Recorded data and provenance for the associated calculation.
| experiment_key | minimal-carrier-exact-low-harmonic-curvature |
|---|---|
| created_utc | 2026-10-12T09:39:43.780820+00:00 |
View complete data
{
"experiment_key": "minimal-carrier-exact-low-harmonic-curvature",
"created_utc": "2026-10-12T09:39:43.780820+00:00",
"sources": {
"experiments/minimal-carrier-exact-curvature.py": "2558def020c2d3aeb27bbb5227ad839d15b6a8addeb962c26d53011864725179",
"experiments/minimal-count-carrier.py": "c32f6a998a844bbccd3bc46483a551addf224b2b254f7b6d218a8fd0ca87ad2b",
"experiments/forward-count-action.py": "5f1dd9a03cf8e6b07a56d507791fed8ff859f10abf22bb755c60c3bd1ed6d909",
"experiments/inverse-current-radial.py": "52d9f1c981635192e06d96b11f0b1e4e5e2d1bf3d5ed420b59411fd45ef7be80",
"experiments/excited-shell-orientation-current.py": "508484d445dbb86da9f88a31642268b5a1dba8264588e6f48ebb6cc00cf9c264",
"experiments/minimal-carrier-ground-response.py": "be27aa03a9b7957c3ec8e6201bbff9977653d9a649e22d085ffc89c0d7c39bfd"
},
"cases": [
{
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[
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"nonzero_squared_frequency_cubic": "(62500*scalar_curvature*z**2 - 222300*scalar_curvature*z + 187600*scalar_curvature + 5625*z**3 - 103954*z**2 + 322137*z - 285100)/5625",
"elementary_symmetric_coefficients": [
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"-(24700*scalar_curvature - 35793)/625",
"-4*(1876*scalar_curvature - 2851)/225"
],
"cubic_discriminant": "16*(614572753906250000*scalar_curvature**4 - 1610652276171875000*scalar_curvature**3 + 535047313465430625*scalar_curvature**2 + 1355082255708111400*scalar_curvature - 913350619402931056)/1001129150390625",
"all_real_scalar_curvature_allowed_set": "scalar_curvature <= CRootOf(614572753906250000*x**4 - 1610652276171875000*x**3 + 535047313465430625*x**2 + 1355082255708111400*x - 913350619402931056, 0)",
"exact_root_certificates": {
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"discriminant_roots_at_or_below_sum_bound": 2,
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"independent_pointwise_source_maximum_error": 7.828241759158203e-16,
"flat_nonreal_squared_frequency_roots": 2,
"flat_negative_squared_frequency_roots": 0,
"classification": "exact closed spatial family for every real scalar curvature; not a full persistence theorem"
},
{
"depth": 3,
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[
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[
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"time_characteristic_polynomial": "-time_eigenvalue**2*(6875*scalar_curvature*time_eigenvalue**4 + 51700*scalar_curvature*time_eigenvalue**2 + 79475*scalar_curvature - 275*time_eigenvalue**6 - 10692*time_eigenvalue**4 - 66843*time_eigenvalue**2 - 110000)/275",
"nonzero_squared_frequency_cubic": "(6875*scalar_curvature*z**2 - 51700*scalar_curvature*z + 79475*scalar_curvature + 275*z**3 - 10692*z**2 + 66843*z - 110000)/275",
"elementary_symmetric_coefficients": [
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"-(51700*scalar_curvature - 66843)/275",
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"classification": "exact closed spatial family for every real scalar curvature; not a full persistence theorem"
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{
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"time_characteristic_polynomial": "-time_eigenvalue**2*(250000*scalar_curvature*time_eigenvalue**4 + 2283600*scalar_curvature*time_eigenvalue**2 + 4800000*scalar_curvature - 5625*time_eigenvalue**6 - 348406*time_eigenvalue**4 - 2789805*time_eigenvalue**2 - 6250000)/5625",
"nonzero_squared_frequency_cubic": "(250000*scalar_curvature*z**2 - 2283600*scalar_curvature*z + 4800000*scalar_curvature + 5625*z**3 - 348406*z**2 + 2789805*z - 6250000)/5625",
"elementary_symmetric_coefficients": [
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"-(152240*scalar_curvature - 185987)/375",
"-80*(96*scalar_curvature - 125)/9"
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{
"depth": 5,
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"nonzero_residual_coefficients": 64,
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"classification": "the fixed-label family is not exactly closed; no projected eigenvalue claim"
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{
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"0",
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"time_characteristic_polynomial": "-time_eigenvalue**2*(6002500*scalar_curvature*time_eigenvalue**4 + 33680060*scalar_curvature*time_eigenvalue**2 + 89536720*scalar_curvature - 60025*time_eigenvalue**6 - 6957906*time_eigenvalue**4 - 39659577*time_eigenvalue**2 - 106427020)/60025",
"nonzero_squared_frequency_cubic": "(6002500*scalar_curvature*z**2 - 33680060*scalar_curvature*z + 89536720*scalar_curvature + 60025*z**3 - 6957906*z**2 + 39659577*z - 106427020)/60025",
"elementary_symmetric_coefficients": [
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"-(33680060*scalar_curvature - 39659577)/60025",
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"all_real_scalar_curvature_allowed_set": "False",
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{
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"-2*(1702473781250*scalar_curvature - 1853034211397)/12257811225",
"-(26276440323500*scalar_curvature - 29349873517409)/12257811225",
"-20*(35401652*scalar_curvature - 39282047)/66429"
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"cubic_discriminant": "-16*(3247215549860787225450729408516227844238281250000*scalar_curvature**4 - 13697867769653231906661533022928560570173046875000*scalar_curvature**3 + 21648783098825199853447600052711064974996489953125*scalar_curvature**2 - 15192890617847501680863617297568018883710606376000*scalar_curvature + 3994769699780294712005358439551273990636917931968)/92906359225625442495385620290823046875",
"all_real_scalar_curvature_allowed_set": "False",
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"independent_pointwise_source_maximum_error": 1.2066547949414795e-15,
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"classification": "exact closed spatial family for every real scalar curvature; not a full persistence theorem"
}
],
"limits": [
"one common c3/5 ground preparation and the fixed ambient-label low spatial family",
"scalar_curvature=f_double_prime*c_squared/lambda varies the local action Hessian while retaining the background",
"all polynomial coefficients are reduced exactly modulo sphere norm squared equal to one",
"failed closure prevents any projected spectral claim",
"allowed coefficients in one low family do not prove all-angular or assigned excited persistence"
]
}