Recorded data and provenance for the associated calculation.
| status | passed |
|---|---|
| source_sha256 | 1c6c3d251edce58b1277490aac8ffb760fbfa722db7342b135488612346a0b5c |
| elapsed_seconds | 4.776353379013017 |
| scope | Rigorous Arb summation plus analytic uniform series tails for the full linear clamped first-mode response. |
View complete data
{
"status": "passed",
"rows": [
{
"depth": 2,
"series_terms": 16384,
"precision_bits": 160,
"constants": {
"F0": "71/1260",
"F1": "-61/1260",
"G0": "-29/630",
"G1": "19/126",
"H0": "-139/630"
},
"exact_boundary_cap": "62/63",
"exact_admissible_load_limit": "63/124",
"compliance_over_volume_lower": "[0.017790643504531074208913884743717876936639647 +/- 6.54e-46]",
"compliance_over_volume_upper": "[0.017812154837646059171589191275835932492195203 +/- 5.09e-46]",
"transverse_overlap_over_volume_lower": "[-0.008367709695022229460764479177213901942215802 +/- 2.05e-46]",
"transverse_overlap_over_volume_upper": "[-0.008346198361907244498089172645095846386660246 +/- 6.10e-46]",
"longitudinal_per_Ca_lower": "[-0.13359116128234544378691893456876949369146402 +/- 4.08e-45]",
"longitudinal_per_Ca_upper": "[-0.13342982628398305656685413557788407702479735 +/- 7.41e-45]",
"transverse_per_Ca_lower": "[0.06259648771430433373566879483821884789995185 +/- 3.21e-45]",
"transverse_per_Ca_upper": "[0.06275782271266672095573359382910426456661851 +/- 6.24e-45]",
"truncation_error_bound": "[1.0755666557492481337653266059027777777777777778e-5 +/- 2.83e-52]",
"full_parallel_negative": true,
"full_transverse_positive": true
},
{
"depth": 3,
"series_terms": 16384,
"precision_bits": 160,
"constants": {
"F0": "23/135 - 11*pi/288",
"F1": "-1/14 + 5*pi/576",
"G0": "-74/135 + 43*pi/288",
"G1": "11/21 - 5*pi/48",
"H0": "-10/21 + 5*pi/64"
},
"exact_boundary_cap": "5*pi/288 + 22/21",
"exact_admissible_load_limit": "1008/(35*pi + 2112)",
"compliance_over_volume_lower": "[0.019989834164404072049465416442331891194202038 +/- 3.71e-46]",
"compliance_over_volume_upper": "[0.020026333528665573869507650388988153963495003 +/- 5.95e-46]",
"transverse_overlap_over_volume_lower": "[-0.006543042830714224724430198156989067025048667 +/- 1.02e-46]",
"transverse_overlap_over_volume_upper": "[-0.006506543466452722904387964210332804255755702 +/- 3.33e-46]",
"longitudinal_per_Ca_lower": "[-0.20398655827802143482241006332816262098917737 +/- 8.16e-45]",
"longitudinal_per_Ca_upper": "[-0.20361477880653793526417777486206846949259166 +/- 8.22e-45]",
"transverse_per_Ca_lower": "[0.06627510752820649744557892824163053761335837 +/- 2.25e-45]",
"transverse_per_Ca_upper": "[0.06664688699968999700381121670772468910994408 +/- 2.31e-45]",
"truncation_error_bound": "[1.8249682130750910021116973328131384646482384501e-5 +/- 4.32e-52]",
"full_parallel_negative": true,
"full_transverse_positive": true
},
{
"depth": 4,
"series_terms": 16384,
"precision_bits": 160,
"constants": {
"F0": "1291/28350",
"F1": "-3061/75600",
"G0": "-1502/14175",
"G1": "1261/5400",
"H0": "-1801/7560"
},
"exact_boundary_cap": "649/540",
"exact_admissible_load_limit": "270/649",
"compliance_over_volume_lower": "[0.020768645399803954936224897977786211729660909 +/- 4.81e-46]",
"compliance_over_volume_upper": "[0.020826133031951922751624067899661211729660909 +/- 4.81e-46]",
"transverse_overlap_over_volume_lower": "[-0.005181161303866048967691521843542055034667638 +/- 5.62e-46]",
"transverse_overlap_over_volume_upper": "[-0.005123673671718081152292351921667055034667638 +/- 5.62e-46]",
"longitudinal_per_Ca_lower": "[-0.27334299604436898611506589118305340395179943 +/- 6.94e-45]",
"longitudinal_per_Ca_upper": "[-0.27258847087242690853795178595844402895179943 +/- 6.94e-45]",
"transverse_per_Ca_lower": "[0.06724821694129981512383711897188009733001274 +/- 3.89e-45]",
"transverse_per_Ca_upper": "[0.06800274211324189270095122419648947233001274 +/- 3.89e-45]",
"truncation_error_bound": "[2.8743816073983907699584960937500000000000000000e-5 +/- 2.38e-52]",
"full_parallel_negative": true,
"full_transverse_positive": true
},
{
"depth": 5,
"series_terms": 16384,
"precision_bits": 160,
"constants": {
"F0": "11/105 - 85*pi/4224",
"F1": "-1/18 + 49*pi/8448",
"G0": "-158/315 + 251*pi/2112",
"G1": "5/9 - 49*pi/528",
"H0": "-4/9 + 49*pi/768"
},
"exact_boundary_cap": "119*pi/2112 + 661/594",
"exact_admissible_load_limit": "9504/(1071*pi + 21152)",
"compliance_over_volume_lower": "[0.020732697315395427100634615163976811054882692 +/- 6.80e-46]",
"compliance_over_volume_upper": "[0.020819169344207624879920725527754073405155028 +/- 5.70e-46]",
"transverse_overlap_over_volume_lower": "[-0.004180293104303329205116046130214478077492828 +/- 3.37e-46]",
"transverse_overlap_over_volume_upper": "[-0.004093821075491131425829935766437215727220492 +/- 4.47e-46]",
"longitudinal_per_Ca_lower": "[-0.33929970812906459906502412179937636085166391 +/- 7.37e-45]",
"longitudinal_per_Ca_upper": "[-0.3378904331646208413547576532843543578293819 +/- 5.09e-44]",
"transverse_per_Ca_lower": "[0.06671891049453494081469056221224768844484520 +/- 2.35e-45]",
"transverse_per_Ca_upper": "[0.06812818545897869852495703072726969146712716 +/- 4.39e-45]",
"truncation_error_bound": "[4.3236014406098889643055181888631175136167945234e-5 +/- 4.67e-52]",
"full_parallel_negative": true,
"full_transverse_positive": true
},
{
"depth": 6,
"series_terms": 16384,
"precision_bits": 160,
"constants": {
"F0": "9529/249480",
"F1": "-1439/41580",
"G0": "-3667/24948",
"G1": "223/770",
"H0": "-1723/6930"
},
"exact_boundary_cap": "12631/9240",
"exact_admissible_load_limit": "4620/12631",
"compliance_over_volume_lower": "[0.020257390879185451625155320444220939661878386 +/- 6.46e-46]",
"compliance_over_volume_upper": "[0.020381691907157702801989426889533439661878386 +/- 6.46e-46]",
"transverse_overlap_over_volume_lower": "[-0.003440019628360961182089164175763209008501908 +/- 5.10e-46]",
"transverse_overlap_over_volume_upper": "[-0.003315718600388710005255057730450709008501908 +/- 5.10e-46]",
"longitudinal_per_Ca_lower": "[-0.40126455942216727391416684188768959334323072 +/- 8.34e-45]",
"longitudinal_per_Ca_upper": "[-0.39881738293396357887024537124559974959323072 +/- 8.34e-45]",
"transverse_per_Ca_lower": "[0.06527820994515272822845894906824833360488130 +/- 5.76e-45]",
"transverse_per_Ca_upper": "[0.06772538643335642327238041971033817735488130 +/- 5.76e-45]",
"truncation_error_bound": "[6.2150513986125588417053222656250000000000000000e-5 +/- 6.01e-52]",
"full_parallel_negative": true,
"full_transverse_positive": true
},
{
"depth": 10,
"series_terms": 16384,
"precision_bits": 160,
"constants": {
"F0": "9379/324324",
"F1": "-2063/77220",
"G0": "-161989/810810",
"G1": "1073/2970",
"H0": "-10069/38610"
},
"exact_boundary_cap": "534701/332640",
"exact_admissible_load_limit": "166320/534701",
"compliance_over_volume_lower": "[0.017074511179553666649727468597567042068635053 +/- 8.10e-46]",
"compliance_over_volume_upper": "[0.017467656692429388060196241203180467994560978 +/- 8.42e-46]",
"transverse_overlap_over_volume_lower": "[-0.0019201966851448799452488159314129428193642770 +/- 4.98e-47]",
"transverse_overlap_over_volume_upper": "[-0.0015270511722691585347800433257995168934383511 +/- 7.57e-47]",
"longitudinal_per_Ca_lower": "[-0.6147114028988138946652653789041126412617182 +/- 2.88e-44]",
"longitudinal_per_Ca_upper": "[-0.6008760594398397767476357992010995390481765 +/- 3.02e-44]",
"transverse_per_Ca_lower": "[0.05373907816786269234309925907081190505072697 +/- 2.23e-45]",
"transverse_per_Ca_upper": "[0.06757442162683681026072883877382500726426864 +/- 3.11e-45]",
"truncation_error_bound": "[0.00019657275643786070523438630280671296296296296296 +/- 3.61e-51]",
"full_parallel_negative": true,
"full_transverse_positive": true
}
],
"source_sha256": "1c6c3d251edce58b1277490aac8ffb760fbfa722db7342b135488612346a0b5c",
"elapsed_seconds": 4.776353379013017,
"scope": "Rigorous Arb summation plus analytic uniform series tails for the full linear clamped first-mode response."
}