Recorded data and provenance for the associated calculation.
| experiment_key | proper-current-count-envelope-ground-response |
|---|---|
| created_utc | 2026-10-12T09:15:59.772366+00:00 |
| evaluations | 90 |
View complete data
{
"experiment_key": "proper-current-count-envelope-ground-response",
"created_utc": "2026-10-12T09:15:59.772366+00:00",
"sources": {
"experiments/proper-envelope-ground-response.py": "e1cfb54cb451a306a3afce7141f687cc1430479d3f8f2b87a3d36eb36fb3070f",
"experiments/discrete-count-ground-response.py": "0ffdb3995d4c0781b8baafb69a4227a94e3aeba68aa41471206380475d0d94a0",
"experiments/inverse-current-radial.py": "52d9f1c981635192e06d96b11f0b1e4e5e2d1bf3d5ed420b59411fd45ef7be80"
},
"evaluations": 90,
"conditions": {
"independent physical source blocks have exactly zero scalar-ratio curvature in the affine chart": 30,
"the complete proper-current Hessian survives the affine count chart": 30,
"the exact squared-frequency polynomial matches the physical normalized linearization": 30
},
"maximum_errors": {
"independent physical source blocks have exactly zero scalar-ratio curvature in the affine chart": 2.101855898694716e-16,
"the complete proper-current Hessian survives the affine count chart": 2.613246212344773e-16,
"the exact squared-frequency polynomial matches the physical normalized linearization": 3.1254394664840602e-15
},
"cases": [
{
"depth": 2,
"angular_harmonic": 1,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "2/5",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "z*(390625*z**3 - 2598850*z**2 + 2899233*z - 923724)/390625",
"zero_squared_frequency_multiplicity": 1,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [
1,
2,
2
],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 2,
"angular_harmonic": 2,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "2/5",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(9765625*z**4 - 121221250*z**3 + 416738025*z**2 - 510072876*z + 166281984)/9765625",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 0,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 2,
"angular_harmonic": 3,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "2/5",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(1953125*z**4 - 41119250*z**3 + 277749765*z**2 - 732314196*z + 615999168)/1953125",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 0,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 2,
"angular_harmonic": 5,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "2/5",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(1953125*z**4 - 91744250*z**3 + 1517056245*z**2 - 10518486012*z + 25660333440)/1953125",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 0,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 2,
"angular_harmonic": 10,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "2/5",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(1953125*z**4 - 316744250*z**3 + 18932085045*z**2 - 494495886204*z + 4760237496960)/1953125",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 0,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 3,
"angular_harmonic": 1,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "18/55",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "z*(171875*z**3 - 1069200*z**2 + 1069488*z - 281600)/171875",
"zero_squared_frequency_multiplicity": 1,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 0,
"zero_generator_power_nullities": [
2,
2,
2
],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 3,
"angular_harmonic": 2,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "18/55",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(859375*z**4 - 8096000*z**3 + 17861040*z**2 - 12223104*z + 901120)/859375",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 3,
"angular_harmonic": 3,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "18/55",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(859375*z**4 - 11946000*z**3 + 46468080*z**2 - 62514688*z + 18247680)/859375",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 3,
"angular_harmonic": 5,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "18/55",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(859375*z**4 - 22946000*z**3 + 199482480*z**2 - 675474432*z + 706478080)/859375",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 3,
"angular_harmonic": 10,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "18/55",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(859375*z**4 - 69696000*z**3 + 2027893680*z**2 - 25110903424*z + 111018885120)/859375",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 4,
"angular_harmonic": 1,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "36/125",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "z*(1250000*z**3 - 6968120*z**2 + 5021649*z - 1012500)/1250000",
"zero_squared_frequency_multiplicity": 1,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [
2,
2,
2
],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 4,
"angular_harmonic": 2,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "36/125",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(31250000*z**4 - 241703000*z**3 + 380505465*z**2 - 183730518*z + 7381125)/31250000",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 4,
"angular_harmonic": 3,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "36/125",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(156250000*z**4 - 1658515000*z**3 + 4452788925*z**2 - 3989677518*z + 651015225)/156250000",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 4,
"angular_harmonic": 5,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "36/125",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(31250000*z**4 - 579203000*z**3 + 3295576665*z**2 - 7026838452*z + 4251528000)/31250000",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 4,
"angular_harmonic": 10,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "36/125",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(31250000*z**4 - 1591703000*z**3 + 28443290265*z**2 - 212069240694*z + 550107865125)/31250000",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 5,
"angular_harmonic": 1,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "36/137",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "z*(267578125*z**3 - 1394965000*z**2 + 777902544*z - 127837440)/267578125",
"zero_squared_frequency_multiplicity": 1,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [
2,
2,
2
],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 5,
"angular_harmonic": 2,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "36/137",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(20904541015625*z**4 - 142696484375000*z**3 + 173902106250000*z**2 - 64801557792000*z + 1623637757952)/20904541015625",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 5,
"angular_harmonic": 3,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "36/137",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(20904541015625*z**4 - 186044140625000*z**3 + 379276796250000*z**2 - 251773891488000*z + 25978204127232)/20904541015625",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 5,
"angular_harmonic": 5,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "36/137",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(33447265625*z**4 - 482620625000*z**3 + 2010437658000*z**2 - 3035737232640*z + 1192876720128)/33447265625",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 5,
"angular_harmonic": 10,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "36/137",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(33447265625*z**4 - 1214714375000*z**3 + 15093428778000*z**2 - 76649724990720*z + 131514658394112)/33447265625",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 6,
"angular_harmonic": 1,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "12/49",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "z*(153125*z**3 - 763200*z**2 + 344991*z - 48020)/153125",
"zero_squared_frequency_multiplicity": 1,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [
2,
2,
2
],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 6,
"angular_harmonic": 2,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "12/49",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(19140625*z**4 - 119900000*z**3 + 118879875*z**2 - 36068580*z + 614656)/19140625",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 6,
"angular_harmonic": 3,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "12/49",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(19140625*z**4 - 150525000*z**3 + 246649875*z**2 - 129350380*z + 9144576)/19140625",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 6,
"angular_harmonic": 5,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "12/49",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(153125*z**4 - 1841200*z**3 + 6006735*z**2 - 6906564*z + 1897280)/153125",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 6,
"angular_harmonic": 10,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "12/49",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(153125*z**4 - 4291200*z**3 + 40042335*z**2 - 149587412*z + 182891520)/153125",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 10,
"angular_harmonic": 1,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "1512/7381",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "z*(14416015625*z**3 - 65673432500*z**2 + 16520916303*z - 1446823620)/14416015625",
"zero_squared_frequency_multiplicity": 1,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [
2,
2,
2
],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 10,
"angular_harmonic": 2,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "1512/7381",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(1126251220703125*z**4 - 5909201757812500*z**3 + 3321706819921875*z**2 - 579769324258500*z + 3375150140736)/1126251220703125",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 10,
"angular_harmonic": 3,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "1512/7381",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(1126251220703125*z**4 - 6817410742187500*z**3 + 6201268924921875*z**2 - 1746589137781500*z + 42426474083136)/1126251220703125",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 10,
"angular_harmonic": 5,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "1512/7381",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(1802001953125*z**4 - 14436897812500*z**3 + 24770095207875*z**2 - 13900108986180*z + 1366796337984)/1802001953125",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
},
{
"depth": 10,
"angular_harmonic": 10,
"ground_c_exact": "3/5",
"diagnostic_epsilon_exact": "1512/7381",
"scalar_hessian_factor_exact": "0",
"polynomial_exact": "(1802001953125*z**4 - 26892335312500*z**3 + 118606797547875*z**2 - 194331515454180*z + 90626965349184)/1802001953125",
"zero_squared_frequency_multiplicity": 0,
"negative_real_squared_frequencies": 0,
"nonreal_squared_frequency_roots": 2,
"zero_generator_power_nullities": [],
"classification": "ground full-matrix reducing spatial family; not an assigned excited or reduced-column state"
}
],
"limits": [
"the Lorentz-scalar proper-current chart is V=m*s+eta*sqrt(j_mu*j^mu)",
"the preferred-time envelope nonlinear unitary theorem does not transfer",
"these full-matrix ground controls are not the assigned excited particles or minimum-column Hessians",
"nonnegative real squared frequencies in this family would not establish full angular or nonlinear persistence"
]
}