Recorded data and provenance for the associated calculation.
| timestamp | 2026-09-12T12:02:02.125947+00:00 |
|---|---|
| scope | Uniform spatial mass controls and the holomorphic shape force. Actual physical CP3, its radius, canonical bundle and common norm are conditional. Numerical resolution never changes the fixed mass grades. |
| checks | 300 |
View complete data
{
"timestamp": "2026-09-12T12:02:02.125947+00:00",
"scope": "Uniform spatial mass controls and the holomorphic shape force.\n\nActual physical CP3, its radius, canonical bundle and common norm are\nconditional. Numerical resolution never changes the fixed mass grades.\n",
"uniform": [
{
"density": 1.0,
"width": 0.001,
"branches": [
{
"degree": 12,
"energy_per_volume": 0.9990004999998751,
"frequency": 0.999999500000375,
"scalar_slope": 9.99998500001875e-07,
"maximum_sampled_eigenvector_condition": 1.0000005663908418
},
{
"degree": 34,
"energy_per_volume": 206.5580445587977,
"frequency": 206.7646025000775,
"scalar_slope": 0.00020676439573568176,
"maximum_sampled_eigenvector_condition": 1.005329741735723
}
]
},
{
"density": 1.0,
"width": 0.1,
"branches": [
{
"degree": 12,
"energy_per_volume": 0.904987562112089,
"frequency": 0.9950371902099893,
"scalar_slope": 0.00985185336841574,
"maximum_sampled_eigenvector_condition": 1.0056373872758815
},
{
"degree": 34,
"energy_per_volume": 187.11948710729368,
"frequency": 205.7385719757713,
"scalar_slope": 2.037015564116548,
"maximum_sampled_eigenvector_condition": 10.284613179820422
}
]
},
{
"density": 1.0,
"width": 1.0,
"branches": [
{
"degree": 12,
"energy_per_volume": 0.4142135623730951,
"frequency": 0.7071067811865475,
"scalar_slope": 0.3535533905932737,
"maximum_sampled_eigenvector_condition": 1.4255549449625868
},
{
"degree": 34,
"energy_per_volume": 85.64474539655465,
"frequency": 146.20472563945378,
"scalar_slope": 73.10236281972688,
"maximum_sampled_eigenvector_condition": 51.70447659849991
}
]
},
{
"density": 0.3,
"width": 0.2,
"branches": [
{
"degree": 12,
"energy_per_volume": 0.16055512754639892,
"frequency": 0.8320502943378436,
"scalar_slope": 0.2560154751808749,
"maximum_sampled_eigenvector_condition": 1.2146176119674148
},
{
"degree": 34,
"energy_per_volume": 33.19713372503483,
"frequency": 172.0386343880894,
"scalar_slope": 52.934964427104426,
"maximum_sampled_eigenvector_condition": 47.7267075285952
}
]
}
],
"probe_spectrum": [
{
"depth": 5,
"probe_degree": 1,
"active_slots": 3,
"source_eigenvalues": [
1.0,
1.0,
6.0
]
},
{
"depth": 5,
"probe_degree": 2,
"active_slots": 3,
"source_eigenvalues": [
1.0,
1.0,
1.0,
3.5,
3.5,
21.0
]
},
{
"depth": 5,
"probe_degree": 4,
"active_slots": 3,
"source_eigenvalues": [
1.0,
1.0,
1.0,
1.0,
1.0,
2.25,
2.25,
2.25,
2.25,
6.0,
6.0,
6.0,
21.0,
21.0,
126.0
]
},
{
"depth": 5,
"probe_degree": 12,
"active_slots": 2,
"source_eigenvalues": [
1.0,
1.4166666666666667,
2.0606060606060606,
3.090909090909091,
4.808080808080808,
7.813131313131313,
13.393939393939394,
24.555555555555557,
49.111111111111114,
110.5,
294.6666666666667,
1031.3333333333333,
6188.0
]
},
{
"depth": 6,
"probe_degree": 1,
"active_slots": 3,
"source_eigenvalues": [
1.0,
1.0,
7.0
]
},
{
"depth": 6,
"probe_degree": 2,
"active_slots": 3,
"source_eigenvalues": [
1.0,
1.0,
1.0,
4.0,
4.0,
28.0
]
},
{
"depth": 6,
"probe_degree": 4,
"active_slots": 3,
"source_eigenvalues": [
1.0,
1.0,
1.0,
1.0,
1.0,
2.5,
2.5,
2.5,
2.5,
7.5,
7.5,
7.5,
30.0,
30.0,
210.0
]
},
{
"depth": 6,
"probe_degree": 12,
"active_slots": 2,
"source_eigenvalues": [
1.0,
1.5,
2.3181818181818183,
3.709090909090909,
6.181818181818182,
10.818181818181818,
20.09090909090909,
40.18181818181818,
88.4,
221.0,
663.0,
2652.0,
18564.0
]
},
{
"depth": 10,
"probe_degree": 1,
"active_slots": 3,
"source_eigenvalues": [
1.0,
1.0,
11.0
]
},
{
"depth": 10,
"probe_degree": 2,
"active_slots": 3,
"source_eigenvalues": [
1.0,
1.0,
1.0,
6.0,
6.0,
66.0
]
},
{
"depth": 10,
"probe_degree": 4,
"active_slots": 3,
"source_eigenvalues": [
1.0,
1.0,
1.0,
1.0,
1.0,
3.5,
3.5,
3.5,
3.5,
15.166666666666666,
15.166666666666666,
15.166666666666666,
91.0,
91.0,
1001.0
]
},
{
"depth": 10,
"probe_degree": 12,
"active_slots": 2,
"source_eigenvalues": [
1.0,
1.8333333333333333,
3.5,
7.0,
14.777777777777779,
33.25,
80.75,
215.33333333333334,
646.0,
2261.0,
9797.666666666666,
58786.0,
646646.0
]
}
],
"holomorphic": [
{
"order": 42,
"degree": 12,
"profile_parameter": 0.03,
"width": 0.0007531102143627649,
"norm": 0.9999999999999996,
"inverse_moment": 1.0033189822504343,
"inverse_derivative": 0.21704761900789646,
"inverse_covariance_derivative": 0.21704761900791927,
"normalized_energy_defect": 0.501659418744203,
"normalized_energy_derivative": 0.1085237095374806,
"minimum_density": 0.7531102143627649
},
{
"order": 42,
"degree": 12,
"profile_parameter": 0.1,
"width": 0.0003948102592173879,
"norm": 0.9999999999999993,
"inverse_moment": 1.0341280056658884,
"inverse_derivative": 0.6500102098107744,
"inverse_covariance_derivative": 0.6500102098107775,
"normalized_energy_defect": 0.5170639782945378,
"normalized_energy_derivative": 0.325004991522996,
"minimum_density": 0.3948102592173879
},
{
"order": 42,
"degree": 12,
"profile_parameter": 0.3,
"width": 7.10293991290816e-05,
"norm": 0.9999999999999992,
"inverse_moment": 1.2721421670552382,
"inverse_derivative": 1.7309847576775967,
"inverse_covariance_derivative": 1.7309847576776043,
"normalized_energy_defect": 0.6360710788264109,
"normalized_energy_derivative": 0.8654923202120225,
"minimum_density": 0.0710293991290816
},
{
"order": 42,
"degree": 34,
"profile_parameter": 0.03,
"width": 0.0004442666046372677,
"norm": 1.000000000000001,
"inverse_moment": 1.0270021219260308,
"inverse_derivative": 1.7894965919105836,
"inverse_covariance_derivative": 1.7894965919104577,
"normalized_energy_defect": 0.5135010314333297,
"normalized_energy_derivative": 0.8947479285887052,
"minimum_density": 0.4442666046372677
},
{
"order": 42,
"degree": 34,
"profile_parameter": 0.1,
"width": 6.715474065287e-05,
"norm": 0.999999999999999,
"inverse_moment": 1.3152775502795522,
"inverse_derivative": 6.864446855514781,
"inverse_covariance_derivative": 6.864446855514747,
"normalized_energy_defect": 0.6576387699465048,
"normalized_energy_derivative": 3.4322231964993435,
"minimum_density": 0.06715474065287
},
{
"order": 42,
"degree": 34,
"profile_parameter": 0.3,
"width": 4.04978613686712e-07,
"norm": 0.9999999999999999,
"inverse_moment": 8.197514392078366,
"inverse_derivative": 101.29906412761426,
"inverse_covariance_derivative": 101.29906412761432,
"normalized_energy_defect": 4.098757171727295,
"normalized_energy_derivative": 50.6495305393752,
"minimum_density": 0.00040497861368671203
},
{
"order": 64,
"degree": 12,
"profile_parameter": 0.03,
"width": 0.0007520376389109826,
"norm": 0.9999999999999984,
"inverse_moment": 1.0033189822504378,
"inverse_derivative": 0.217047619007888,
"inverse_covariance_derivative": 0.21704761900792538,
"normalized_energy_defect": 0.5016594189502266,
"normalized_energy_derivative": 0.10852370982201641,
"minimum_density": 0.7520376389109826
},
{
"order": 64,
"degree": 12,
"profile_parameter": 0.1,
"width": 0.00039293974571494344,
"norm": 0.9999999999999992,
"inverse_moment": 1.03412800566589,
"inverse_derivative": 0.6500102098107734,
"inverse_covariance_derivative": 0.6500102098107992,
"normalized_energy_defect": 0.5170639785265005,
"normalized_energy_derivative": 0.32500499259480686,
"minimum_density": 0.39293974571494344
},
{
"order": 64,
"degree": 12,
"profile_parameter": 0.3,
"width": 7.002562654597974e-05,
"norm": 0.9999999999999962,
"inverse_moment": 1.2721421670552462,
"inverse_derivative": 1.7309847576776036,
"inverse_covariance_derivative": 1.7309847576776374,
"normalized_energy_defect": 0.6360710789583452,
"normalized_energy_derivative": 0.8654923218573192,
"minimum_density": 0.07002562654597974
},
{
"order": 64,
"degree": 34,
"profile_parameter": 0.03,
"width": 0.00044247623158522346,
"norm": 1.0000000000000042,
"inverse_moment": 1.0270021219260261,
"inverse_derivative": 1.7894965919104928,
"inverse_covariance_derivative": 1.7894965919104804,
"normalized_energy_defect": 0.5135010316708564,
"normalized_energy_derivative": 0.894747931543634,
"minimum_density": 0.4424762315852235
},
{
"order": 64,
"degree": 34,
"profile_parameter": 0.1,
"width": 6.625718985695806e-05,
"norm": 0.9999999999999996,
"inverse_moment": 1.31527755027955,
"inverse_derivative": 6.864446855514737,
"inverse_covariance_derivative": 6.864446855514502,
"normalized_energy_defect": 0.6576387700844006,
"normalized_energy_derivative": 3.4322232026397153,
"minimum_density": 0.06625718985695805
},
{
"order": 64,
"degree": 34,
"profile_parameter": 0.3,
"width": 3.8897247164631603e-07,
"norm": 0.9999999999999991,
"inverse_moment": 8.197514392078457,
"inverse_derivative": 101.2990641276163,
"inverse_covariance_derivative": 101.29906412761582,
"normalized_energy_defect": 4.098757173611156,
"normalized_energy_derivative": 50.649530657496584,
"minimum_density": 0.00038897247164631604
}
],
"checks": 300,
"source_sha256": {
"smooth_spatial_mass_selection_checks.py": "33501803be52628a21420dfc8b0869e985990d33ef97e9352e0eeaf734cfc355",
"graded_current_tower.py": "cf0f72cb6d078df086ec594550155d6518b00255ed46a16d669790edb093a602",
"coherent_mode_algebra.py": "4fbcbb6a1fbaa5a1a7de387746eda4d00f69fe22bbdb1e906c8795f8bb786dff"
}
}