898016722328919150262834870056342062720821267, 487.7059335650368566553942085340580389144898016722328919150262834870056342072935303602]",
"[487.7059187562252121590702889034030702755335668908233025863145520749904020058107641976, 487.7059187562252121590702889034030702755335668908233025863145520749904020068350888149]",
"[487.7059039474135676627463692727481016365773321094137132576028206629751698053494468082, 487.7059039474135676627463692727481016365773321094137132576028206629751698063766472697]",
"[489.6070953946355607896946930164952230173462353783858711084670128114703585397711290044, 489.6070953946355607896946930164952230173462353783858711084670128114703585408188144577]",
"[494.1699751353727377414901335267220161418526088596964831231215934962451660020417792088, 494.1699751353727377414901335267220161418526088596964831231215934962451660031558832754]",
"[501.2677955434680318712726189642390764053494694897322894119789612859464422211445929993, 501.2677955434680318712726189642390764053494694897322894119789612859464422224125622835]",
"[510.3619008480029793577073180711110235131095831320603279297926032176950089546966016587, 510.3619008480029793577073180711110235131095831320603279297926032176950089562654134938]",
"[520.5333942920543380038765700182070389844915550138960842015847282504078731871242602965, 520.5333942920543380038765700182070389844915550138960842015847282504078731892326081258]",
"[530.4260745101308679723123615402376076934839043413696101010739698655473177347008784897, 530.4260745101308679723123615402376076934839043413696101010739698655473177377526532467]",
"[538.5176759281848716475683743529115302537335736811439578723330204667939012940467085694, 538.5176759281848716475683743529115302537335736811439578723330204667939012987918880857]",
"[543.7194129323719088400912713713994798707831301679760727091963308068717889910867812697, 543.7194129323719088400912713713994798707831301679760727091963308068717889990517532818]",
"[545.886792945887091131310258094316480615458380412732969126656802689607448026914741058, 545.886792945887091131310258094316480615458380412732969126656802689607448041358609901]",
"[545.8867754696436560045455494843397150344630898036101685249284127565513369748498205503, 545.8867754696436560045455494843397150344630898036101685249284127565513370027441030636]",
"[545.8867579934002208777808408743629494534677991944873679232000228234952259155161910526, 545.8867579934002208777808408743629494534677991944873679232000228234952259713866150826]"
]
},
{
"lower_level": 24,
"upper_level": 25,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "427.4326763148450770934752504568410029383643717581089279245649963027797616120036497833612041210641075",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[427.4327112673319473470046676767945341003549529763545291280217761688919837026745111287, 427.4327112673319473470046676767945341003549529763545291280217761688919837036609969133]",
"[427.432693791088512220239959066817768519359662367231728526293386235835872657339080456, 427.4326937910885122202399590668177685193596623672317285262933862358358726583289591753]",
"[427.4326763148450770934752504568410029383643717581089279245649963027797616120036497834, 427.4326763148450770934752504568410029383643717581089279245649963027797616129969214374]",
"[429.1144441616524511649020034095526665593240436635583006325149117463389394936452095621, 429.1144441616524511649020034095526665593240436635583006325149117463389394946575029171]",
"[433.15071089793554441332372025387601406133718494484250400374488086636072936769221061, 433.1507108979355444133237202538760140613371849448425040037448808663607293687643002564]",
"[439.4293568455622153488465211519773551272295140772665230689490872631819188676333096552, 439.4293568455622153488465211519773551272295140772665230689490872631819188688428504012]",
"[447.4990884327859327555825572354132870665405646738018070672999100845501373446731086067, 447.4990884327859327555825572354132870665405646738018070672999100845501373461509972399]",
"[456.5722553416500012438640385182319245937689333681268524021804231254842673706772595305, 456.5722553416500012438640385182319245937689333681268524021804231254842673726381388445]",
"[465.4390993302552170555552379095271375708215479300134502346306523118030764517019522241, 465.4390993302552170555552379095271375708215479300134502346306523118030764545165783324]",
"[472.7097060387567248467369043619921713324950163316547941156440161387942305919389913708, 472.7097060387567248467369043619921713324950163316547941156440161387942305963160342313]",
"[477.3836594638560433904702544504320094276595225027227873904781393200475554522282920709, 477.3836594638560433904702544504320094276595225027227873904781393200475554596510152522]",
"[479.3311277224096138788449780462472881708132974524789393922753272017396035560191824609, 479.3311277224096138788449780462472881708132974524789393922753272017396035697206144667]",
"[479.3311070138370845119017116437319815423962880956606042232825020173571776382751290134, 479.3311070138370845119017116437319815423962880956606042232825020173571776652628210966]",
"[479.331086305264555144958445241216674913979278738842269054289676832974751713165065024, 479.3310863052645551449584452412166749139792787388422690542896768329747517681590868907]"
]
},
{
"lower_level": 23,
"upper_level": 24,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "362.7137131228749579718584193157963287519989458841597082905393326911638588239546654962112206463392666",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[362.7137545400200167057449521208269420088329645977963786285249830599287106461566305213, 362.7137545400200167057449521208269420088329645977963786285249830599287106471628742403]",
"[362.7137338314474873388016857183116353804159552409780434595321578755462847350556480088, 362.7137338314474873388016857183116353804159552409780434595321578755462847360659113244]",
"[362.7137131228749579718584193157963287519989458841597082905393326911638588239546654962, 362.7137131228749579718584193157963287519989458841597082905393326911638588249689484086]",
"[364.1505544131983726835443768788494157890917326998938015826587733276343091067586058337, 364.1505544131983726835443768788494157890917326998938015826587733276343091077918634879]",
"[367.5990018165237501276571397770225154489886989632011295108171248788947097233244425845, 367.5990018165237501276571397770225154489886989632011295108171248788947097244157379902]",
"[372.9632637332296845371745127557880123249679955269702312165027800869688343246452207069, 372.9632637332296845371745127557880123249679955269702312165027800869688343258690321817]",
"[379.8895876136446992560998408169118387326041859919544389663792824691229718045212312897, 379.889587613644699256099840816911838732604185991954438966379282469122971806003620986]",
"[387.7368488925693721251506700382116336413764302052516623781062972004775123337716350496, 387.7368488925693721251506700382116336413764302052516623781062972004775123357219938909]",
"[395.4587429065188874895066256838163335725144667065656404765980874488715564275747745673, 395.4587429065188874895066256838163335725144667065656404765980874488715564303643234011]",
"[401.8130460237724519861338318708491377539328054494915515509627813831324099680995268992, 401.8130460237724519861338318708491377539328054494915515509627813831324099724627011525]",
"[405.8979455925246688039316792529761982704420366558560246640758908385970291155528611196, 405.8979455925246688039316792529761982704420366558560246640758908385970291230754238071]",
"[407.5999723887631781188910837886889717119134549475831866247866558484871445934665435786, 407.5999723887631781188910837886889717119134549475831866247866558484871446076802758019]",
"[407.5999477387591721880176073434486612116095067005059930901493742159189173229283516627, 407.5999477387591721880176073434486612116095067005059930901493742159189173515892010079]",
"[407.5999230887551662571441308982083507113055584534287995555120925833506900441886873384, 407.5999230887551662571441308982083507113055584534287995555120925833506901037141953666]"
]
},
{
"lower_level": 22,
"upper_level": 23,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "293.0899162985907721713992373744799991676168911381436932694138931029273839993392091155560249726087809",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[293.0899655985987840331461902649606201682247876322980803386884563680638385259834531007, 293.0899655985987840331461902649606201682247876322980803386884563680638385272880100527]",
"[293.0899409485947781022727138197203096679208393852208868040511747354956112626613311081, 293.0899409485947781022727138197203096679208393852208868040511747354956112639706719577]",
"[293.0899162985907721713992373744799991676168911381436932694138931029273839993392091156, 293.0899162985907721713992373744799991676168911381436932694138931029273840006533338628]",
"[294.2520246865082472783969286995105938995314525787591928555400064859820073182740758219, 294.2520246865082472783969286995105938995314525787591928555400064859820073196106821352]",
"[297.0411184870847552978048522043488737111629252210493528638602480246631722353973919271, 297.0411184870847552978048522043488737111629252210493528638602480246631722368026703539]",
"[301.3797211839555993662069584429040165278653677681083475058134737009672034656341914127, 301.3797211839555993662069584429040165278653677681083475058134737009672034671961445106]",
"[307.023518004632430761920245593080369383528174798855002600211593342357948399989773338, 307.0235180046324307619202455930803693835281747988550026002115933423579484018578332713]",
"[313.4957680353599488666541883549148816052109210300749924200937564711104032347246199179, 313.495768035359948866654188354914881605210921030074992420093756471110403237150477024]",
"[319.9335008246739589887312606951676437078971963843665077568493257492876197174184998447, 319.9335008246739589887312606951676437078971963843665077568493257492876197208616754764]",
"[325.2601107229823583034832724868668290465895683948992012369445473371717695740528936167, 325.2601107229823583034832724868668290465895683948992012369445473371717695794572600041]",
"[328.6843484595927559141275760690118084610568678194460638005114677420863826312234339182, 328.6843484595927559141275760690118084610568678194460638005114677420863826406933263109]",
"[330.1110965983415120603931599885073166961195369986409598855736969307244322885852749893, 330.1110965983415120603931599885073166961195369986409598855736969307244323069070787626]",
"[330.1110671094416766684823662058865770892948344191969153288140226163142709221495612053, 330.1110671094416766684823662058865770892948344191969153288140226163142709599621168068]",
"[330.1110376205418412765715724232658374824701318397528707720543483019041095443789809063, 330.1110376205418412765715724232658374824701318397528707720543483019041096243499270952]"
]
},
{
"lower_level": 21,
"upper_level": 22,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "217.9733000881540951018999457457310161084642168659620101031026834051525498415328064568711481256446623",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[217.9733590659537658857215333109724953221136220248500992166220320339728725549130887112, 217.9733590659537658857215333109724953221136220248500992166220320339728725566283683456]",
"[217.973329577053930493810739528351755715288919445406054659862357719562711198222947584, 217.9733295770539304938107395283517557152889194454060546598623577195627111999439492199]",
"[217.9733000881540951018999457457310161084642168659620101031026834051525498415328064569, 217.9733000881540951018999457457310161084642168659620101031026834051525498432595300942]",
"[218.825412847095807679997938232178398100447183993091416636351228602248236227897307423, 218.8254128470958076799979382321783981004471839930914166363512286022482362296508784794]",
"[220.8705237150466349723042209102991490491408434545141933409247789062791680513204270015, 220.8705237150466349723042209102991490491408434545141933409247789062791680531559601553]",
"[224.0518219978530986399268160305025491885935993510036435163725588544087124171789055472, 224.0518219978530986399268160305025491885935993510036435163725588544087124192013928587]",
"[228.2485062288500813155826742287789226518699231179335565157276593232506288899100724017, 228.2485062288500813155826742287789226518699231179335565157276593232506288922986938574]",
"[233.1693470611358904600652726451906805173729372547767296696071466756038873893251306997, 233.1693470611358904600652726451906805173729372547767296696071466756038873923874607439]",
"[238.1582278342653369780287452152130748971631540436872243430792997739563183292195086277, 238.1582278342653369780287452152130748971631540436872243430792997739563183335380727524]",
"[242.3253682242389207199833352903522462688876734443040189881189447510276146030314768998, 242.3253682242389207199833352903522462688876734443040189881189447510276146098548753522]",
"[245.0042303409878275139512379569800178067064259427685531584175473405295469390862452448, 245.0042303409878275139512379569800178067064259427685531584175473405295469512921322407]",
"[246.1204017222581584714803074422808416021851426440193621382953185352360154073510907235, 246.1204017222581584714803074422808416021851426440193621382953185352360154316187818478]",
"[246.1203662484427729785895516119124602079713648400966916806186357235203517277932341454, 246.1203662484427729785895516119124602079713648400966916806186357235203517791339632091]",
"[246.1203307746273874856987957815440788137575870361740212229419529118046880321515518628, 246.1203307746273874856987957815440788137575870361740212229419529118046881427342146927]"
]
},
{
"lower_level": 20,
"upper_level": 21,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "136.6134558280434772048165502525837358219614465800768992354434543029907268038657932698039968443985555",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[136.613526775674248190598061913320498610389002187922240150796819926422054135916176537, 136.6135267756742481905980619133204986103890021879222401507968199264220541378925234987]",
"[136.6134913018588626977073060829521172161752243839995696931201371147063904698909847685, 136.6134913018588626977073060829521172161752243839995696931201371147063904718742147565]",
"[136.6134558280434772048165502525837358219614465800768992354434543029907268038657932698, 136.6134558280434772048165502525837358219614465800768992354434543029907268058559060143]",
"[137.1133364789063022016669341464458037002508001987337885383855353905997965105165687143, 137.113336478906302201666934146445803700250800198733788538385535390599796512535376748]",
"[138.3130984121618191535922139331079641008590586336639638047171598249596221802266823525, 138.3130984121618191535922139331079641008590586336639638047171598249596221823311984218]",
"[140.1794123786486701111802806582408508911945266137172220372799567522678257645285218225, 140.1794123786486701111802806582408508911945266137172220372799567522678257668274982293]",
"[142.7318510282656227884692479503393673981527649754058592388110434149367586358173809295, 142.7318510282656227884692479503393673981527649754058592388110434149367586384979205354]",
"[145.8900044856198465526065518141427784162080644931874765888493367658118028489037398357, 145.8900044856198465526065518141427784162080644931874765888493367658118028522954331075]",
"[149.2327801140284835464751383834239620166696738792369225160539365777836789584813296981, 149.2327801140284835464751383834239620166696738792369225160539365777836789632378128795]",
"[152.0826214524553160541499068490796777417905037202036649144669574744075953871005387352, 152.0826214524553160541499068490796777417905037202036649144669574744075953946931342725]",
"[153.9146455061823385328540675337290852618262294911098015755437099140775198103651515895, 153.9146455061823385328540675337290852618262294911098015755437099140775198243070218147]",
"[154.6779632233922850742128386658788391773404587998417125681425106012559706047539838876, 154.677963223392285074212838665878839177340458799841712568142510601255970633369824491]",
"[154.6779202870216069847869453517220238994455736537848467790559639574126232739848240492, 154.6779202870216069847869453517220238994455736537848467790559639574126233361927719103]",
"[154.6778773506509288953610520375652086215506885077279809899694173135692759228172273179, 154.6778773506509288953610520375652086215506885077279809899694173135692760593980397825]"
]
},
{
"lower_level": 19,
"upper_level": 20,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "48.0536092991201663040602895123216822585482133547558045361662662462947896827579480905686420308464389",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[48.053695171861522482912076140635312814337983646869536114339359533981484310695833489, 48.0536951718615224829120761406353128143379836468695361143393595339814843125695416115]",
"[48.05365223549084439348618282647849753644309850081267032525281289013813699672689078978, 48.05365223549084439348618282647849753644309850081267032525281289013813699860892917155]",
"[48.05360929912016630406028951232168225854821335475580453616626624629478968275794809057, 48.05360929912016630406028951232168225854821335475580453616626624629478968464831673161]",
"[48.15002795971476112012581160292557629731923255092420301429216933068938760791516940734, 48.15002795971476112012581160292557629731923255092420301429216933068938760983201930744]",
"[48.38149123341856063945369985835509252809706416415968147409593209345804163265044541551, 48.38149123341856063945369985835509252809706416415968147409593209345804163464130559338]",
"[48.74156645401844966231312298341006207555275577819033169282816853010976823700222184828, 48.74156645401844966231312298341006207555275577819033169282816853010976823915793089828]",
"[49.41065379671076116137921259357477311668342861192990080432213273942080343324913450775, 49.4106537967107611613792125935747731166834286119299008043221327394208034357274934463]",
"[50.54986198315487152226464506141137276538267384101575604777011754877024500087364100664, 50.54986198315487152226464506141137276538267384101575604777011754877024500396073971718]",
"[52.0072898707332428603924048841412390823942464025935018428848293051035287333602677124, 52.00728987073324286039240488414123908239424640259350184288482930510352873765100630439]",
"[53.34840721478675452155820712251304303305600198005318611827611652305035188336111448229, 53.34840721478675452155820712251304303305600198005318611827611652305035189025808539918]",
"[54.21053353640167593381497651041208516586955583201566693307413825787190435286745253076, 54.21053353640167593381497651041208516586955583201566693307413825787190436582742001059]",
"[54.56972156821362272609759040201723255369975779052056822589368045972140625317590560097, 54.56972156821362272609759040201723255369975779052056822589368045972140628054237416704]",
"[54.56966924386826865147345622692673723915431495808826655798182778512209039072941218727, 54.56966924386826865147345622692673723915431495808826655798182778512209045166473674646]",
"[54.56961691952291457684932205183624192460887212565596489006997511052277450750430930715, 54.56961691952291457684932205183624192460887212565596489006997511052277464358327685071]"
]
}
],
"pointwise_nonnegative_pair_energy_certified": true,
"second_is_unassigned_mathematical_control": false
},
{
"depth": 5,
"shell_levels": [
9,
14
],
"other_unsmoothed_chart_minimum_source_cost_lower_bound": "6.021653859725143127504202008833914979459360956078715741714169424600264728869133698057279991999798227",
"common_smoothing_width_interval": "[0.0000000009560186767665473489840416876308890792116918898909371811707678008717334033705832106858, 0.0000000009560186767665473489840416876308890792116918898909371811707678008717334073239074393973]",
"smoothing_bands": [
{
"lower_level": 13,
"upper_level": 14,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "12.00930629503173394547597720819162135259428303876927659654966606708372170189084689852917247374769588",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[12.70072481743099908324628585646791040225059896669800797498280919182192576881902417612, 12.70072481743099908324628585646791040225059896669800797498280919182192576882404610814]",
"[12.70072789809254221921141125290909853978854795165410460088669405615721122779201505281, 12.70072789809254221921141125290909853978854795165410460088669405615721122779704973667]",
"[12.7007309787540853551765366493502866773264969366102012267905789204924966867650059295, 12.7007309787540853551765366493502866773264969366102012267905789204924966867700533652]",
"[12.60380414104940855187559936686225007609866573114492486355989879096693575645209563539, 12.60380414104940855187559936686225007609866573114492486355989879096693575645734612225]",
"[12.37117529570175650026065452206797747329259529236810125708336463296151654547867706382, 12.37117529570175650026065452206797747329259529236810125708336463296151654548462819359]",
"[12.00930629503173394547597720819162135259428303876927659654966606708372170189084689853, 12.00930629503173394547597720819162135259428303876927659654966606708372170189844736782]",
"[12.05336635983688810084480394513749430415250969496440024031503281423598469994721612599, 12.05336635983688810084480394513749430415250969496440024031503281423598469995817726245]",
"[13.05791035896872169274455263195090162983985035884797577492460917836114113394164173301, 13.05791035896872169274455263195090162983985035884797577492460917836114113395948038012]",
"[14.88899897465353528517088650212796182044416736493774389183977225557652078072823437855, 14.88899897465353528517088650212796182044416736493774389183977225557652078076170091484]",
"[16.75098721522281457251136756670743810688178381894734399163515386300584619566316951144, 16.7509872152228145725113675667074381068817838189473439916351538630058461957361161236]",
"[17.94797997690186758413483527377558258701401232563775769995863956047372757377041854997, 17.94797997690186758413483527377558258701401232563775769995863956047372757394687810976]",
"[18.44672790257031193378795192932917532469493184411763941098526295791329222795876074821, 18.44672790257031193378795192932917532469493184411763941098526295791329222840043252383]",
"[18.44672975032625171910394028691932303965451247917040573990001101367453150698196469776, 18.44672975032625171910394028691932303965451247917040573990001101367453150806926651646]",
"[18.4467315980821915044199286445094707546140931142231720688147590694357707855871359542, 18.44673159808219150441992864450947075461409311422317206881475906943577078815677703533]"
]
},
{
"lower_level": 12,
"upper_level": 13,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "29.48314631163401476765042118877154990720493989328217538665709552598610071838152447185809096527143223",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[29.48314631163401476765042118877154990720493989328217538665709552598610071838152447186, 29.48314631163401476765042118877154990720493989328217538665709552598610071838982595515]",
"[29.48314815938995455296640954636169762216452052833494171557184358174733999772731114351, 29.4831481593899545529664095463616976221645205283349417155718435817473399977356252437]",
"[29.48315000714589433828239790395184533712410116338770804448659163750857927707309781517, 29.48315000714589433828239790395184533712410116338770804448659163750857927708142453226]",
"[29.64142280845074920252124281261264896759679458738178396390797636129872898725648738236, 29.64142280845074920252124281261264896759679458738178396390797636129872898726528099231]",
"[30.02127452601876059630545147473461777611198544913303802184356760397223334923449318951, 30.02127452601876059630545147473461777611198544913303802184356760397223334924493954623]",
"[30.61215327446250254692788431219806156641238799506218920917503489389659339119165144407, 30.6121532744625025469278843121980615664123879950621892091750348938965933912060104237]",
"[31.84429841952459031613791612455026063215029296773432600077146079339765784207818102212, 31.84429841952459031613791612455026063215029296773432600077146079339765784210038295846]",
"[34.11629474722191654953609038237376179546300034649306927191547593901397815937935295058, 34.11629474722191654953609038237376179546300034649306927191547593901397815941660600822]",
"[37.12520870994578199502734461672395914791814947518816693654185895334792608248536303906, 37.12520870994578199502734461672395914791814947518816693654185895334792608255299422442]",
"[39.92717620462420096757425774466088840576705998401271211564647833048358064778359033073, 39.92717620462420096757425774466088840576705998401271211564647833048358064791858632962]",
"[41.72843974566525012486598493430597287911314361719312378101251966983649221058713079364, 41.72843974566525012486598493430597287911314361719312378101251966983649221088222772858]",
"[42.47896509949913802274243140939334766921201296646073462513418224550570545799262721771, 42.47896509949913802274243140939334766921201296646073462513418224550570545867424262335]",
"[42.4789637168784574781740850565695476155429310535546648291239967993229984808251512656, 42.47896371687845747817408505656954761554293105355466482912399679932299848241749132982]",
"[42.47896233425777693360573870374574756187384914064859503311381135314029150308553069852, 42.47896233425777693360573870374574756187384914064859503311381135314029150673305204449]"
]
},
{
"lower_level": 11,
"upper_level": 12,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "37.23510919654149848374048708585913342192914119407026286564408072221061319374289761245299609032606987",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[37.23511196178285957287717979150673352926730501988240245766445161457602714716769923077, 37.23511196178285957287717979150673352926730501988240245766445161457602714717765234756]",
"[37.23511057916217902830883343868293347559822310697633266165426616839332017045529842161, 37.23511057916217902830883343868293347559822310697633266165426616839332017046527171195]",
"[37.23510919654149848374048708585913342192914119407026286564408072221061319374289761245, 37.23510919654149848374048708585913342192914119407026286564408072221061319375289107634]",
"[37.49489666719358207545847610919939397916851970310307262193901386342712762090545772559, 37.49489666719358207545847610919939397916851970310307262193901386342712762091611651181]",
"[38.11838754583976832932580610140213435066783350175205911847701981800148775915275390498, 38.11838754583976832932580610140213435066783350175205911847701981800148775916576847605]",
"[39.08826142457698358990888524844462877452707724843225960234024029448663981994920516548, 39.08826142457698358990888524844462877452707724843225960234024029448663981996780700026]",
"[40.79176075418551104587107771179328876242347624691811315830813611805597432910190017071, 40.79176075418551104587107771179328876242347624691811315830813611805597432913173833548]",
"[43.56416975663926971072854829092695692857616125286307933159481825960127180095207834044, 43.56416975663926971072854829092695692857616125286307933159481825960127180100361730762]",
"[47.03583199434527350734252542932035059877912402367409798070067954672220933167020205629, 47.03583199434527350734252542932035059877912402367409798070067954672220933176599383067]",
"[50.20608347876495019423411377868845455882088906132901671085063183568689245880433485343, 50.2060834787649501942341137786884545588208890613290167108506318356868924589994207059]",
"[52.24409767621187662438947855879294250901901849442520474692279219522492255394974047887, 52.24409767621187662438947855879294250901901849442520474692279219522492255438310766758]",
"[53.09326471346940147884042276505768251151152389948255578240623060502040793694256253422, 53.09326471346940147884042276505768251151152389948255578240623060502040793795496087267]",
"[53.09325632321509431887182770964410933883993306710882409824688144037529332824681378264, 53.0932563232150943188718277096441093388399330671088240982468814403752933306292585561]",
"[53.0932479329607871589032326542305361661683422347350924140875322757301787186853101166, 53.09324793296078715890323265423053616616834223473509241408753227573017872416818271713]"
]
},
{
"lower_level": 10,
"upper_level": 11,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "33.50884792652669772197945332042581459462134477704173380525390199304696842395444797111008181636291845",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[33.50886470703531204191664343125296093996452644178919717357260032233719763997562241198, 33.50886470703531204191664343125296093996452644178919717357260032233719763998722537432]",
"[33.50885631678100488194804837583938776729293560941546548941325115769208303196503515781, 33.50885631678100488194804837583938776729293560941546548941325115769208303197668123352]",
"[33.50884792652669772197945332042581459462134477704173380525390199304696842395444797111, 33.50884792652669772197945332042581459462134477704173380525390199304696842396613702525]",
"[33.70606636056390430669684899321937218427492697049111653647595926320728054019252097576, 33.70606636056390430669684899321937218427492697049111653647595926320728054020501204658]",
"[34.17940026979178239724173163986896291783539923439587702569770264576765955415112563998, 34.17940026979178239724173163986896291783539923439587702569770264576765955416641354748]",
"[34.91569877397207298835397252778326699057349171200777223181166230335257155677330354583, 34.91569877397207298835397252778326699057349171200777223181166230335257155679521229099]",
"[36.32512058410371243669184089723907026252374021288042374827652669400646691936925888226, 36.32512058410371243669184089723907026252374021288042374827652669400646691940458391527]",
"[38.77837848178086941876463151537120768516153397238356088998996293897923569465392607677, 38.7783784817808694187646315153712076851615339723835608899899629389792356947158776319]",
"[41.94836712623962617418472223351911467869676142735234769035744567667660487377777974695, 41.94836712623962617418472223351911467869676142735234769035744567667660487389689066077]",
"[44.8755873504767730118123688675869161485084720385518505274636649850947435374702195035, 44.87558735047677301181236886758691614850847203855185052746366498509474353772544237111]",
"[46.75736049050869437424003332686443215986946349983435191633926954877244219300772206334, 46.75736049050869437424003332686443215986946349983435191633926954877244219360542204564]",
"[47.54141814229681979559550699704500744846094645873534866850248914942452358350775152045, 47.54141814229681979559550699704500744846094645873534866850248914942452358496333616885]",
"[47.54139551546447404938667209658839679353519967565899272793424542074125594614731383772, 47.5413955154644740493866720965883967935351996756589927279342454207412559496695846962]",
"[47.5413728886321283031778371961317861386094528925826367873660016920579883074552048723, 47.54137288863212830317783719613178613860945289258263678736600169205798831570508745855]"
]
},
{
"lower_level": 9,
"upper_level": 10,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "15.78570504722214660994974790162701903159306092641287342233497349133275407861456810877160335803354726",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[16.18907252333021519665652928829168717804312194112212878042465941990783344576276016395, 16.18907252333021519665652928829168717804312194112212878042465941990783344577706233378]",
"[16.18904989649786945044769438783507652311737515804577283985641569122456580943671842291, 16.18904989649786945044769438783507652311737515804577283985641569122456580945111697373]",
"[16.18902726966552370423885948737846586819162837496941689928817196254129817311067671561, 16.18902726966552370423885948737846586819162837496941689928817196254129817312517157995]",
"[16.13247612485897010518611114333330292739630577285131738604226777055561631020479142208, 16.13247612485897010518611114333330292739630577285131738604226777055561631022025158067]",
"[15.99678083559125202139698797776908518119657044710129598658888478029316458965699483935, 15.99678083559125202139698797776908518119657044710129598658888478029316458967570283828]",
"[15.78570504722214660994974790162701903159306092641287342233497349133275407861456810877, 15.78570504722214660994974790162701903159306092641287342233497349133275407864090020838]",
"[16.00896844453406404106943289762717561901151944307671071572935086697144743287805785938, 16.00896844453406404106943289762717561901151944307671071572935086697144743292006172057]",
"[17.18759564136823902536092848774746421451830580515224687294176117543094898378682378575, 17.18759564136823902536092848774746421451830580515224687294176117543094898386175624438]",
"[19.16442731665737752816696723798085529442900336186846624867520314769445646063672236468, 19.16442731665737752816696723798085529442900336186846624867520314769445646078959729032]",
"[21.13555806595172087184323492765113074927840946686513736230228098965973052599244420705, 21.13555806595172087184323492765113074927840946686513736230228098965973052634994484778]",
"[22.40268899381331750043547323018474363180199676792781435272196694315085387206925624594, 22.40268899381331750043547323018474363180199676792781435272196694315085387297775145737]",
"[22.93062789944695296620758152151625439847803874722438769839689812078819049587407786244, 22.93062789944695296620758152151625439847803874722438769839689812078819049821821087171]",
"[22.93057686779459740481003581636127799314722571197061656464521224566648456707276647419, 22.93057686779459740481003581636127799314722571197061656464521224566648457295128034183]",
"[22.93052583614224184341249011120630158781641267671684543089352637054477863594694109018, 22.93052583614224184341249011120630158781641267671684543089352637054477865000936831513]"
]
}
],
"pointwise_nonnegative_pair_energy_certified": true,
"second_is_unassigned_mathematical_control": false
},
{
"depth": 5,
"shell_levels": [
9,
21
],
"other_unsmoothed_chart_minimum_source_cost_lower_bound": "6.021653859725143127504202008833914979459360956078715741714169424600264728869133698057279991999798227",
"common_smoothing_width_interval": "[0.0000000009560186767665473489840416876308890792116918898909371811707678008717334033705832106858, 0.0000000009560186767665473489840416876308890792116918898909371811707678008717334073239074393973]",
"smoothing_bands": [
{
"lower_level": 20,
"upper_level": 21,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "16.60186564732642194690661416635377786147885067700933458299590343480505025307099960284224655937352406",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[16.88805148639291143756528779580359130036985528261503409373324096092056358922397488711, 16.8880514863929114375652877958035913003698552826150340937332409609205635892273943713]",
"[16.88805182703913285568165938144708600686751143078277958506029288959466122586189204476, 16.88805182703913285568165938144708600686751143078277958506029288959466122586531297956]",
"[16.88805216768535427379803096709058071336516757895052507638734481826875886249980923614, 16.88805216768535427379803096709058071336516757895052507638734481826875886250323158781]",
"[16.84793276159512406896804229624058919331136301482913885396235752055533407003165760665, 16.84793276159512406896804229624058919331136301482913885396235752055533407003512394881]",
"[16.75164570632982383222326549004446552343378446133130841931328106322163555935142764443, 16.7516457063298238322232654900444655234337844613313084193132810632216355593550490328]",
"[16.60186564732642194690661416635377786147885067700933458299590343480505025307099960284, 16.60186564732642194690661416635377786147885067700933458299590343480505025307498779223]",
"[16.98472103502594628706732865399811503227711725175840853874518946590047404737693987424, 16.98472103502594628706732865399811503227711725175840853874518946590047404738165498613]",
"[18.49436424449882539307271480494759342192498933893627345582352157593638073968515472959, 18.49436424449882539307271480494759342192498933893627345582352157593638073969120858254]",
"[20.92950952744330394601579679842355941584596833196166019622075658338365695079710341368, 20.92950952744330394601579679842355941584596833196166019622075658338365695080563270965]",
"[23.33369020373667679775300411079139379694715469838333953012340185805804065264164436479, 23.33369020373667679775300411079139379694715469838333953012340185805804065265503504775]",
"[24.87923500875757559421763336239745761502539150446547699815207719751735112515164968, 24.87923500875757559421763336239745761502539150446547699815207719751735112517531969753]",
"[25.52321217055890558883421839241154491471871102480311179967333049684581389499065497845, 25.52321217055890558883421839241154491471871102480311179967333049684581389503708278446]",
"[25.52321245646964180494448558311978115426192019991294741869932348489239445016676611295, 25.52321245646964180494448558311978115426192019991294741869932348489239445026390816578]",
"[25.52321274238037802105475277382801739380512937502278303772531647293897500531299306809, 25.52321274238037802105475277382801739380512937502278303772531647293897500552073043519]"
]
},
{
"lower_level": 19,
"upper_level": 20,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "48.04495421589784991630740588190339454238169489827889766579546688046293715938966016060261498338223166",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[48.0449542158978499163074058819033945423816948982788976657954668804629371593896601606, 48.04495421589784991630740588190339454238169489827889766579546688046293715939818891681]",
"[48.04495450180858613241767307261163078192490407338873328482145986850951771459109362082, 48.04495450180858613241767307261163078192490407338873328482145986850951771459962392884]",
"[48.04495478771932234852794026331986702146811324849856890384745285655609826979252708104, 48.0449547877193223485279402633198670214681132484985689038474528565560982698010588734]",
"[48.50172724641581222008358137476312476412008490327599637102193337084537625708991368571, 48.50172724641581222008358137476312476412008490327599637102193337084537625709859877007]",
"[49.59798072811369620631341728400736295829233200150897892259641327661301906403609817629, 49.59798072811369620631341728400736295829233200150897892259641327661301906404533219711]",
"[51.30326373258366347674952502803541910804943065938588538726390438687190758203629359655, 51.30326373258366347674952502803541910804943065938588538726390438687190758204682938484]",
"[53.9821544823697375144225574624696776245397313158638484195878093871410017263211850723, 53.98215448236973751442255746246967762453973131586384841958780938714100172633428350867]",
"[57.9078767416750752151492936693023649360345834612805357125793010941860524243522450862, 57.90787674167507521514929366930236493603458346128053571257930109418605242436992757384]",
"[62.55700086412254922264784164943295444726879421365287301249492952437116504151870172855, 62.55700086412254922264784164943295444726879421365287301249492952437116504154429150562]",
"[66.71412977973693912265118606183909622550186529740146722241554229704950262038716605043, 66.71412977973693912265118606183909622550186529740146722241554229704950262042657464177]",
"[69.38656980573520002172500768562065333247327524438557629951394260173527489807619048461, 69.38656980573520002172500768562065333247327524438557629951394260173527489814093503063]",
"[70.5000865449617982439411983151362272095259565269507678330138154369632890308309462344, 70.50008654496179824394119831513622720952595652695076783301381543696328903094481883971]",
"[70.50008667729567316285616947448065759429792122248245269107990946820870567243517246037, 70.50008667729567316285616947448065759429792122248245269107990946820870567264803471881]",
"[70.50008680962954808177114063382508797906988591801413754914600349945412231398801334849, 70.50008680962954808177114063382508797906988591801413754914600349945412231440255834519]"
]
},
{
"lower_level": 18,
"upper_level": 19,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "78.05222338256580527754201884570735181134878963189809843153299116577410626711035093419903487705835709",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[78.0522233825658052775420188457073518113487896318980984315329911657741062671103509342, 78.05222338256580527754201884570735181134878963189809843153299116577410626712196604115]",
"[78.0522235148996801964569900050517821961207543274297832895990851970195229087640957362, 78.05222351489968019645699000505178219612075432742978328959908519701952290877571300219]",
"[78.05222364723355511537196116439621258089271902296146814766517922826493955041784067314, 78.05222364723355511537196116439621258089271902296146814766517922826493955042945982829]",
"[78.89049368652374793352708225411209289442491568670165791835348167231071083378624495434, 78.89049368652374793352708225411209289442491568670165791835348167231071083379810497763]",
"[80.90234155227561684003656493295354109847919062206077716671557532967873257641856174806, 80.90234155227561684003656493295354109847919062206077716671557532967873257643128457856]",
"[84.03188253352655886646948079498164822557316883350312040029180173100929571799727644862, 84.03188253352655886646948079498164822557316883350312040029180173100929571801204578119]",
"[88.47482595696106287292405181216643516203829532422018271747462027342563301559977202814, 88.47482595696106287292405181216643516203829532422018271747462027342563301561856568031]",
"[94.25922714679312245131864758777550854551676404791096013053792766929142039141892101989, 94.25922714679312245131864758777550854551676404791096013053792766929142039144488390643]",
"[100.6138325521027532324572551720312658566666853354597287825788211162373107502423117252, 100.613832552102753232457255172031265856666685335459728782578821116237310750280513412]",
"[106.1223305383762895461536947828448665478225210651857585902274093943413070670070436294, 106.1223305383762895461536947828448665478225210651857585902274093943413070670662251334]",
"[109.6635076805378608367189486513335196748795198043442255902211635823408284261969343443, 109.6635076805378608367189486513335196748795198043442255902211635823408284262935392005]",
"[111.1389980243261335256272603287898774954130824601856745786595045207430955835611542972, 111.1389980243261335256272603287898774954130824601856745786595045207430955837281864333]",
"[111.1389978471110728918563369511966794979597602992543570765635324700359714814525509359, 111.1389978471110728918563369511966794979597602992543570765635324700359714817578440823]",
"[111.138997669896012258085413573603481500506438138323039574467560419328847379275016241, 111.138997669896012258085413573603481500506438138323039574467560419328847379856655986]"
]
},
{
"lower_level": 17,
"upper_level": 18,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "103.8960853796966863631001871086744334779358255984432058390481246251603789641958700946734904090518029",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[103.8960857341268076306420338638608294728424699203058408432400687265746271682749958171, 103.8960857341268076306420338638608294728424699203058408432400687265746271682868314163]",
"[103.8960855569117469968711104862676314753891477593745233411440966758675030662354329559, 103.8960855569117469968711104862676314753891477593745233411440966758675030662472717936]",
"[103.8960853796966863631001871086744334779358255984432058390481246251603789641958700947, 103.896085379696686363100187108674433477935825598443205839048124625160378964207712036]",
"[105.0158268171992742142361390679186991374528538299986265865204583265973415703917006187, 105.0158268171992742142361390679186991374528538299986265865204583265973415704038406427]",
"[107.7032064330852663022059659838207265000389256383413682516618359287455889443750649813, 107.7032064330852663022059659838207265000389256383413682516618359287455889443882745408]",
"[111.8835746904295274698475629254985035319407866698041701107405459273518813010414785351, 111.8835746904295274698475629254985035319407866698041701107405459273518813010572268583]",
"[117.6283499390053757031235574146988657267197224528719859935864343581386512264492447912, 117.6283499390053757031235574146988657267197224528719859935864343581386512264699912969]",
"[124.7850021900742561288773562639593406946089263059370897456730174573485066008574223332, 124.7850021900742561288773562639593406946089263059370897456730174573485066008870850083]",
"[132.3993110020913234663205070572923433468485078440386589449361793442452364230780814908, 132.3993110020913234663205070572923433468485078440386589449361793442452364231229903769]",
"[138.9062096863670209744922327624998048047824462810321036548237879982578245219827328615, 138.9062096863670209744922327624998048047824462810321036548237879982578245220538293094]",
"[143.0892155979794360953517349925858814607167749903912216787416194204910174441171146382, 143.0892155979794360953517349925858814607167749903912216787416194204910174442350363921]",
"[144.8321342503974929703204184879400521598638391986932639913076838943701334861910202758, 144.8321342503974929703204184879400521598638391986932639913076838943701334863972749208]",
"[144.8321335171624528672727337786751482988645582585362509393555613376104136772243901561, 144.8321335171624528672727337786751482988645582585362509393555613376104136776044085605]",
"[144.8321327839274127642250490694102444378652773183792378874034387808506938681707722285, 144.8321327839274127642250490694102444378652773183792378874034387808506938688986660277]"
]
},
{
"lower_level": 16,
"upper_level": 17,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "123.6638190752019121408902941045209624556699391435745570788910429297033613009044838473911667672269353",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[123.6638205416719923469856635230507701776685010238885831827952880432228009186639700719, 123.663820541671992346985663523050770177668501023888583182795288043222800918676335446]",
"[123.6638198084369522439379788137858663166692200837315701308431654864630811097842269597, 123.6638198084369522439379788137858663166692200837315701308431654864630811097965975964]",
"[123.6638190752019121408902941045209624556699391435745570788910429297033613009044838474, 123.6638190752019121408902941045209624556699391435745570788910429297033613009168597468]",
"[124.9753205839507692988494757616571331877586794575207748043682089827461007822909354614, 124.9753205839507692988494757616571331877586794575207748043682089827461007823037299451]",
"[128.1229250869935142843878686522296468975620245692391512484498019151786564802289484787, 128.1229250869935142843878686522296468975620245692391512484498019151786564802432421473]",
"[133.0191989329406013893406153783959332035740733151809637982675487226907428572419039889, 133.0191989329406013893406153783959332035740733151809637982675487226907428572597576481]",
"[139.6503719095281728836146560468015559125355635385824788821875910318576565112436497681, 139.6503719095281728836146560468015559125355635385824788821875910318576565112685203143]",
"[147.7403733504341234130294860075955945636679013134325334681129007622496244253172603049, 147.7403733504341234130294860075955945636679013134325334681129007622496244253546805534]",
"[156.2105361167720134360707685084978762316801594205965413870237616966955090163913830697, 156.2105361167720134360707685084978762316801594205965413870237616966955090164503945492]",
"[163.3953301981247367345864549061215825806503251592779392918114984918333216923876230975, 163.3953301981247367345864549061215825806503251592779392918114984918333216924841417269]",
"[168.0141255866051827901854189675484466901129145213648085317714332509093976074375774836, 168.0141255866051827901854189675484466901129145213648085317714332509093976076022430396]",
"[169.9386226015725560139264748825342737065053286620208158561775892827302225098454788576, 169.9386226015725560139264748825342737065053286620208158561775892827302225101410020685]",
"[169.9386209205992409646503850716234087002789919484176649977468364505479848838543910865, 169.9386209205992409646503850716234087002789919484176649977468364505479848844114244981]",
"[169.938619239625925915374295260712543694052655234814514139316083618365747257729122085, 169.9386192396259259153742952607125436940526552348145141393160836183657472588159752615]"
]
},
{
"lower_level": 15,
"upper_level": 16,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "136.2040056900932394118266397758844824050424726504811024419768163032420405754923923098580886315581497",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[136.2040090520398695103788193977062124174951460776874041588383219676065158272130295838, 136.2040090520398695103788193977062124174951460776874041588383219676065158272273267608]",
"[136.2040073710665544611027295867953474112688093640842533004075691354242782013527109468, 136.2040073710665544611027295867953474112688093640842533004075691354242782013670172998]",
"[136.2040056900932394118266397758844824050424726504811024419768163032420405754923923099, 136.2040056900932394118266397758844824050424726504811024419768163032420405755067075689]",
"[137.6239120865257733402275938622981934509514996650509827935852864681669686685010530577, 137.6239120865257733402275938622981934509514996650509827935852864681669686685158705639]",
"[141.0316895466502086274788013857217141517362027773523674241034430061500570994601680045, 141.0316895466502086274788013857217141517362027773523674241034430061500570994767742771]",
"[146.3326772464860206997880728820522395829167529358445564536272451016080127330551300102, 146.3326772464860206997880728820522395829167529358445564536272451016080127330759796103]",
"[153.463521294609775364252723110826356542646169834282195110927732418972677291570848306, 153.4635212946097753642527231108263565426461698342821951109277324189726772916000641943]",
"[162.076886195169752030095418596855981702091403916142177536874748914112702238714773601, 162.0768861951697520300954185968559817020914039161421775368747489141127022387590085961]",
"[171.0243227853127455057300335726548791568483603884181601280242885457038805518585340214, 171.0243227853127455057300335726548791568483603884181601280242885457038805519288726456]",
"[178.5859583298143089776630143484165559606003909671999063562312622886385819040263740622, 178.5859583298143089776630143484165559606003909671999063562312622886385819041429215858]",
"[183.4470082487932343128859390625092547927560987877769266857702123428554728100728250518, 183.4470082487932343128859390625092547927560987877769266857702123428554728102755699039]",
"[185.4724436784818167194952106048837061825762734786176086930945244961859489423323828479, 185.4724436784818167194952106048837061825762734786176086930945244961859489427053303894]",
"[185.4724404211286906638906877795797312667165151293009149930121973885119983396071771756, 185.4724404211286906638906877795797312667165151293009149930121973885119983403284270624]",
"[185.4724371637755646082861649542757563508567567799842212929298702808380477366969531969, 185.4724371637755646082861649542757563508567567799842212929298702808380477381362044216]"
]
},
{
"lower_level": 14,
"upper_level": 15,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "140.8589504757330833479712014783009087737921196915521801343965958312486508755226767690274971301748208",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[140.8589569904393354591802471289088586055116363901855675345612500465965520806242581524, 140.8589569904393354591802471289088586055116363901855675345612500465965520806396774916]",
"[140.8589537330862094035757243036048836896518780408688738344789229389226014780734674607, 140.8589537330862094035757243036048836896518780408688738344789229389226014780889021831]",
"[140.858950475733083347971201478300908773792119691552180134396595831248650875522676769, 140.8589504757330833479712014783009087737921196915521801343965958312486508755381268746]",
"[142.3066500231289588266030156023399632728807521576952977990558159814485792249497213929, 142.306650023128958826603015602339963272880752157695297799055815981448579224965803558]",
"[145.7811330894360685084088276203721942867507021210833908046073524448796545377475056522, 145.7811330894360685084088276203721942867507021210833908046073524448796545377658343007]",
"[151.1858856786109683167244438594124461555327588896445929307170101865776547368118874785, 151.1858856786109683167244438594124461555327588896445929307170101865776547368355465321]",
"[158.4417907014593532500036823390756405447663601069741554337208518319907125083499982343, 158.4417907014593532500036823390756405447663601069741554337208518319907125083841836979]",
"[167.1801905460050115125403492315138222594657414837838226853142345446882778328805548858, 167.1801905460050115125403492315138222594657414837838226853142345446882778329337536841]",
"[176.2359643456750046316130994543848496432373654822729026921707879833462907468325021669, 176.2359643456750046316130994543848496432373654822729026921707879833462907469192419547]",
"[183.8805525593438515128946399926357812759771462202547905284672845123932114731645964605, 183.8805525593438515128946399926357812759771462202547905284672845123932114733123189333]",
"[188.7949280497775237824725351144448880016695960597441901036956494816090183198227130063, 188.7949280497775237824725351144448880016695960597441901036956494816090183200883002882]",
"[190.8425808644764970908259288672867170097201017916204605814565315233961429994816826959, 190.8425808644764970908259288672867170097201017916204605814565315233961429999884438908]",
"[190.8425750080637521562764435174957921240212011790124682526340871270546081355290260362, 190.8425750080637521562764435174957921240212011790124682526340871270546081365437283425]",
"[190.8425691516510072217269581677048672383223005664044759238116427307130732712958515085, 190.8425691516510072217269581677048672383223005664044759238116427307130732733790392101]"
]
},
{
"lower_level": 13,
"upper_level": 14,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "137.2368342908317013534418054187025014199263988398186764549473217172845663483535500281072719564166825",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[137.2368460036571912225407761182843511913242000650346611125922105099676360757503306586, 137.2368460036571912225407761182843511913242000650346611125922105099676360757668762081]",
"[137.2368401472444462879912907684934263056252994524266687837697661136261012120519403433, 137.2368401472444462879912907684934263056252994524266687837697661136261012120685118014]",
"[137.2368342908317013534418054187025014199263988398186764549473217172845663483535500281, 137.2368342908317013534418054187025014199263988398186764549473217172845663483701473947]",
"[138.6305014206977054496790652897326385258752019749509887277020227260445861092747468778, 138.630501420697705449679065289732638525875201974950988727702022726044586109292125008]",
"[141.9753100540366192439570473565366109539894430002058286057937228662850848450450479866, 141.9753100540366192439570473565366109539894430002058286057937228662850848450651815943]",
"[147.1783478681935250708073094263398187233838447625668697982543490108994945856229052402, 147.1783478681935250708073094263398187233838447625668697982543490108994945856495621238]",
"[154.1785425054486601602955147709462934059867315511923983661988167481474984280117898281, 154.1785425054486601602955147709462934059867315511923983661988167481474984280513515765]",
"[162.6360870916761164825321579822025694471990684298988280614771280307181133214031928449, 162.6360870916761164825321579822025694471990684298988280614771280307181133214662741188]",
"[171.4233075019234056351700439867275603557050042141310498742764586417192932146992245473, 171.4233075019234056351700439867275603557050042141310498742764586417192932148047253318]",
"[178.8501978345776042403414521404824497506003964432444797319936725189067535340106878957, 178.8501978345776042403414521404824497506003964432444797319936725189067535341962556784]",
"[183.6246227957667845725733075674525855534962723459390245662282133583203419248190956533, 183.6246227957667845725733075674525855534962723459390245662282133583203419251666175049]",
"[185.6139602419103303286039877230275465083003982088044888961829687381820288135113935813, 185.6139602419103303286039877230275465083003982088044888961829687381820288142043924017]",
"[185.6139500932499769223389760251429324333563364323447108425647995162466358138607269748, 185.6139500932499769223389760251429324333563364323447108425647995162466358153042501342]",
"[185.6139399445896235160739643272583183584122746558849327889466302943112428137797964652, 185.6139399445896235160739643272583183584122746558849327889466302943112428168347096599]"
]
},
{
"lower_level": 12,
"upper_level": 13,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "124.9972429339003854437438919702950669938811271600924921317663466316573789094338491618805782017315942",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[124.9972632312210922562739153660642951437692507130120482390026850755281649079847828555, 124.9972632312210922562739153660642951437692507130120482390026850755281649080017552207]",
"[124.9972530825607388500089036681796810688251889365522701853845158535927719087093159412, 124.9972530825607388500089036681796810688251889365522701853845158535927719087263316222]",
"[124.9972429339003854437438919702950669938811271600924921317663466316573789094338491619, 124.9972429339003854437438919702950669938811271600924921317663466316573789094509078888]",
"[126.248714386914704555901214791389040986883936568339339815836860501116104969679138921, 126.2487143869147045559012147913890409868839365683393398158368605011161049696970062092]",
"[129.2522589502077540098867184913583565002978790214999577790059299834307809780736605025, 129.2522589502077540098867184913583565002978790214999577790059299834307809780943360298]",
"[133.924443196228271277980393052060322229622948231499005329366242605316827504772409695, 133.9244431962282712779803930520603222296229482314990053293662426053168275047997075443]",
"[140.2582216963609915370953334712400267143882094398985083578183724641955079712241962616, 140.2582216963609915370953334712400267143882094398985083578183724641955079712646205473]",
"[147.9962528476078141904051164384473845421422084626630182920555633744802904288781332203, 147.9962528476078141904051164384473845421422084626630182920555633744802904289427968023]",
"[156.1067965979021846474967213777432462930732358306259010000314575510014533719881833343, 156.1067965979021846474967213777432462930732358306259010000314575510014533720979366222]",
"[162.9900635251629712554974978211405846623396336165299824163922377000553795544272045675, 162.9900635251629712554974978211405846623396336165299824163922377000553795546263338336]",
"[167.4150131328067056609988958401325782848592792442427248021437166614600823894140141963, 167.415013132806705660998895840132578284859279244242724802143716661460082389804073766]",
"[169.2587314285358637868235620591983034019169464639318133535571493572037839500361426124, 169.2587314285358637868235620591983034019169464639318133535571493572037839508526947782]",
"[169.2587141225626491666432722384609024163712616203078667972235097033979386725158024941, 169.2587141225626491666432722384609024163712616203078667972235097033979386742893962375]",
"[169.2586968165894345464629824177235014308255767766839202408898700495920933944243749494, 169.2586968165894345464629824177235014308255767766839202408898700495920933982961946627]"
]
},
{
"lower_level": 11,
"upper_level": 12,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "103.6224863796267096974921094731583179971716116972544100307846570350647133957875167436198819206487953",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[103.622520991573138937852689114633119968262981384502303143451936342676403949871052983, 103.6225209915731389378526891146331199682629813845023031434519363426764039498890052834]",
"[103.6225036855999243176723992938957189827172965408783565871182966888705586728292847958, 103.6225036855999243176723992938957189827172965408783565871182966888705586728473096941]",
"[103.6224863796267096974921094731583179971716116972544100307846570350647133957875167436, 103.6224863796267096974921094731583179971716116972544100307846570350647133958056141047]",
"[104.6297587569692689652033710214636713078125309021558303623037596346883458114344964927, 104.6297587569692689652033710214636713078125309021558303623037596346883458114534936346]",
"[107.0472347724778036652130286379046686430768051850986250527617346041553043483274389709, 107.047234772477803665213028637904668643076805185098625052761734604155304348349505731]",
"[110.8077595423528015486768035684786423712049658971816948993840940827083896828893987157, 110.8077595423528015486768035684786423712049658971816948993840940827083896829186861223]",
"[115.9995744863814861435765547255346131417350849829603913537131980206831616359393135931, 115.9995744863814861435765547255346131417350849829603913537131980206831616359829976276]",
"[122.5094633284166113320650974828530969334650547000076979772624498994110986330095105809, 122.5094633284166113320650974828530969334650547000076979772624498994110986330803529367]",
"[129.4694365206242707117811167076980088777313376517506224636401623677213547077703669198, 129.4694365206242707117811167076980088777313376517506224636401623677213547078940686994]",
"[135.4303309741534011075487147428338603952382566573006276306782362722600857200314196332, 135.430330974153401107548714742833860395238256657300627630678236272260085720266828094]",
"[139.2623214540215363524578260740017263920815754786970222945323353306283623795064952156, 139.2623214540215363524578260740017263920815754786970222945323353306283623799961468112]",
"[140.8589659408602821089389292332934349805240782797172166153550076483455855880654446081, 140.8589659408602821089389292332934349805240782797172166153550076483455855891508981855]",
"[140.8589364995074502020119359222671598119735298959924882614636950492482860414616288134, 140.8589364995074502020119359222671598119735298959924882614636950492482860439262849862]",
"[140.8589070581546182950849426112408846434229815122677599075723824501509864940058960125, 140.8589070581546182950849426112408846434229815122677599075723824501509864995524331657]"
]
},
{
"lower_level": 10,
"upper_level": 11,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "72.13736305220211440185011041465585852450785419950979062361631385108223219732019510524722458904684303",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[72.13742193490777821570409703670840886160895096695924733139893904927683128914850292312, 72.13742193490777821570409703670840886160895096695924733139893904927683128916874920583]",
"[72.13739249355494630877710372568213369305840258323451897750762645017953174323434901418, 72.1373924935549463087771037256821336930584025832345189775076264501795317432547176876]",
"[72.13736305220211440185011041465585852450785419950979062361631385108223219732019510525, 72.13736305220211440185011041465585852450785419950979062361631385108223219734068603443]",
"[72.77265316270264091552397866590862588355180494684677356483808067940718899212961707262, 72.7726531627026409155239786659086258835518049468467735648380806794071889921511056142]",
"[74.2973873257634438130148131693405042727180626988864901293487161794910556614915164338, 74.29738732576344381301481316934050427271806269888649012934871617949105566151630682552]",
"[76.66920703120836586530777512453870056976110523329467853567967002086419041059667235543, 76.66920703120836586530777512453870056976110523329467853567967002086419041062918550594]",
"[80.12303296806395308590276797985024231110386073235863589910169908868819736048934444962, 80.12303296806395308590276797985024231110386073235863589910169908868819736053736815885]",
"[84.76672228133139775884174943794116131484618679129063882814512995097640961577260286395, 84.76672228133139775884174943794116131484618679129063882814512995097640961585080944252]",
"[89.98110884614986502097879788170580855581273822313644715459137043674591588686420810958, 89.98110884614986502097879788170580855581273822313644715459137043674591588700497441846]",
"[94.54383972073467148132054329357186751862298915556424121756177841279935361840758530007, 94.54383972073467148132054329357186751862298915556424121756177841279935361869151256545]",
"[97.47700132215829367813806134703708258539066622400699194041618144054879182903539475952, 97.477001322158293678138061347037082585390666224006991940416181440548791829668519698]",
"[98.69912071950067921408379542956224717301109245049939560336012889742431786247217018182, 98.69912071950067921408379542956224717301109245049939560336012889742431786396316501045]",
"[98.69907021349369437129065206935732118435270219995542532263902300873105594006064516833, 98.69907021349369437129065206935732118435270219995542532263902300873105594359540601811]",
"[98.69901970748670952849750870915239519569431194941145504191791712003779401634690832743, 98.69901970748670952849750870915239519569431194941145504191791712003779402452754260577]"
]
},
{
"lower_level": 9,
"upper_level": 10,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "28.71654215046253679242517712314166533193486226955218573939961540031023032317224877151996619223189575",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[28.71664316247650647801146384355151730925164277064012630084182717769675416594950145605, 28.71664316247650647801146384355151730925164277064012630084182717769675416597496499663]",
"[28.71659265646952163521832048334659132059325252009615602012072128900349224456087511379, 28.71659265646952163521832048334659132059325252009615602012072128900349224458654767663]",
"[28.71654215046253679242517712314166533193486226955218573939961540031023032317224877152, 28.71654215046253679242517712314166533193486226955218573939961540031023032319813035663]",
"[28.80608493131528115980615700794965171000640382997153021552708327986654365248423646663, 28.80608493131528115980615700794965171000640382997153021552708327986654365251131530808]",
"[29.02105240360565001655493516687089694763703985412865295991505340825210724036973578233, 29.02105240360565001655493516687089694763703985412865295991505340825210724040061099576]",
"[29.35546478635298902796661652573361280656648147355139006571599630560676261092789702799, 29.35546478635298902796661652573361280656648147355139006571599630560676261096755863208]",
"[30.26059177424294491059578706671643527780415101241433531547759809912657797967057567784, 30.26059177424294491059578706671643527780415101241433531547759809912657797972808510498]",
"[32.1697848981977574186557217493359822507601054429852769173834943821553951587116986514, 32.16978489819775741865572174933598225076010544298527691738349438215539515880575151975]",
"[34.82847170962815486199148513501039197580184888822062055749014923168918453623124380987, 34.82847170962815486199148513501039197580184888822062055749014923168918453640842135238]",
"[37.34507625746381468268386993198366974979224839034614195900141868420712921275764604583, 37.34507625746381468268386993198366974979224839034614195900141868420712921314510086611]",
"[38.96285388333717869103385389701297520684556108830136155782796812660007494762486353584, 38.96285388333717869103385389701297520684556108830136155782796812660007494856482992381]",
"[39.63687318728907284664136429950086714643768804228032934274244808942402143847582399732, 39.63687318728907284664136429950086714643768804228032934274244808942402144083572115156]",
"[39.63678497622299017763245453781099022497440271952125364405521483565675925296139578036, 39.6367849762229901776324545378109902249744027195212536440552148356567592587911610741]",
"[39.63669676515690750862354477612111330351111739676217794536798158188949706518120660305, 39.63669676515690750862354477612111330351111739676217794536798158188949707901271934595]"
]
}
],
"pointwise_nonnegative_pair_energy_certified": true,
"second_is_unassigned_mathematical_control": false
},
{
"depth": 5,
"shell_levels": [
14,
21
],
"other_unsmoothed_chart_minimum_source_cost_lower_bound": "6.789477836569374837325287975021366796994032860856065338721530776729540553141057837265109138890455886",
"common_smoothing_width_interval": "[0.0000000009560186767665473489840416876308890792116918898909371811707678008717334033705832106858, 0.0000000009560186767665473489840416876308890792116918898909371811707678008717334073239074393973]",
"smoothing_bands": [
{
"lower_level": 20,
"upper_level": 21,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "19.15977382520927085328785317511559161105713242886879151629262306259606168094744852098978548184901229",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[20.02536813705369061449251861317356769760456611151939152006249064846600262994616753989, 20.02536813705369061449251861317356769760456611151939152006249064846600262994679919465]",
"[20.02536854098223109119437318906511610143582126467520618832207057660537260845830795276, 20.02536854098223109119437318906511610143582126467520618832207057660537260845894132801]",
"[20.02536894491077156789622776495666450526707641783102085658165050474474258697044839937, 20.02536894491077156789622776495666450526707641783102085658165050474474258697108342764]",
"[19.90402407591241208251825367762057486684647725391126079476891177888911209865110186171, 19.90402407591241208251825367762057486684647725391126079476891177888911209865175342015]",
"[19.61279581250427003281847474721656106987203180698204797195183702161961062166116111539, 19.61279581250427003281847474721656106987203180698204797195183702161961062166186799928]",
"[19.15977382520927085328785317511559161105713242886879151629262306259606168094744852099, 19.15977382520927085328785317511559161105713242886879151629262306259606168094828467753]",
"[19.16357676852529018809673510181552647124553075882426984218133748804866827421462747239, 19.16357676852529018809673510181552647124553075882426984218133748804866827421572554772]",
"[20.26709233324779691371724307167805611776503377784667382759606737175835218203070658415, 20.26709233324779691371724307167805611776503377784667382759606737175835218203233308505]",
"[22.3231851290222028292701855425977383211819272961585684935978114521526530750661744296, 22.3231851290222028292701855425977383211819272961585684935978114521526530750689749434]",
"[24.42412380430566326790001335848833965007062942728718340463075606186086311384717829952, 24.42412380430566326790001335848833965007062942728718340463075606186086311385287867679]",
"[25.77472731995656266329297363979982160235173892224028578338043821941242294886821532694, 25.77472731995656266329297363979982160235173892224028578338043821941242294888139907921]",
"[26.33747895053128266463300418717863720789292109874002556474920098005372075807593598329, 26.33747895053128266463300418717863720789292109874002556474920098005372075810811127744]",
"[26.3374792528664619553754551637675773820302474689085079457157943464330462000576089531, 26.3374792528664619553754551637675773820302474689085079457157943464330462001357571026]",
"[26.33747955520164124611790614035651755616757383907699032668238771281237164200973873727, 26.33747955520164124611790614035651755616757383907699032668238771281237164219306614263]"
]
},
{
"lower_level": 19,
"upper_level": 20,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "50.15300616483855646309033933135455402755121098225459005036027491882492009102372561113087602704849771",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[50.15300616483855646309033933135455402755121098225459005036027491882492009102372561113, 50.15300616483855646309033933135455402755121098225459005036027491882492009102484055399]",
"[50.15300646717373575383279030794349420168853735242307243132686828520424553302834116994, 50.15300646717373575383279030794349420168853735242307243132686828520424553302945773207]",
"[50.15300676950891504457524128453243437582586372259155481229346165158357097503295679621, 50.15300676950891504457524128453243437582586372259155481229346165158357097503407491016]",
"[50.3614873913273260556844859437836345792025667949127174262043640134987457397722381921, 50.3614873913273260556844859437836345792025667949127174262043640134987457397734062339]",
"[50.86184043131772644328918796819662312794261968469012746683639337243112210656411470751, 50.86184043131772644328918796819662312794261968469012746683639337243112210656545877872]",
"[51.64016716757225394727049927970255855358723311695924549721619106285089449757412928916, 51.64016716757225394727049927970255855358723311695924549721619106285089449757588931332]",
"[53.16036255632186899679903260593601398094668906387199557712416678372418903134734556568, 53.16036255632186899679903260593601398094668906387199557712416678372418903134993479697]",
"[55.84462547378377556871583755596446296675332497538262044046904527556264928962903321931, 55.84462547378377556871583755596446296675332497538262044046904527556264928963318660915]",
"[59.33505418432809003437373063018432938376223198902099292633065204162604461550020931457, 59.33505418432809003437373063018432938376223198902099292633065204162604461550740985505]",
"[62.56522674531058361399060081511939572167305476983476433095792156171771066825567061363, 62.56522674531058361399060081511939572167305476983476433095792156171771066826932183225]",
"[64.64176623315796696010154632827053121800000289672782876635545015032648954876342773224, 64.641766233157966960101546328270531218000002896727828766355450150326489548791774876]",
"[65.50699105454270659914219511214550172011806660123987779318702209003296677354734525522, 65.50699105454270659914219511214550172011806660123987779318702209003296677361011090418]",
"[65.50699114797393224449323635262672625083923355460286409696199431056417009339676866733, 65.50699114797393224449323635262672625083923355460286409696199431056417009353904131293]",
"[65.5069912414051578898442775931079507815604005079658504007369665310953734131973711439, 65.50699124140515788984427759310795078156040050796585040073696653109537341351673328356]"
]
},
{
"lower_level": 18,
"upper_level": 19,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "70.83899997071095082642275008045859258230742132038698956747946312551182639130623765598744419836597918",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[70.83899997071095082642275008045859258230742132038698956747946312551182639130623765599, 70.83899997071095082642275008045859258230742132038698956747946312551182639130762470562]",
"[70.83900006414217647177379132093981711302858827374997587125443534604302971119543966528, 70.83900006414217647177379132093981711302858827374997587125443534604302971119682873902]",
"[70.83900015757340211712483256142104164374975522711296217502940756657423303108464180952, 70.83900015757340211712483256142104164374975522711296217502940756657423303108603277242]",
"[71.24954006878770250445372868283448946766717719625119179887053152760648148172210069526, 71.24954006878770250445372868283448946766717719625119179887053152760648148172356574029]",
"[72.23483566937546280594241674710095570744003419187663269806213637371371924549183375745, 72.23483566937546280594241674710095570744003419187663269806213637371371924549356072128]",
"[73.76751757337956615813871327475106767850405582281133197201832980329513127234440672261, 73.7675175733795661581387132747510676785040558228113319720183298032951312723467538713]",
"[76.21438713400427089415930654946925635306749717361564729301796023710296655052369189766, 76.21438713400427089415930654946925635306749717361564729301796023710296655052727293893]",
"[79.86013772902308295278730431011242908222236453169345115565462082720864148826384590778, 79.86013772902308295278730431011242908222236453169345115565462082720864148826973375063]",
"[84.21866921057236794615224836712813644423812963740132375077787401852073787643455208171, 84.21866921057236794615224836712813644423812963740132375077787401852073787644485138742]",
"[88.13030801608037783040701527162339285008284957857269658031099617197723888512980830781, 88.13030801608037783040701527162339285008284957857269658031099617197723888514921027011]",
"[90.64493277761909257683611604223364416073831240987271767557142924452739342864543313335, 90.64493277761909257683611604223364416073831240987271767557142924452739342868507948921]",
"[91.69269289653296253034119807190361456761802688802769659243933195700737212200264123339, 91.69269289653296253034119807190361456761802688802769659243933195700737212208888821982]",
"[91.69269261443930602092922749611611998931264603434596080152883120134938691299427669743, 91.69269261443930602092922749611611998931264603434596080152883120134938691318704542538]",
"[91.69269233234564951151725692032862541100726518066422501061833044569140170392134020388, 91.69269233234564951151725692032862541100726518066422501061833044569140170434996539388]"
]
},
{
"lower_level": 17,
"upper_level": 18,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "80.16331325805985342268895108249792996457948103587779739741931026658246164539244478912846024858004069",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[80.16331382224716644151289223407291912119024274324126897924031177789843206330278665484, 80.16331382224716644151289223407291912119024274324126897924031177789843206330433738686]",
"[80.16331354015350993210092165828542454288486188955953318832981102224044685434761565451, 80.16331354015350993210092165828542454288486188955953318832981102224044685434916949015]",
"[80.16331325805985342268895108249792996457948103587779739741931026658246164539244478913, 80.16331325805985342268895108249792996457948103587779739741931026658246164539400145851]",
"[80.65418839959343229342113388780691925631006598478716085319397901172531999926288905335, 80.654188399593432293421133887806919256310065984787160853193979011725319999264533029]",
"[81.83228903716737371677576781531302819246215727799659772224188313614855591111448939207, 81.83228903716737371677576781531302819246215727799659772224188313614855591111644049146]",
"[83.664890029330329161717503765995100823907056653887896707657240886306614942505637667, 83.66489002933032916171750376599510082390705665388789670765724088630661494250831474432]",
"[86.47495619123018347681167410776545589007434824896763938547784188480207176535179968967, 86.4749561912301834768116741077654558900743482489676393854778418848020717653559229204]",
"[90.48727724886382826368891893900406105034758021484159726401085806016478414563905503243, 90.48727724886382826368891893900406105034758021484159726401085806016478414564589609239]",
"[95.16687690052857804321824956774659142091258979595305654622053873046530029544494465937, 95.16687690052857804321824956774659142091258979595305654622053873046530029545704285199]",
"[99.32600819451531725079844214711776842018549899842241561879713579146923131355876569856, 99.32600819451531725079844214711776842018549899842241561879713579146923131358188148322]",
"[101.9997349883381582545973914359609382231623902470832149751974615770763417381077385175, 101.9997349883381582545973914359609382231623902470832149751974615770763417381557245784]",
"[103.1137872279606705687256117078195106673582268386567614901941859848322519144079791992, 103.1137872279606705687256117078195106673582268386567614901941859848322519145138359558]",
"[103.1137863103661522925116162191381162791696725717067658809994925367232597172737131067, 103.1137863103661522925116162191381162791696725717067658809994925367232597175127619824]",
"[103.113785392771634016297620730456721890981118304756770271804799088614267520058050046, 103.1137853927716340162976207304567218909811183047567702718047990886142675205932602645]"
]
},
{
"lower_level": 16,
"upper_level": 17,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "76.62305928460862989376007996507770688777532186182981546953708007865101333951420844607244928050649259",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[76.62306111979766644618807094244049566415243039572980668792646697486899773364962488807, 76.62306111979766644618807094244049566415243039572980668792646697486899773365156694648]",
"[76.62306020220314816997407545375910127596387612877981107873177352676000553658191666707, 76.6230602022031481699740754537591012759638761287798110787317735267600055365838638532]",
"[76.62305928460862989376007996507770688777532186182981546953708007865101333951420844607, 76.62305928460862989376007996507770688777532186182981546953708007865101333951616062499]",
"[77.07111354953551286926791657371869415201927006752215460751975030431723720253499952246, 77.07111354953551286926791657371869415201927006752215460751975030431723720253706437639]",
"[78.1464449074125856681125541085070428062411253618166470541885196193698977625865831631, 78.1464449074125856681125541085070428062411253618166470541885196193698977625890423121]",
"[79.81918282306331728708425102738367310250941640559725241345179507123657066373154342249, 79.81918282306331728708425102738367310250941640559725241345179507123657066373493379335]",
"[82.42093589450607695156924134811519030302645555778948364318901249519000066848042375076, 82.42093589450607695156924134811519030302645555778948364318901249519000066848567697016]",
"[86.19370169120726692195923731404534265407885619381297798019640598250829509500335678259, 86.19370169120726692195923731404534265407885619381297798019640598250829509501216432511]",
"[90.6344444624743771898610520074645428415806565462061583406345179388172864216270220103, 90.63444446247437718986105200746454284158065654620615834063451793881728642164291849781]",
"[94.59570246085086709206620081997488625464501526524944894594648339197007246132046919426, 94.59570246085086709206620081997488625464501526524944894594648339197007246135184156088]",
"[97.14222453400011462697069458002178891285128084178023039452692079864814348889848681162, 97.14222453400011462697069458002178891285128084178023039452692079864814348896611853674]",
"[98.20327416270709545396310022514388744469449594020412603247780110081064390874855539913, 98.20327416270709545396310022514388744469449594020412603247780110081064390890281369728]",
"[98.20327220059268070406368137139373283185806103824526061417284156299539835726935909413, 98.20327220059268070406368137139373283185806103824526061417284156299539835762626441273]",
"[98.20327023847826595416426251764357821902162613628639519586788202518015280566404625586, 98.20327023847826595416426251764357821902162613628639519586788202518015280647587740615]"
]
},
{
"lower_level": 15,
"upper_level": 16,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "58.82657643319021190293239473478398233932615038576900766261825480126738030065686370705150696456869625",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[58.82658035741904140273123244228429156499902018968673849922817387689787140341266954737, 58.82658035741904140273123244228429156499902018968673849922817387689787140341502553464]",
"[58.82657839530462665283181358853413695216258528772787308092321433908262585203476659348, 58.82657839530462665283181358853413695216258528772787308092321433908262585203713141932]",
"[58.82657643319021190293239473478398233932615038576900766261825480126738030065686370705, 58.82657643319021190293239473478398233932615038576900766261825480126738030065923723653]",
"[59.09933907386302192766120309289076316774912599193505982618591580292899238010974163361, 59.09933907386302192766120309289076316774912599193505982618591580292899238011223937548]",
"[59.75397189142634866601292529971410477560576974613210163383192992587577846017157417624, 59.75397189142634866601292529971410477560576974613210163383192992587577846017449785664]",
"[60.77229026751980808888259640625022532114186281771699248013243979770198926911696825323, 60.77229026751980808888259640625022532114186281771699248013243979770198926912089366172]",
"[62.54979768390783634002952084928211637906725784627617836990163550411348099957612622239, 62.54979768390783634002952084928211637906725784627617836990163550411348099958206635455]",
"[65.4274447296569333328537642265310959615549344260682159504933341776977136723755301507, 65.42744472965693333285376422653109596155493442606821595049333417769771367238541019741]",
"[69.0215445771228764847523423422445186428730366968665505404107773928429001413994756879, 69.0215445771228764847523423422445186428730366968665505404107773928429001414176063792]",
"[72.30051060953916718637866993033315454738004315502107553777123863852517102724877541489, 72.3005106095391671863786699303331545473800431550210755377712386385251710272860192966]",
"[74.40841567608750613877901838837666953113953850887924227779275963197335590058719750061, 74.40841567608750613877901838837666953113953850887924227779275963197335590067148218763]",
"[75.28670717442184458445998269524558215818502896931922089211835930143622668690651028538, 75.28670717442184458445998269524558215818502896931922089211835930143622668710685212352]",
"[75.28670351672279832205682495887850162688198409687349522144056705497534078302419840065, 75.28670351672279832205682495887850162688198409687349522144056705497534078350120124786]",
"[75.28669985902375205965366722251142109557893922442776955076277480851445487896621780652, 75.28669985902375205965366722251142109557893922442776955076277480851445488007104352447]"
]
},
{
"lower_level": 14,
"upper_level": 15,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "24.80433428536249187520939552942487975029821691688284600945334400305261214689959800062554284690875443",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[25.18998710928887598179086761275014765277208104392718015113797538843811834885486135775, 25.1899871092888759817908676127501476527720810439271801511379753884381183488579174819]",
"[25.18998345158982971938770987638306712146903617148145448046018314197723244511091182343, 25.18998345158982971938770987638306712146903617148145448046018314197723244511398329701]",
"[25.18997979389078345698455214001598659016599129903572880978239089551634654136696232283, 25.18997979389078345698455214001598659016599129903572880978239089551634654137004911212]",
"[25.13591547446477867075730476180708766885513962882119641843282216226884759133056069612, 25.13591547446477867075730476180708766885513962882119641843282216226884759133378283037]",
"[25.00616579299056099030643417284169531531647347715589230647982298506775512712347511983, 25.00616579299056099030643417284169531531647347715589230647982298506775512712714785291]",
"[24.80433428536249187520939552942487975029821691688284600945334400305261214689959800063, 24.80433428536249187520939552942487975029821691688284600945334400305261214690432488604]",
"[25.05200922817689406144363143057740200061939265368692810165560392694477617749862493034, 25.05200922817689406144363143057740200061939265368692810165560392694477617750549830846]",
"[26.28159108953524537585407009306346567771892903255547458619607018908827653948482784397, 26.28159108953524537585407009306346567771892903255547458619607018908827653949609763911]",
"[28.32913467066630858428076513308485125601372292942554280079761099829810271385498390207, 28.32913467066630858428076513308485125601372292942554280079761099829810271387625799004]",
"[30.36713855240997521438300371622908197286067661889794358500049825164134329671580966708, 30.36713855240997521438300371622908197286067661889794358500049825164134329676239174339]",
"[31.67728103310363069070201040682014778991133490676968184479623739618405828862540306515, 31.67728103310363069070201040682014778991133490676968184479623739618405828873840702708]",
"[32.22316976187028544650143026844081154755683126304661854403637246716362671992317297323, 32.22316976187028544650143026844081154755683126304661854403637246716362672020646521034]",
"[32.22316335645436577909871804480667887493051454212812163966664883965960672488328946576, 32.2231633564543657790987180448066788749305145421281216396666488396596067255812735819]",
"[32.22315695103844611169600582117254620230419782120962473529692521215558672957450670572, 32.22315695103844611169600582117254620230419782120962473529692521215558673122472178363]"
]
}
],
"pointwise_nonnegative_pair_energy_certified": true,
"second_is_unassigned_mathematical_control": false
},
{
"depth": 6,
"shell_levels": [
12,
34
],
"other_unsmoothed_chart_minimum_source_cost_lower_bound": "11.08400424725245104508551100401825736577542745572953414613045338506697862736593856731163669783069007",
"common_smoothing_width_interval": "[0.0000000000006880302197329862899450721283956323504916728695858806639617808525104119832974643572613, 0.0000000000006880302197329862899450721283956323504916728695858806639617808525104162001766416494705]",
"smoothing_bands": [
{
"lower_level": 33,
"upper_level": 34,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "28.82377267235799905804482372497418547906177111133570229546505844277702009320186885043994428336635658",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[29.08928666932459947912120382293937711950529137527418499165121549887340041501820652292, 29.08928666932459947912120382293937711950529137527418499165121549887340041516409644121]",
"[29.08928666984580529727185894289584738630652427172928261053669662115648000124127260187, 29.08928666984580529727185894289584738630652427172928261053669662115648000138716575872]",
"[29.08928667036701111542251406285231765310775716818438022942217774343955958746433871455, 29.08928667036701111542251406285231765310775716818438022942217774343955958761023507623]",
"[29.0520650821647646901117775545633217083817695436523616604047742726659546546489704745, 29.05206508216476469011177755456332170838176954365236166040477427266595465479529014338]",
"[28.96273326974679767239888548792844317044109825685995140408548572402430660407489235708, 28.96273326974679767239888548792844317044109825685995140408548572402430660422272608799]",
"[28.82377267235799905804482372497418547906177111133570229546505844277702009320186885044, 28.82377267235799905804482372497418547906177111133570229546505844277702009335328618649]",
"[29.67409845346171832697561193910236112174039582424576848284885452069190863980557050805, 29.67409845346171832697561193910236112174039582424576848284885452069190863996400837443]",
"[32.56007009423382756781329099656751242182642904397115420406393202397520130466229239097, 32.56007009423382756781329099656751242182642904397115420406393202397520130483311087968]",
"[37.09689137593437131723804953658317800916460980666975511337119760619841119172791306619, 37.09689137593437131723804953658317800916460980666975511337119760619841119191937098569]",
"[41.54556962370780725468891393029220951678739837553041330139289730290044627340338964175, 41.5455696237078072546889139302922095167873983755304133013928973029004462736286560021]",
"[44.40543421170733854832951218949447450633413180252883925716627742789950660648182454816, 44.40543421170733854832951218949447450633413180252883925716627742789950660676335514183]",
"[45.59704445696895988980771440629454171609840718105954001072184621990357726390564724576, 45.59704445696895988980771440629454171609840718105954001072184621990357726428451339641]",
"[45.59704445743163649822952259873773238437821826772299970335085493917222868512304324511, 45.59704445743163649822952259873773238437821826772299970335085493917222868567788988434]",
"[45.59704445789431310665133079118092305265802935438645939597986365844088010626408033368, 45.59704445789431310665133079118092305265802935438645939597986365844088010714760160107]"
]
},
{
"lower_level": 32,
"upper_level": 33,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "88.40365882114245834792412191664541630095905311531096057049982187728788771883505788836252509378534934",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[88.40365882114245834792412191664541630095905311531096057049982187728788771883505788836, 88.40365882114245834792412191664541630095905311531096057049982187728788771917358368605]",
"[88.40365882160513495634593010908860696923886420197442026312883059655653914014045536577, 88.4036588216051349563459301090886069692388642019744202631288305965565391404789846719]",
"[88.40365882206781156476773830153179763751867528863787995575783931582519056144585284318, 88.40365882206781156476773830153179763751867528863787995575783931582519056178438552282]",
"[89.36908230150705345615129638568738595000785853849333271650736290422484240763519257519, 89.36908230150705345615129638568738595000785853849333271650736290422484240797502715723]",
"[91.68609865149277684905862580713316353764530836753022477612717464256048022988072261846, 91.68609865149277684905862580713316353764530836753022477612717464256048023022524232194]",
"[95.29034630673571851784570021998496342733458391897395311610577620708465545443214067684, 95.29034630673571851784570021998496342733458391897395311610577620708465545478778106662]",
"[100.7889796091557471532104416968051420539521632836011565843327973200247309762940718081, 100.7889796091557471532104416968051420539521632836011565843327973200247309766714985523]",
"[108.5960682048486263661419676365513256834739635090898052772634252434932228658495682195, 108.5960682048486263661419676365513256834739635090898052772634252434932228662651876095]",
"[117.6706669477258475624206631035213959192500498907256920727393363351082443810395269795, 117.6706669477258475624206631035213959192500498907256920727393363351082443815176677768]",
"[125.7250049287997109047070240391376815664371007640130090757433360259157927939498282532, 125.7250049287997109047070240391376815664371007640130090757433360259157927945264286588]",
"[130.9027936309788958757293977564539324912317359191717376808517864207438745502617585411, 130.9027936309788958757293977564539324912317359191717376808517864207438745509913515064]",
"[133.0602055903721998798704994140972053750178799339589258309923140942858577027525451538, 133.0602055903721998798704994140972053750178799339589258309923140942858577037220349587]",
"[133.0602055906627228722278965640519675826703070742399299629170536167065204430700680641, 133.0602055906627228722278965640519675826703070742399299629170536167065204444256048588]",
"[133.0602055909532458645852937140067297903227342145209340948417931391271831832594699055, 133.060205590953245864585293714006729790322734214520934094841793139127183185257027567]"
]
},
{
"lower_level": 31,
"upper_level": 32,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "153.7970283175616079394850770835390959046084114705739360401074737534226900770330267008949249351658736",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[153.7970283175616079394850770835390959046084114705739360401074737534226900770330267009, 153.7970283175616079394850770835390959046084114705739360401074737534226900774984492557]",
"[153.7970283178521309318424742334938581122608386108549401720322132758433528175439552566, 153.7970283178521309318424742334938581122608386108549401720322132758433528180093823994]",
"[153.7970283181426539241998713834486203199132657511359443039569527982640155580548838123, 153.7970283181426539241998713834486203199132657511359443039569527982640155585203152732]",
"[155.6031265147786392120777804529215044506513239335408299587438762759854458398461667237, 155.6031265147786392120777804529215044506513239335408299587438762759854458403135429418]",
"[159.9377621862513696128073996134805074142247984914396607032045174532118757417519075347, 159.9377621862513696128073996134805074142247984914396607032045174532118757422262938927]",
"[166.6805287860830771834280551539746084405190359249642131389320024414784054970912276222, 166.6805287860830771834280551539746084405190359249642131389320024414784054975822709903]",
"[176.0791257245634646294438067357367528385509608987673244048488701054925477983415881854, 176.0791257245634646294438067357367528385509608987673244048488701054925477988652843671]",
"[188.0200327726904271268671697291474656318591414073919170945867548402249274050856145436, 188.0200327726904271268671697291474656318591414073919170945867548402249274056665221034]",
"[200.9111289906695432118926707739268594193432180735543886811931756067798854798671130991, 200.9111289906695432118926707739268594193432180735543886811931756067798854805414148844]",
"[212.0001169159609133229482057002145148889848241332096023893811821565633130676777447326, 212.0001169159609133229482057002145148889848241332096023893811821565633130684981211018]",
"[219.1287520106974374965436424834353129921236369244730096306009885646310586315733498278, 219.1287520106974374965436424834353129921236369244730096306009885646310586326177475997]",
"[222.099016633446605678538869011846029331511718749800807827624921439154015995478748226, 222.0990166334466056785388690118460293315117187498008078276249214391540159968671208131]",
"[222.0990166334010032429400399142850162082183865127044441254590382531089101470583301603, 222.0990166334010032429400399142850162082183865127044441254590382531089101489846901687]",
"[222.0990166333554008073412108167240030849250542756080804232931550670638042984740254131, 222.0990166333554008073412108167240030849250542756080804232931550670638043012662212326]"
]
},
{
"lower_level": 30,
"upper_level": 31,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "219.6004001439324274553168933826204284345914798884852001542130453167549950468833998852067680744444782",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[219.6004001440236323265145515777424546811781443626779275585448116888452067431862205277, 219.600400144023632326514551577742454681178144362677927558544811688845206743790318629]",
"[219.6004001439780298909157224801814415578848121255815638563789285028001008950348102065, 219.6004001439780298909157224801814415578848121255815638563789285028001008956389147849]",
"[219.6004001439324274553168933826204284345914798884852001542130453167549950468833998852, 219.6004001439324274553168933826204284345914798884852001542130453167549950474875106708]",
"[222.1071847941231199579997251398669672945040500645297359854482834639678702846774026642, 222.1071847941231199579997251398669672945040500645297359854482834639678702852845690342]",
"[228.1234679545596708927007127174258481402992359670828667087539041468539396870411774495, 228.123467954559670892700712717425848140299235967082866708753904146853939687659344679]",
"[237.4821306484605118289035797583751604004063307739591220786406809426109158317382617357, 237.4821306484605118289035797583751604004063307739591220786406809426109158323825439292]",
"[250.1330143838134046178208687322584266589083036808204486380211948444919236156589505406, 250.1330143838134046178208687322584266589083036808204486380211948444919236163543931268]",
"[265.5246037385460934507995840832778721510935755794352833037673779511945394013907178265, 265.5246037385460934507995840832778721510935755794352833037673779511945394021757379915]",
"[281.6046867985701458675937936769623252239387371970149524306113832708572987023049107112, 281.6046867985701458675937936769623252239387371970149524306113832708572987032360024914]",
"[295.2307975407148002692029308533034644400782494224520074993041517241062938806986429078, 295.2307975407148002692029308533034644400782494224520074993041517241062938818577441114]",
"[303.9904401603184978936975395249574036134370915783646325613963053941907164091399248997, 303.9904401603184978936975395249574036134370915783646325613963053941907164106474614996]",
"[307.6402912514093149278754515207425384306155970609050125375835995517726263779551523076, 307.6402912514093149278754515207425384306155970609050125375835995517726263799946315506]",
"[307.6402912507921007612512005510651391510412922581891476269227227243138102820822206365, 307.6402912507921007612512005510651391510412922581891476269227227243138102849469985948]",
"[307.6402912501748865946269495813877398714669874554732827162618458968549941859641874848, 307.6402912501748865946269495813877398714669874554732827162618458968549941901442954757]"
]
},
{
"lower_level": 29,
"upper_level": 30,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "281.8342036105347031786096875826217551172514973956441248381817027394133062404601249228997578062368896",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[281.8342036117691315118581895219765536764001070010758546595034563943309384313801913509, 281.8342036117691315118581895219765536764001070010758546595034563943309384320767598776]",
"[281.8342036111519173452339385522991543968258021983599897488425795668721223359201581369, 281.834203611151917345233938552299154396825802198359989748842579566872122336616736919]",
"[281.8342036105347031786096875826217551172514973956441248381817027394133062404601249229, 281.8342036105347031786096875826217551172514973956441248381817027394133062411567134207]",
"[284.9190381104864419291698012665953365516706853596060599649472825258162803735311431442, 284.9190381104864419291698012665953365516706853596060599649472825258162803742315914696]",
"[292.3226409110948145573216607177355636560014075056956377100826583627356705500702067611, 292.322640911094814557321660717735563656001407505695637710082658362735670550784579289]",
"[303.8393563788252911697435586038895189525851977668179646910986001855387284727361876658, 303.8393563788252911697435586038895189525851977668179646910986001855387284734836750423]",
"[319.1744320146754159771217447313612887981828376221784459333961412370170341341449252648, 319.1744320146754159771217447313612887981828376221784459333961412370170341349573690433]",
"[337.4161484195317042110546218752135985938192520038967783018215863532370817830125983737, 337.4161484195317042110546218752135985938192520038967783018215863532370817839388814272]",
"[356.1322767391636977744991270282409784965283505842240261141930210779611738761735321859, 356.1322767391636977744991270282409784965283505842240261141930210779611738772855900204]",
"[371.8565244352252326937795682307231112019482137377308669868526338630876900927277320457, 371.8565244352252326937795682307231112019482137377308669868526338630876900941299597459]",
"[381.9649693819525667069584501385980628017116462067132035265448616861664470695193902645, 381.9649693819525667069584501385980628017116462067132035265448616861664470713653324304]",
"[386.1768214421198931533331424128159460634039818052622087133451060962224379124585708054, 386.1768214421198931533331424128159460634039818052622087133451060962224379149824122606]",
"[386.1768214405935735526845688276177604833023800347414102358199461352143012381130848785, 386.1768214405935735526845688276177604833023800347414102358199461352143012416895559935]",
"[386.1768214390672539520359952424195749032007782642206117582947861742061645634543397495, 386.1768214390672539520359952424195749032007782642206117582947861742061645687099902348]"
]
},
{
"lower_level": 28,
"upper_level": 29,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "337.8078703801438586405777492600972925581261420363378978240259284458563954234488010864773984604479541",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[337.8078703831964978418748964304936637183293455773794947790762483678726687710867055345, 337.8078703831964978418748964304936637183293455773794947790762483678726687718537883775]",
"[337.8078703816701782412263228452954781382277438068586963015510884068645320972677533105, 337.8078703816701782412263228452954781382277438068586963015510884068645320980348518065]",
"[337.8078703801438586405777492600972925581261420363378978240259284458563954234488010865, 337.8078703801438586405777492600972925581261420363378978240259284458563954242159146957]",
"[341.362118028006387818015742265819559469464230950541222903638533581834814872217601701, 341.3621180280063878180157422658195594694642309505412229036385335818348148729894349764]",
"[349.8923123847942580655748748801059975079571382584078015316157731524085011898804454455, 349.8923123847942580655748748801059975079571382584078015316157731524085011906692547295]",
"[363.1615036069592632175794687506822655151999358271906557396557187696473324500384497162, 363.1615036069592632175794687506822655151999358271906557396557187696473324508675488855]",
"[380.6769771085469429032148215425934056009369409818205669187154307866590804056655374371, 380.6769771085469429032148215425934056009369409818205669187154307866590804065735415001]",
"[401.2351687737513246448082110200846480300578573298473865832432345078667762691422120957, 401.2351687737513246448082110200846480300578573298473865832432345078667762701883619303]",
"[422.0949863801045998074187682235838648337337299394430963509341821219761113247220910867, 422.0949863801045998074187682235838648337337299394430963509341821219761113259935860866]",
"[439.5260280431803480892004444071516747202646831578619913553186669755777394988678421993, 439.5260280431803480892004444071516747202646831578619913553186669755777395004914812902]",
"[450.7316976823909850257884801603712857515446405037241772991466317895649172220529578334, 450.7316976823909850257884801603712857515446405037241772991466317895649172242160379208]",
"[455.4007266969070213198406433595655875176658795042871912407183868368955427535974145689, 455.4007266969070213198406433595655875176658795042871912407183868368955427565875238439]",
"[455.4007266939878118070081357003443769953147153229175906226330105350898187611093311012, 455.4007266939878118070081357003443769953147153229175906226330105350898187653904822641]",
"[455.4007266910686022941756280411231664729635511415479900045476342332840947682303185095, 455.4007266910686022941756280411231664729635511415479900045476342332840947745848388601]"
]
},
{
"lower_level": 27,
"upper_level": 28,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "385.8126937189604837383533045116352924253686334719061946107567951649000364165451804087693403573294948",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[385.8126937247989027640183198300777134700709618346453958469275477685114844002300317978, 385.8126937247989027640183198300777134700709618346453958469275477685114844009906051286]",
"[385.8126937218796932511858121708565029477197976532757952288421714667057604083876061033, 385.8126937218796932511858121708565029477197976532757952288421714667057604091482037234]",
"[385.8126937189604837383533045116352924253686334719061946107567951649000364165451804088, 385.8126937189604837383533045116352924253686334719061946107567951649000364173058017783]",
"[389.7392225374217054841577315150370147581375350123110329159911087109151143748489967026, 389.7392225374217054841577315150370147581375350123110329159911087109151143756152186275]",
"[399.1628917054824371576760255287085933336804674437563610806914496540994482423238903318, 399.1628917054824371576760255287085933336804674437563610806914496540994482431102404668]",
"[413.8219326346619699213791440217172601400905928752553863577978127959958435971326325417, 413.8219326346619699213791440217172601400905928752553863577978127959958435979667412286]",
"[433.066922557568106484491023461300179374028514763046969449722048284200751977708507534, 433.0669225575681064844910234613001793740285147630469694497220482842007519786361513239]",
"[455.4631329425937577351773599425110963499776647655109115095891536518106857574632811382, 455.4631329425937577351773599425110963499776647655109115095891536518106857585547546649]",
"[478.0244024043433524216899012989647673852056291672760850167016997679029482833326878024, 478.0244024043433524216899012989647673852056291672760850167016997679029482846917384382]",
"[496.8103689809985018404816108095465037393345898672184568847097691540136504366094618437, 496.8103689809985018404816108095465037393345898672184568847097691540136504383878303087]",
"[508.8870617780498186557616916016403338566100666851639012711547771700324382474166622966, 508.8870617780498186557616916016403338566100666851639012711547771700324382498407209205]",
"[513.91901710705725427558000165117979916298101535420620512743988494688848391551841932, 513.9190171070572542755800016511797991629810153542062051274398849468884839189406597995]",
"[513.9190171020501915031426627813906304878467590781907371200728491320160361992965179612, 513.9190171020501915031426627813906304878467590781907371200728491320160362042948883491]",
"[513.9190170970431287307053239116014618127125028021752691127058133171435884825799519809, 513.9190170970431287307053239116014618127125028021752691127058133171435884901439520846]"
]
},
{
"lower_level": 26,
"upper_level": 27,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "424.8814509002037827261809641135974967897286447771972579714553474578505558681244561113454212971461194",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[424.8814509102179082710556418531758341399971573292281939861894190875954512989944515101, 424.8814509102179082710556418531758341399971573292281939861894190875954512998247467888]",
"[424.8814509052108454986183029833866654648629010532127259788223832727230035835594535408, 424.881450905210845498618302983386665464862901053212725978822383272723003584389786063]",
"[424.8814509002037827261809641135974967897286447771972579714553474578505558681244561113, 424.8814509002037827261809641135974967897286447771972579714553474578505558689548247974]",
"[429.0927082271445911975125167600792116277852419204576983057895417046290192939026671787, 429.0927082271445911975125167600792116277852419204576983057895417046290192947391033129]",
"[439.1997258183145712728758620597290154574697447937083895213548249258009389069053383264, 439.1997258183145712728758620597290154574697447937083895213548249258009389077636191093]",
"[454.9217531843362973088464305268754096356626642729420977847338208586477252476071555106, 454.9217531843362973088464305268754096356626642729420977847338208586477252485173693534]",
"[475.4894918545013438469370485453492516450543472496477191166394459744724016776699659091, 475.4894918545013438469370485453492516450543472496477191166394459744724016786820681889]",
"[499.2913918918242826491244336006025939417487970725659635766172366947793836316105896893, 499.2913918918242826491244336006025939417487970725659635766172366947793836328014784703]",
"[523.1538666235159300750235999676643576631050176614435252918911773121988788600406773458, 523.1538666235159300750235999676643576631050176614435252918911773121988788615243214456]",
"[542.9760099759374440603289408269042852672564456759981269906830266437032120932571089792, 542.9760099759374440603289408269042852672564456759981269906830266437032120952014376159]",
"[555.7188164132427501957938652777689649232683979672501173125317388162916755400783376951, 555.7188164132427501957938652777689649232683979672501173125317388162916755427369508787]",
"[561.0283190904704233245988861616111074022250656896899842928992820000755779231165970384, 561.0283190904704233245988861616111074022250656896899842928992820000755779268909708136]",
"[561.0283190823733464151820597731553707794901734934709689790905591311210648407640094992, 561.0283190823733464151820597731553707794901734934709689790905591311210648463247153664]",
"[561.0283190742762695057652333846996341567552812972519536652818362621665517578277184406, 561.0283190742762695057652333846996341567552812972519536652818362621665517663427895607]"
]
},
{
"lower_level": 25,
"upper_level": 26,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "454.5970087541327916857881836087700815083028510822561013001092312320466085110439647459600655101761094",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[454.5970087703269455046218363856815547537726354746941319277266769699556346739643919296, 454.5970087703269455046218363856815547537726354746941319277266769699556346747916634697]",
"[454.5970087622298685952050099972258181310377432784751166139179541010011215925041780679, 454.5970087622298685952050099972258181310377432784751166139179541010011215933315052034]",
"[454.597008754132791685788183608770081508302851082256101300109231232046608511043964746, 454.597008754132791685788183608770081508302851082256101300109231232046608511871346937]",
"[459.013462990262868210419537180981783940832293039258510538423017161387859916533887311, 459.0134629902628682104195371809817839408322930392585105384230171613878599173674940205]",
"[469.6129531675740483715727692953456193322116565645786850494850394807958715620360669744, 469.6129531675740483715727692953456193322116565645786850494850394807958715628920451389]",
"[486.1010490022580418604767615898262271794181484282249061782877202179697930356250672624, 486.1010490022580418604767615898262271794181484282249061782877202179697930365342469239]",
"[507.6217494147807633202158015989967782867680244940845289081720650560093007203835671453, 507.6217494147807633202158015989967782867680244940845289081720650560093007213972358101]",
"[532.43576247695033546774164500275758268839278172378361366313152493392886780177372933, 532.435762476950335467741645002757582688392781723783613663131524933928867802971100635]",
"[557.2345531120468769031949480541988608046539821638976956073650995676580664479275061344, 557.2345531120468769031949480541988608046539821638976956073650995676580664494266996557]",
"[577.8020501107211553419789569674870446965564065910774629718070386576727454459911315793, 577.8020501107211553419789569674870446965564065910774629718070386576727454479680973764]",
"[591.0240124615527523653819120786144466509434484594520742891950875399457212787861879344, 591.0240124615527523653819120786144466509434484594520742891950875399457212815111268925]",
"[596.5331634333125140020491267228650024393323304028627096258970519810391812851701148332, 596.5331634333125140020491267228650024393323304028627096258970519810391812890801541803]",
"[596.533163420672444872415817801721035368632390079450140896911173040366013507326010999, 596.5331634206724448724158178017210353686323900794501408969111730403660135131682041441]",
"[596.5331634080323757427825088805770682979324497560375721679252940996928457288179088683, 596.5331634080323757427825088805770682979324497560375721679252940996928457379204672291]"
]
},
{
"lower_level": 24,
"upper_level": 25,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "474.9375412844253769593966673323017718017655280863002390886746914583997884504619744855158472883567373",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[474.9375413097055152186632851745897059431654087331253765466464493397461240042184882318, 474.9375413097055152186632851745897059431654087331253765466464493397461240050029751135]",
"[474.9375412970654460890299762534457388724654684097128078176605703990729562273402313587, 474.9375412970654460890299762534457388724654684097128078176605703990729562281248013634]",
"[474.9375412844253769593966673323017718017655280863002390886746914583997884504619744855, 474.9375412844253769593966673323017718017655280863002390886746914583997884512466276134]",
"[479.4863402346730004806742282273549990376965763184381641432629952896544970589768913306, 479.4863402346730004806742282273549990376965763184381641432629952896544970597698308622]",
"[490.4034577318774725483340561029721477535084013212141953017081093311127341243582877398, 490.4034577318774725483340561029721477535084013212141953017081093311127341251809200382]",
"[507.3856405105792845835749492700269609533677544758156197518874944270532598632795528654, 507.3856405105792845835749492700269609533677544758156197518874944270532598641726546798]",
"[529.5203402774115178470486780927333395226275320053118360063652340185827268700905790909, 529.5203402774115178470486780927333395226275320053118360063652340185827268711218941469]",
"[554.9852489467266823540079556452103988991440705481757380566928559034948138110877355859, 554.9852489467266823540079556452103988991440705481757380566928559034948138123619547573]",
"[580.3850453599456760141846429159204689732094904057040343221517151687951978489882996781, 580.3850453599456760141846429159204689732094904057040343221517151687951978506622082869]",
"[601.4304595180599649268390361222426238923009857521848190212508384741024250019386874881, 601.4304595180599649268390361222426238923009857521848190212508384741024250042482699195]",
"[614.9596543257142650769890941301327264976977968559708892990087041271932313406533865617, 614.9596543257142650769890941301327264976977968559708892990087041271932313439675659027]",
"[620.596818817086831925827933540988236485315283794225890855142310237773348751671470311, 620.5968188170868319258279335409882364853152837942258908551423102377733487566012565663]",
"[620.5968187977826216569991691114918511338969212922562730340180536354895125224885756141, 620.5968187977826216569991691114918511338969212922562730340180536354895125301036629729]",
"[620.5968187784784113881704046819954657824785587902866552128937970332056762923350381838, 620.5968187784784113881704046819954657824785587902866552128937970332056763045764443916]"
]
},
{
"lower_level": 23,
"upper_level": 24,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "486.1493570440114955752099328558880708006093460825536983701526737542566286859421576073476674815677825",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[486.1493570826199161128674617148808415034460710864929340124011869588243011416227792186, 486.1493570826199161128674617148808415034460710864929340124011869588243011424968274862]",
"[486.1493570633157058440386972853844561520277085845233161912769303565404649137824681431, 486.1493570633157058440386972853844561520277085845233161912769303565404649146566405556]",
"[486.1493570440114955752099328558880708006093460825536983701526737542566286859421576073, 486.149357044011495575209932855888070800609346082553698370152673754256628686816453625]",
"[490.7630822577049098771220217297888222844822782677658783470539339340788284597089520095, 490.7630822577049098771220217297888222844822782677658783470539339340788284605945198464]",
"[501.8360227959956327728981305450202837745918306535367930181714533259209888680421748228, 501.8360227959956327728981305450202837745918306535367930181714533259209888689679985402]",
"[519.0605969748178056718237529833024783365945024663274143013697658236257104843033868322, 519.0605969748178056718237529833024783365945024663274143013697658236257104853245327997]",
"[541.4954257669869821399501071586544305402451189273075091609486675982768006686048354028, 541.4954257669869821399501071586544305402451189273075091609486675982768006698126597103]",
"[567.2763850991752484856192315801439984295690798802108529009341173200891758640830930215, 567.2763850991752484856192315801439984295690798802108529009341173200891758656189503168]",
"[592.9660137230874695594160598441592871603136761938346785398653825003450505314401320199, 592.9660137230874695594160598441592871603136761938346785398653825003450505335170355595]",
"[614.2410054662501795538474531978290136842796417490704350604520098818721571498041084363, 614.2410054662501795538474531978290136842796417490704350604520098818721571527471840578]",
"[627.9177858601533902631564491037596433589737170707272432947869630287242327238534988454, 627.9177858601533902631564491037596433589737170707272432947869630287242327281827054286]",
"[633.6164443398283316472733010861141466257216286940808282816827243622457498761148628635, 633.6164443398283316472733010861141466257216286940808282816827243622457498827157520523]",
"[633.616444310737484149376642638419041480138581732476177212907709715077485671233499163, 633.6164443107374841493766426384190414801385817324761772129077097150774856816990511103]",
"[633.61644428164663665147998419072393633455553477087152614413269506790922146487611602, 633.6164442816466366514799841907239363345555347708715261441326950679092214821603645657]"
]
},
{
"lower_level": 22,
"upper_level": 23,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "488.6403840796622288799885908483745718762105870302121155309311034954362588537965994061911998670263935",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[488.640384137843923875781907743764782167376680953421417668481132789772787259702928862, 488.6403841378439238757819077437647821673766809534214176684811327897727872606269287285]",
"[488.6403841087530763778852492960696770217936339918167665997061181426045230567497641341, 488.6403841087530763778852492960696770217936339918167665997061181426045230576739475192]",
"[488.6403840796622288799885908483745718762105870302121155309311034954362588537965994062, 488.6403840796622288799885908483745718762105870302121155309311034954362588547209663099]",
"[493.2557933913166977424233313023944274989623402610874874925579962929618579622818804089, 493.2557933913166977424233313023944274989623402610874874925579962929618579632171774635]",
"[504.3327757776529193385200337228109690264317030616231541330404624557440787791346200045, 504.3327757776529193385200337228109690264317030616231541330404624557440787801089843867]",
"[521.5636372798658094938829931769421826992534823827862686130890130590962773116878287514, 521.563637279865809493882993176942182699253482382786268613089013059096277312754961237]",
"[544.0040109904268284029207097534487739638576609270519048931610488949109567545897174938, 544.0040109904268284029207097534487739638576609270519048931610488949109567558390580226]",
"[569.7864481343461393481180383402718428927659281286903901163740861977199293899961371732, 569.786448134346139348118038340271842892765928128690390116374086197719929391566831693]",
"[595.4732904197946864036695826281110441268356671377590934261728607121853390216123204928, 595.4732904197946864036695826281110441268356671377590934261728607121853390237161829122]",
"[616.7442016981167195714223482118640603742521764447312025020028400550647715164352097159, 616.7442016981167195714223482118640603742521764447312025020028400550647715194013870883]",
"[630.4183589299393394475649880096523221509806680880626232751142652027421393509706605072, 630.4183589299393394475649880096523221509806680880626232751142652027421393553395988633]",
"[636.1159244166118451520287645654969242043532615597446898115393499034133668329446119498, 636.1159244166118451520287645654969242043532615597446898115393499034133668396654046234]",
"[636.1159243730926300928861264733137858572206692229975918904790391267815017915002731879, 636.1159243730926300928861264733137858572206692229975918904790391267815018023296723141]",
"[636.1159243295734150337434883811306475100880768862504939694187283501496367483909718084, 636.1159243295734150337434883811306475100880768862504939694187283501496367666613110339]"
]
},
{
"lower_level": 21,
"upper_level": 22,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "482.8884931414646214796905816089224922419228058460044295479301696574508068771412863190884257738679056",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[482.8884932285030515979758577932887689361879905194986253900507912107145369559282274624, 482.888493228503051597975857793288768936187990519498625390050791210714536956803393574]",
"[482.8884931849838365388332197011056305890553981827515274689904804340826719165347568907, 482.8884931849838365388332197011056305890553981827515274689904804340826719174101950417]",
"[482.8884931414646214796905816089224922419228058460044295479301696574508068771412863191, 482.8884931414646214796905816089224922419228058460044295479301696574508068780169959696]",
"[487.4451405731044555884501140338986064517133186042199531520467322012975408095194357767, 487.4451405731044555884501140338986064517133186042199531520467322012975408104081552754]",
"[498.381094466461238389239210597795565251001908772953670189051302896745329009449565569, 498.3810944664612383892392105977955652510019087729536701890513028967453290103847158086]",
"[515.3925783191009355531532411977527360604942679220795922354558130714385495147303475175, 515.3925783191009355531532411977527360604942679220795922354558130714385495157758636732]",
"[537.5568071198865233989196216233093700374705554711931594412465555394053460304789336714, 537.5568071198865233989196216233093700374705554711931594412465555394053460317416635]",
"[563.0396663636751386688678122876185711958755870126246923285841750616088819413126242821, 563.039666363675138668867812287618571195875587012624692328584175061608881942959944287]",
"[588.443441475722765437459477794979159497524838683250570470352599911274046079470032667, 588.4434414757227654374594777949791594975248386832505704703525999112740460817603316136]",
"[609.4863607290698772526286379452248093924439522180147365052939988216772059794086691998, 609.4863607290698772526286379452248093924439522180147365052939988216772059827535835852]",
"[623.0139516500343565974676082540230139294520589379453471508562470746253177506243300942, 623.0139516500343565974676082540230139294520589379453471508562470746253177557234921258]",
"[628.6504478274481087757990457389078707625266525029640168911987457632218549591510325326, 628.6504478274481087757990457389078707625266525029640168911987457632218549672794505118]",
"[628.6504477625222331455384582274133935844160414398923824003429467915283150845149903894, 628.6504477625222331455384582274133935844160414398923824003429467915283150981086381538]",
"[628.6504476975963575152778707159189164063054303768207479094871478198347752075139777476, 628.6504476975963575152778707159189164063054303768207479094871478198347752313014166663]"
]
},
{
"lower_level": 20,
"upper_level": 21,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "469.3592554458337226142798814735459247066142928483655388675551622994970440536301039605831786144264517",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[469.3592555756854738748010564965348790628355149745088078492667602428841237974395304208, 469.3592555756854738748010564965348790628355149745088078492667602428841237982702434741]",
"[469.3592555107595982445404689850404018847249039114371733584109612711905839255348169208, 469.3592555107595982445404689850404018847249039114371733584109612711905839263659331752]",
"[469.3592554458337226142798814735459247066142928483655388675551622994970440536301039606, 469.3592554458337226142798814735459247066142928483655388675551622994970440544616223366]",
"[473.7978568691241091461893711729889891295364032771519559905244749472127716027412107021, 473.7978568691241091461893711729889891295364032771519559905244749472127716035898729522]",
"[484.4505003706734754754782985506402881669667383862282972503078044464619471179528642594, 484.4505003706734754754782985506402881669667383862282972503078044464619471188622069286]",
"[501.0212791784828964874173450483153596971204711466887792790290514398349613077787182485, 501.0212791784828964874173450483153596971204711466887792790290514398349613088315076774]",
"[522.6329785473030470264531033098243707764782257436611097560100262922165812933647979094, 522.6329785473030470264531033098243707764782257436611097560100262922165812946989369773]",
"[547.5206634357624369057115399602089272300358249598472528298832665745721602425750840421, 547.5206634357624369057115399602089272300358249598472528298832665745721602444071651574]",
"[572.3659758454198848894528817514102461233979798641214914650618803929602013615231678823, 572.3659758454198848894528817514102461233979798641214914650618803929602013641919372001]",
"[592.9608064241184161503035035671666775366738715731160541710473257061248074021814922855, 592.9608064241184161503035035671666775366738715731160541710473257061248074062410787659]",
"[606.2003403263092607810981621031262687328160203635368600069092319647481159854215913075, 606.2003403263092607810981621031262687328160203635368600069092319647481159918492659431]",
"[611.7168127263288677918369448264811872290539723355272640855624288219135535322103337913, 611.7168127263288677918369448264811872290539723355272640855624288219135535428557609367]",
"[611.7168126293699939696079975441223737680132310086769390649115228820903445891426130909, 611.7168126293699939696079975441223737680132310086769390649115228820903446076491439698]",
"[611.7168125324111201473790502617635603069724896818266140442606169422671356424621326351, 611.7168125324111201473790502617635603069724896818266140442606169422671356760524508565]"
]
},
{
"lower_level": 19,
"upper_level": 20,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "448.4274776289421167133475577884711802534439158929819182756320143542812832765649548314746019200679276",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[448.4274778228598643578054523531888071755253985466825683169338262339277011548472242798, 448.4274778228598643578054523531888071755253985466825683169338262339277011558198123101]",
"[448.4274777259009905355765050708299937144846572198322432962829202941044922157060892857, 448.4274777259009905355765050708299937144846572198322432962829202941044922166792764503]",
"[448.4274776289421167133475577884711802534439158929819182756320143542812832765649548315, 448.4274776289421167133475577884711802534439158929819182756320143542812832775387400507]",
"[452.6878463362740148735660876934622506189125000793132857924136297642549554509290599587, 452.6878463362740148735660876934622506189125000793132857924136297642549554519250843915]",
"[462.9127313616916216904262778218525073631380915883042350449971421022377381569298102294, 462.9127313616916216904262778218525073631380915883042350449971421022377381580045824856]",
"[478.818108109000532076886726491578513768338116010670092302409504189695092407096985558, 478.8181081090005320768867264915785137683381160106700923024095041896950924083582191704]",
"[499.5965946165407532469721417359902040458732597436097770605639858920104498843812100284, 499.5965946165407532469721417359902040458732597436097770605639858920104498860090112128]",
"[523.5887351640424540684870224440347082651234609271567385210324994672751410971445526448, 523.5887351640424540684870224440347082651234609271567385210324994672751410994243046705]",
"[547.5955776584875579015350940975771161429841628922780089079825356606485958605889441252, 547.5955776584875579015350940975771161429841628922780089079825356606485958639758497211]",
"[567.5184640583260853243590354969256447775322805564829841696661832195840767568847628491, 567.5184640583260853243590354969256447775322805564829841696661832195840767621489296762]",
"[580.32603382482179195078146420090388566786458251598372844212966737164824635837700257, 580.3260338248217919507814642009038856678645825159837284421296673716482463669345841503]",
"[585.6625211386672379439515008507631524971785776260826619675303173388645133644432917857, 585.6625211386672379439515008507631524971785776260826619675303173388645133790805222836]",
"[585.662520993258078020295946746251400452939328414924378331485171661205473366283926665, 585.6625209932580780202959467462514004529393284149243783314851716612054733926486573656]",
"[585.6625208478489180966403926417396484087000792037660946954400259835464333624220627437, 585.6625208478489180966403926417396484087000792037660946954400259835464334119194520969]"
]
},
{
"lower_level": 18,
"upper_level": 19,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "420.2958332036347466030193919070335533961046965378878498213156113002287582475927018066344490207938905",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[420.2958334944530664503305001160570574845831949602044170934059026555468382321783048416, 420.2958334944530664503305001160570574845831949602044170934059026555468382330913961478]",
"[420.2958333490439065266749460115453054403439457490461334573607569778877982398855030543, 420.2958333490439065266749460115453054403439457490461334573607569778877982407994898231]",
"[420.2958332036347466030193919070335533961046965378878498213156113002287582475927018066, 420.2958332036347466030193919070335533961046965378878498213156113002287582485075834984]",
"[424.3141302365916650359821921884821048549061486753814633959368996976408602400724738641, 424.3141302365916650359821921884821048549061486753814633959368996976408602410137530846]",
"[433.9580433071495046861325463885912311166192391368974863713377525505244798420912108606, 433.9580433071495046861325463885912311166192391368974863713377525505244798431256835158]",
"[448.959685922620258795007877786448669651367228168508417319347430145983994464441789427, 448.9596859226202587950078777864486696513672281685084173193474301459839944656970252203]",
"[468.6071689733249728679607132562110620566034432009819910945530877185418791366011124294, 468.6071689733249728679607132562110620566034432009819910945530877185418791382912235699]",
"[491.3849439172311332536486497310633666934041464835835746035475483764793373040586165312, 491.3849439172311332536486497310633666934041464835835746035475483764793373065265900723]",
"[514.2559740647894752767899599518750576928503006941571730561956126206401464021877777022, 514.2559740647894752767899599518750576928503006941571730561956126206401464059943503524]",
"[533.2691419256049830038081182064634313803251683613921358517860871163472063402145655625, 533.2691419256049830038081182064634313803251683613921358517860871163472063463471390801]",
"[545.4918925994197869801919161105058526452379837265847091863661074793352150915232777653, 545.4918925994197869801919161105058526452379837265847091863661074793352151018839229346]",
"[550.5847052458537274357350731705589560744959370766287071464964978499816385322636499117, 550.5847052458537274357350731705589560744959370766287071464964978499816385507483679878]",
"[550.584705026214384253958537767370821268730544366042566603507820384055653879209809159, 550.5847050262143842539585377673708212687305443660425666035078203840556539139453394658]",
"[550.5847048065750410721820023641826864629651516554564260605191429181296692177990125781, 550.5847048065750410721820023641826864629651516554564260605191429181296692855007737834]"
]
},
{
"lower_level": 17,
"upper_level": 18,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "384.901826373723714331392338002934674831697926162042100725906407739930980219192100586792319939388417",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[384.9018268130024006949454088093109444432287115832143818118837626717829495090475389563, 384.9018268130024006949454088093109444432287115832143818118837626717829495099948500008]",
"[384.9018265933630575131688734061228096374633188726282412688950852058569648641198195017, 384.901826593363057513168873406122809637463318872628241268895085205856964865068481027]",
"[384.9018263737237143313923380029346748316979261620421007259064077399309802191921005868, 384.9018263737237143313923380029346748316979261620421007259064077399309802201421115135]",
"[388.6067347737059827377135514472920636586995001115604687725182391751007129440233551198, 388.6067347737059827377135514472920636586995001115604687725182391751007129449994974733]",
"[397.4985152223729206814830647234001599451249797190737374917318847681083649196726633054, 397.49851522237292068148306472340015994512497971907373749173188476810836492073973048]",
"[411.3301737898331607594926257781422838440356506272653089332675931772823133221942140689, 411.3301737898331607594926257781422838440356506272653089332675931772823133234758684416]",
"[429.5139209766439815007076469607211904661443144105352746491071028519529135996982395092, 429.5139209766439815007076469607211904661443144105352746491071028519529136014027390462]",
"[450.7209855643389424221348022371584554765624708639935002597083379099400136043912952495, 450.7209855643389424221348022371584554765624708639935002597083379099400136068569219117]",
"[472.1237588946379863193263590905376520559341260818574274940539722776121883730490967403, 472.123758894637986319326359090537652055934126081857427494053972277612188376846855101]",
"[489.9613166150699303711427566063626178725424067838586236358837542322221636727676613242, 489.9613166150699303711427566063626178725424067838586236358837542322221636789536360503]",
"[501.4283178630743867310322126405001647426857334339361168186156329767064860788550628431, 501.4283178630743867310322126405001647426857334339361168186156329767064860895728222184]",
"[506.2062348446050290703115834999481731680199509116173306777949883481360486591857622422, 506.2062348446050290703115834999481731680199509116173306777949883481360486790133505526]",
"[506.2062345095086999292877988283216959233189635011109247452407400963314811707869871121, 506.2062345095086999292877988283216959233189635011109247452407400963314812095466626829]",
"[506.206234174412370788264014156695218678617976090604518812686491844526913672109330818, 506.2062341744123707882640141566952186786179760906045188126864918445269137503668546885]"
]
},
{
"lower_level": 16,
"upper_level": 17,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "341.8005949078632058964180335916261454737381706070883581769947739167109210456099845138910306812013056",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[341.8005955780558641784656029348790999631401454281011700421032704203200560034945107763, 341.8005955780558641784656029348790999631401454281011700421032704203200560043844431169]",
"[341.8005952429595350374418182632526227184391580175947641095490221685154885245522473752, 341.800595242959535037441818263252622718439158017594764109549022168515488525444237283]",
"[341.8005949078632058964180335916261454737381706070883581769947739167109210456099845139, 341.8005949078632058964180335916261454737381706070883581769947739167109210465040309093]",
"[345.1077961253725223998789557898906972446219785201061835577147334100476196730078336642, 345.1077961253725223998789557898906972446219785201061835577147334100476196739349420117]",
"[353.0450794869017965362838938305577741107165058246987200313146521707611737744618749587, 353.0450794869017965362838938305577741107165058246987200313146521707611737755031367218]",
"[365.3919648543779805238257955884491471333797222941089210262235941172681088102519321123, 365.3919648543779805238257955884491471333797222941089210262235941172681088115621759813]",
"[381.7185407124693407887498242745890889842584319229211923826624205987953078637705079041, 381.7185407124693407887498242745890889842584319229211923826624205987953078656118556283]",
"[400.9334552425537539763529538221127853198964218345433298942562001032264220073189308545, 400.9334552425537539763529538221127853198964218345433298942562001032264220101253601593]",
"[420.4747197680876273621877568496061591186357655303876365125925340005472509261538932718, 420.4747197680876273621877568496061591186357655303876365125925340005472509306885964062]",
"[436.8221065126995986070232328580660207896861947517917777449561017248577360638956515318, 436.8221065126995986070232328580660207896861947517917777449561017248577360716532432284]",
"[447.3311406254390524354278358773092956182982057484065649855773335510674977023720760969, 447.3311406254390524354278358773092956182982057484065649855773335510674977165561387632]",
"[451.7099045216620182267523717659099447316526619929749187350674274125683923394798977581, 451.7099045216620182267523717659099447316526619929749187350674274125683923672072398948]",
"[451.7099040038183522013070818567179200258578376124832621817878503368716864628795541784, 451.7099040038183522013070818567179200258578376124832621817878503368716865197978979177]",
"[451.7099034859746861758617919475258953200630132319916056285082732611749805696493175275, 451.7099034859746861758617919475258953200630132319916056285082732611749806889966329704]"
]
},
{
"lower_level": 15,
"upper_level": 16,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "290.0045866832862858595310174582428483221431448082683268905661953164801987301204880198136421839272859",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[290.004587718973617910421597276626897733732793569251639997125349467873610454157793663, 290.00458771897361791042159727662689773373279356925163999712534946787361045516462788]",
"[290.0045872011299518849763073674348730279379691887599834438457723921769045921391408414, 290.0045872011299518849763073674348730279379691887599834438457723921769045931491515491]",
"[290.0045866832862858595310174582428483221431448082683268905661953164801987301204880198, 290.0045866832862858595310174582428483221431448082683268905661953164801987311336746785]",
"[292.8085195417021299344698613663479411102656448347929071736285468051969653594646391718, 292.8085195417021299344698613663479411102656448347929071736285468051969653605218719095]",
"[299.5379590792440160585930503906429621849942241320509298949486919549786381210571179316, 299.5379590792440160585930503906429621849942241320509298949486919549786381222649999935]",
"[310.0059763485844358520880846254737831681219371397309582337018097149998085374113719275, 310.0059763485844358520880846254737831681219371397309582337018097149998085389730400318]",
"[323.9827976108664755892994514405940555681135880522244416500263921606197689493056381271, 323.9827976108664755892994514405940555681135880522244416500263921606197689515669951138]",
"[340.6778624626222951387611668988380447018964618957695147448587475616427327316180576267, 340.6778624626222951387611668988380447018964618957695147448587475616427327351672087622]",
"[357.8651621420061087694740806261132719198962172567085265925284961596940376905376511773, 357.8651621420061087694740806261132719198962172567085265925284961596940376964682355075]",
"[372.3284413192954197399167549526458829582044325272467815732329746256393109288416384813, 372.3284413192954197399167549526458829582044325272467815732329746256393109394517496347]",
"[381.6262632953963537841807227794932588260236455710787129404799030803325039114226724503, 381.6262632953963537841807227794932588260236455710787129404799030803325039319382071526]",
"[385.5003552863402523016844183738005192333144421952397656130089276407629566743597328566, 385.5003552863402523016844183738005192333144421952397656130089276407629567168402109695]",
"[385.500354473371254555474592975992279967630123348515368462413137631933479479213641978, 385.5003544733712545554745929759922799676301233485153684624131376319334795707466506862]",
"[385.5003536604022568092647675781840407019458045017909713118173476231040022549392939601, 385.5003536604022568092647675781840407019458045017909713118173476231040024537178673852]"
]
},
{
"lower_level": 14,
"upper_level": 15,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "227.7498873021547283323954934872254038087574395652249395774499808539531702325317558385156086940664972",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[227.7498889280927238248151442828418823401260772586737338786415608716121245737400709327, 227.7498889280927238248151442828418823401260772586737338786415608716121245749188215788]",
"[227.7498881151237260786053188850336430744417584119493367280457708627826474031359132507, 227.7498881151237260786053188850336430744417584119493367280457708627826474043196485853]",
"[227.7498873021547283323954934872254038087574395652249395774499808539531702325317558385, 227.7498873021547283323954934872254038087574395652249395774499808539531702337204753219]",
"[229.9110699179578947025995558590082604976325482103009991177181190379139773743250783329, 229.9110699179578947025995558590082604976325482103009991177181190379139773755669002674]",
"[235.0979092557357107767655140358298409762626088019583959585247220600203583012064654266, 235.0979092557357107767655140358298409762626088019583959585247220600203583026272735736]",
"[243.1663263288792123005962007437152470406073392487896831077874598182303305774794162365, 243.1663263288792123005962007437152470406073392487896831077874598182303305793197030614]",
"[254.1425101805237481835595368931361087636030938593042325244714075066231172877806638634, 254.1425101805237481835595368931361087636030938593042325244714075066231172904552822962]",
"[267.6204131835890158261961896576998326370597389223715009170908732081792140305076738898, 267.6204131835890158261961896576998326370597389223715009170908732081792140347513473198]",
"[281.8029814182747576971774742520699600234113654871801039859665365513510294000254073608, 281.80298141827475769717747425206996002341136548718010398596653655135102940730834066]",
"[293.8615655216710399120280023589027529069637917359007305010591472060205156444734312244, 293.861565521671039912028002358902752906963791735900730501059147206020515658139870015]",
"[301.6135118781826586686208967702293969177910198834877510177436290136465247136679064949, 301.6135118781826586686208967702293969177910198834877510177436290136465247417796666241]",
"[304.843488726738915360362776460928984612282778717058895612099995984613690127780832082, 304.8434887267389153603627764609289846122827787170588956120999959846136901895981293357]",
"[304.8434874260685068011920078033879425417413196249978513363549235659996127824965863463, 304.8434874260685068011920078033879425417413196249978513363549235659996129221126547365]",
"[304.8434861253980982420212391458469004711998605329368070606098511473855353893097638971, 304.8434861253980982420212391458469004711998605329368070606098511473855357024443375871]"
]
},
{
"lower_level": 13,
"upper_level": 14,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "152.1390692800375595624767999848363500692803612193303534023243234500503937260537515563137770273677257",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[152.1390718813783766808183372999184342103632794034524419538144682872785483387903335631, 152.1390718813783766808183372999184342103632794034524419538144682872785483400783908452]",
"[152.1390705807079681216475686423773921398218203113913976780693958686644710324220424248, 152.1390705807079681216475686423773921398218203113913976780693958686644710337180727796]",
"[152.1390692800375595624767999848363500692803612193303534023243234500503937260537515563, 152.1390692800375595624767999848363500692803612193303534023243234500503937273577544441]",
"[153.463999440688546404111254645712137164581694531489361394661040532210763361978901073, 153.4639994406885464041112546457121371645816945314893613946610405322107633633422168966]",
"[156.6438335151659248526336102021598580057883270295482202199356735764903186393828557063, 156.6438335151659248526336102021598580057883270295482202199356735764903186409398756629]",
"[161.5902425853540878158373233358190717587937135408215117338149604984981643702488749146, 161.5902425853540878158373233358190717587937135408215117338149604984981643722565598331]",
"[168.6628217418769318260601122606246344299035841744151183019921839522770182642469137417, 168.6628217418769318260601122606246344299035841744151183019921839522770182671563568843]",
"[177.956179805360017103324282743970879531227883555586488745705090696135787718517772197, 177.9561798053600171033242827439708795312278835555864887457050906961357877231745462245]",
"[188.2312020585221561462404149774474662763367338890682564015095455848033049029178734604, 188.2312020585221561462404149774474662763367338890682564015095455848033049111748084229]",
"[197.1628733062942215821578985306055313385795920050959096996101748003560173345030334901, 197.1628733062942215821578985306055313385795920050959096996101748003560173509429475856]",
"[202.9046610306400325768541819275404861148088331376041331162990672006615970124572207826, 202.9046610306400325768541819275404861148088331376041331162990672006615970487418362963]",
"[205.2970712706903791788868034533562396090300554582843099058297735775165602671626152778, 205.2970712706903791788868034533562396090300554582843099058297735775165603520002526842]",
"[205.2970691425756609603290982749403900976536223535495077178084298767429696278928507654, 205.2970691425756609603290982749403900976536223535495077178084298767429698280894536502]",
"[205.2970670144609427417713930965245405862771892488147055297870861759693789155004484651, 205.2970670144609427417713930965245405862771892488147055297870861759693793774590379601]"
]
},
{
"lower_level": 12,
"upper_level": 13,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "58.57436266777708104362823082457695037371819174728442162795773689336360189721811604349376341151424656",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[58.57436692400651748074364118140864939647105795675402600400042429491078306049333287435, 58.57436692400651748074364118140864939647105795675402600400042429491078306209275358473]",
"[58.57436479589179926218593600299279988509462485201922381597908059413719247885572442519, 58.57436479589179926218593600299279988509462485201922381597908059413719248046818858383]",
"[58.57436266777708104362823082457695037371819174728442162795773689336360189721811604349, 58.57436266777708104362823082457695037371819174728442162795773689336360189884362351546]",
"[58.78265428028206950906767481665422044860364770190960803674630274975019935972090234206, 58.78265428028206950906767481665422044860364770190960803674630274975019936141644360846]",
"[59.28255690050287221353537769442519245562847082014872219828428536675462252459430378275, 59.28255690050287221353537769442519245562847082014872219828428536675462252650940890693]",
"[60.06018401172110384217424939740658340334921102642699518507407472615022246992546004705, 60.06018401172110384217424939740658340334921102642699518507407472615022247234670948729]",
"[61.92075941802398217865992500015086011569274001261523444046328651592412912418899816441, 61.92075941802398217865992500015086011569274001261523444046328651592412912763486166858]",
"[65.62784820590151604324087308530190488111253107026435657238733413360380194388420880689, 65.62784820590151604324087308530190488111253107026435657238733413360380194941483085083]",
"[70.68717134235037268892748682982753158745657249711356138638897637826865071019032129017, 70.68717134235037268892748682982753158745657249711356138638897637826865072041606437892]",
"[75.44546169630693349236760441776280507686997504403483921660000158431781980629594461942, 75.44546169630693349236760441776280507686997504403483921660000158431781982828034477807]",
"[78.50436105374475965651890025474124370654102542273683157752503489520338379081071829505, 78.50436105374475965651890025474124370654102542273683157752503489520338384347709113552]",
"[79.7789002435047323673432600711562292356026466823734155103336946012461989495590108987, 79.77890024350473236734326007115622923560264668237341551033369460124619908076505744358]",
"[79.77889666849022562305313804604201345753787613166678214919323796931325569761601296279, 79.77889666849022562305313804604201345753787613166678214919323796931325602034618063781]",
"[79.77889309347571887876301602092779767947310558096014878805278133738031232069675071283, 79.77889309347571887876301602092779767947310558096014878805278133738031308459377434144]"
]
}
],
"pointwise_nonnegative_pair_energy_certified": true,
"second_is_unassigned_mathematical_control": false
},
{
"depth": 10,
"shell_levels": [
22,
23
],
"other_unsmoothed_chart_minimum_source_cost_lower_bound": "53.35740414886933755156749644053862381764774739431138495134755080781046075406555096485742048093419194",
"common_smoothing_width_interval": "[0.000000000000001201325060964117757081416556663318998012326354893798941037337433848225669281159530203, 0.000000000000001201325060964117757081416556663318998012326354893798941037337433852442548458451739493]",
"smoothing_bands": [
{
"lower_level": 22,
"upper_level": 23,
"strict_positive_certificate": true,
"normalized_contact_lower_bound": "9.318936483751072272870618275828362856127965151944380314005738972653296547229400369974821400344338277",
"subdivision_depth": 0,
"bernstein_coefficient_intervals": [
"[30.76652719953010546816134561864417414107080208929109164689690387840297059381706409924, 30.76652719953010546816134561864417414107080208929109164689690387840297059381717572847]",
"[30.76652719953032896897607431057038287096678302619206787205837367110509092391947008436, 30.76652719953032896897607431057038287096678302619206787205837367110509092391958252322]",
"[30.76652719953055246979080300249659160086276396309304409721984346380721125402187610321, 30.76652719953055246979080300249659160086276396309304409721984346380721125402198931798]",
"[28.57840261738318179514969987308653305154363152211366844997649483362974114239186966681, 28.57840261738318179514969987308653305154363152211366844997649483362974114239199556596]",
"[23.32690362022909767732752632508912976518361705535830788356309104444363161763803599621, 23.32690362022909767732752632508912976518361705535830788356309104444363161763820588584]",
"[15.15790518021137791236233647246128386742451515680448876004508284499302174148535098394, 15.15790518021137791236233647246128386742451515680448876004508284499302174148562492928]",
"[9.318936483751072272870618275828362856127965151944380314005738972653296547229400369975, 9.318936483751072272870618275828362856127965151944380314005738972653296547229902009922]",
"[11.49515163369865380446390634898040922506699864839589697039237224958417592983285580163, 11.49515163369865380446390634898040922506699864839589697039237224958417592983392734436]",
"[21.39638861006093409154342694079977837693005841391142129845344573625832403834106898359, 21.3963886100609340915434269407997783769300584139114212984534457362583240383438293527]",
"[32.81520167399993932576647389068759707512735604240837217887745530786202802966718832024, 32.81520167399993932576647389068759707512735604240837217887745530786202802967520281959]",
"[40.15586721510327040649127314707404772687227297948983780771013753508205684616372740418, 40.15586721510327040649127314707404772687227297948983780771013753508205684618736304571]",
"[43.21447785722934359383051703809811602679762431416903000841639448533346489530508875945, 43.21447785722934359383051703809811602679762431416903000841639448533346489537171646251]",
"[43.21447785722891605527011381612142338264982611512323654732953062940123985074178901243, 43.21447785722891605527011381612142338264982611512323654732953062940123985091779358783]",
"[43.21447785722848851670971059414473073850202791607744308624266677346901480610380874001, 43.21447785722848851670971059414473073850202791607744308624266677346901480653853410116]"
]
}
],
"pointwise_nonnegative_pair_energy_certified": true,
"second_is_unassigned_mathematical_control": true
}
],
"limits": [
"certificates concern orthogonal column blocks with their isolated initial clocks",
"all maintained distinct pairs are checked; depth ten adds one unassigned adjacent control",
"a pointwise energy inequality is not a physical radial force calculation",
"coherent fields and time-evolved encounters are not covered",
"the diagnostic geometric scales and stated compact smoothing remain premises"
]
}