Recorded data and provenance for the associated calculation.
| experiment_key | uniform-ground-harmonic-no-growth-window |
|---|---|
| created_utc | 2026-10-12T04:38:48.740100+00:00 |
View complete data
{
"experiment_key": "uniform-ground-harmonic-no-growth-window",
"created_utc": "2026-10-12T04:38:48.740100+00:00",
"sources": {
"experiments/ground-harmonic-uniform.py": "a7d0cda7373463b9d0186100eccfb892c357c7dd7f43f3f24c1fd5588d5c87b1",
"experiments/ground-harmonic-repair.py": "d76a036de187a8328a6c05bb7366e91737455177458f37eb094737e46e5bf9de",
"experiments/inverse-current-ground-proof.py": "8f941c0913b297522f5578c78c6361834e0179d20c702c46ccdd3c58f7ca5c2c",
"experiments/inverse-current-radial.py": "52d9f1c981635192e06d96b11f0b1e4e5e2d1bf3d5ed420b59411fd45ef7be80"
},
"cases": [
{
"depth": 3,
"c_exact": "3/10",
"kappa_exact": "11/10",
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"first_harmonic_cubic": "z**3 - 3567649*z**2/1406250 + 167894471*z/773437500 - 4139191/878906250",
"elementary_symmetric_positive_certificates": [
{
"expression": "(225000*L**2 + 450000*L + 2892649)/1406250",
"shifted_numerator_coefficients": [
"4/25",
"24/25",
"4692649/1406250"
],
"shifted_denominator_coefficients": [
"1"
]
},
{
"expression": "(7425000*L**4 + 29700000*L**3 + 157789577*L**2 + 256179154*L - 283199260)/773437500",
"shifted_numerator_coefficients": [
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"46744507/70312500",
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],
"shifted_denominator_coefficients": [
"1"
]
},
{
"expression": "(225000*L**6 + 1350000*L**5 + 5666560*L**4 + 13666240*L**3 - 1801131*L**2 - 27334742*L + 12367264)/878906250",
"shifted_numerator_coefficients": [
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"4966624/29296875",
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"25665863/48828125",
"11560452/48828125"
],
"shifted_denominator_coefficients": [
"1"
]
},
{
"expression": "L**2*(L - 1)*(L + 2)**2*(L + 3)*(37500*L**2 + 75000*L + 137137)/14648437500",
"shifted_numerator_coefficients": [
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],
"shifted_denominator_coefficients": [
"1"
]
}
],
"hermite_leading_minor_positive_certificates": [
{
"expression": "4",
"shifted_numerator_coefficients": [
"4"
],
"shifted_denominator_coefficients": [
"1"
]
},
{
"expression": "(4711894275000*L**2 + 9423788550000*L + 113281545109211)/7250976562500",
"shifted_numerator_coefficients": [
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"1"
]
},
{
"expression": "(27760194897715695194954212500*L**6 + 166561169386294171169725275000*L**5 + 617362890912266116814126027339*L**4 + 1359043767740436659458335609356*L**3 - 732106860006260105506889749296*L**2 - 3738138137129942406811183317304*L + 3178978716952787865888821730608)/6506361812353134155273437500000",
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"shifted_denominator_coefficients": [
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{
"expression": "(205437603997210585343249305128142404337500*L**12 + 2465251247966527024118991661537708852050000*L**11 + 14269937542890551786034752633723551111787309*L**10 + 52306829670132860309317832080852853209373090*L**9 + 105996668325207992391534844891742170523619828*L**8 + 26493654160584047953593321624105645124804464*L**7 - 351183259557505607021495878099216840287412160*L**6 - 698528640328717125672893585222015369645063808*L**5 - 64793017152809626891636919384937693251481744*L**4 + 1668033303937641822420009314019585919844159552*L**3 + 748891083938888147902360197375436488847399872*L**2 - 2070143004852215584493939938573479156314417152*L + 566687645521886006013867651331807434344153088)/36857403912904374010395258665084838867187500000000",
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],
"positive_trace_metric_symmetrizes_companion": true,
"first_harmonic_generator_power_nullities": [
1,
2,
2
],
"classification": "all integer harmonics L>=1 have no exponentially growing eigenvalue in this reducing family"
},
{
"depth": 4,
"c_exact": "3/10",
"kappa_exact": "11/10",
"polynomial": "(512578125*L**8 + 6150937500*L**7 - 91125000000*L**6*z + 27831171510*L**6 - 820125000000*L**5*z + 56726012340*L**5 + 6075000000000*L**4*z**2 - 3646332719568*L**4*z + 36812491605*L**4 + 36450000000000*L**3*z**2 - 9576121317408*L**3*z - 48751641720*L**3 - 180000000000000*L**2*z**3 + 159193003161600*L**2*z**2 - 1954616631120*L**2*z - 79281549360*L**2 - 540000000000000*L*z**3 + 313554009484800*L*z**2 + 26157008534976*L*z + 2000000000000000*z**4 - 2315952212480000*z**3 - 360090661478400*z**2 - 11922900986880*z)/2000000000000000",
"first_harmonic_cubic": "z**3 - 1185918833*z**2/781250000 + 606177153*z/7812500000 - 362151/390625000",
"elementary_symmetric_positive_certificates": [
{
"expression": "(70312500*L**2 + 210937500*L + 904668833)/781250000",
"shifted_numerator_coefficients": [
"9/100",
"63/100",
"1607793833/781250000"
],
"shifted_denominator_coefficients": [
"1"
]
},
{
"expression": "9*(52734375*L**4 + 316406250*L**3 + 1381883708*L**2 + 2721822999*L - 3125786992)/156250000000",
"shifted_numerator_coefficients": [
"243/80000",
"1701/40000",
"1278547371/4882812500",
"123603595479/156250000000",
"50491772271/78125000000"
],
"shifted_denominator_coefficients": [
"1"
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},
{
"expression": "81*(70312500*L**6 + 632812500*L**5 + 2813528333*L**4 + 7388982498*L**3 + 1508191845*L**2 - 20182876956*L + 9199769280)/125000000000000",
"shifted_numerator_coefficients": [
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"2691618221061/62500000000000",
"586008324513/5000000000000",
"1157670159471/7812500000000",
"420167639043/6250000000000"
],
"shifted_denominator_coefficients": [
"1"
]
},
{
"expression": "6561*L**2*(L - 1)*(L + 3)**2*(L + 4)*(15625*L**2 + 46875*L + 67132)/400000000000000",
"shifted_numerator_coefficients": [
"6561/25600000000",
"45927/6400000000",
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"shifted_denominator_coefficients": [
"1"
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}
],
"hermite_leading_minor_positive_certificates": [
{
"expression": "4",
"shifted_numerator_coefficients": [
"4"
],
"shifted_denominator_coefficients": [
"1"
]
},
{
"expression": "3*(42162085921875000*L**2 + 126486257765625000*L + 1111468227901581889)/610351562500000000",
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"shifted_denominator_coefficients": [
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{
"expression": "81*(50391682063931677739243803382812500*L**6 + 453525138575385099653194230445312500*L**5 + 1768004071303286749960554321613631821*L**4 + 3805147349188944004965412473002103426*L**3 - 1935972430475636170613574916937915371*L**2 - 16808490992009457688866958768311492780*L + 15455274681025109830873576172625901504)/29802322387695312500000000000000000000000",
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"shifted_denominator_coefficients": [
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{
"expression": "531441*(1941364751213805023104392457563410321751294632812500*L**12 + 34944565521848490415879064236141385791523303390625000*L**11 + 266683740690994268768421060626592823910367593731362881*L**10 + 1117329454812413572216293109917228030854841376243880715*L**9 + 2393408683975465042158011823533373808877103783483647638*L**8 - 479278472197747433235439818727853219388925594318911954*L**7 - 15860514556909215873512658718463331004595096051239643955*L**6 - 27752349530473846091648874292019399196013041931364724801*L**5 + 10986478440094339347608780900797578705604175748977797560*L**4 + 68838071997151307630485355149255838935222652740020832752*L**3 + 20477436743173630030008052077634796744640298411650165504*L**2 - 85058540056116561292353132055421916169801319192168509440*L + 25126158860203949494569429343880295887254309156960665600)/58207660913467407226562500000000000000000000000000000000000000000000",
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"shifted_denominator_coefficients": [
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}
],
"positive_trace_metric_symmetrizes_companion": true,
"first_harmonic_generator_power_nullities": [
1,
2,
2
],
"classification": "all integer harmonics L>=1 have no exponentially growing eigenvalue in this reducing family"
}
],
"limits": [
"ground states and exactly reducing rotational spatial family only",
"no assigned excited electron or full angular stability follows",
"kappa=11/10 changes the potential and lies outside positive blends",
"zero-frequency Jordan structure is reported separately from exponential spectral growth",
"no color selection or observed decay claim is made"
]
}