Recorded data and provenance for the associated calculation.
| timestamp | 2026-09-12T09:01:40.982237+00:00 |
|---|---|
| checks | 80 |
| status | passed |
| execution_mode | normal |
| scope | Canonical physical overlap of exact coherent fields on conditional CP3. The physical radius and volume remain unspecified. This calculates initial matrix elements, not a joint stationary solution or an electric charge. |
| units | pair coefficient multiplies kappa Q_N Q_M / physical volume |
| same_grade_scope | Diagonal entries are bilinear current references; a same-grade field also has interference. |
| uniform_probe_scope | Fixed unit-norm coherent probe with constant physical density; not a solved particle. |
View complete data
{
"timestamp": "2026-09-12T09:01:40.982237+00:00",
"checks": 80,
"status": "passed",
"execution_mode": "normal",
"scope": "Canonical physical overlap of exact coherent fields on conditional CP3.\n\nThe physical radius and volume remain unspecified. This calculates initial\nmatrix elements, not a joint stationary solution or an electric charge.\n",
"units": "pair coefficient multiplies kappa Q_N Q_M / physical volume",
"same_grade_scope": "Diagonal entries are bilinear current references; a same-grade field also has interference.",
"uniform_probe_scope": "Fixed unit-norm coherent probe with constant physical density; not a solved particle.",
"sources": {
"marginal_spatial_overlap_checks.py": "2d97e1d5587158eb7029abfc60688c02ef1289230a2665467e22dfac4445c053",
"coherent_spatial_bundle_checks.py": "2fe91619467ae08a40bb053b88fad079deaf0a1b23836f713db8cd83107c207a"
},
"results": [
{
"N": 12,
"M": 12,
"one_minus_cos_theta": "0",
"pair_coefficient": 0.0,
"uniform_density_probe": 0.0,
"exact_pair_coefficient": "0",
"cubature_errors": [
1.021405182655144e-14,
6.8833827526759706e-15
]
},
{
"N": 12,
"M": 12,
"one_minus_cos_theta": "1/2",
"pair_coefficient": 0.2826434965755349,
"uniform_density_probe": 0.1867589151748412,
"exact_pair_coefficient": "1058642208123879828438340671612643650/3745503508661002148471232997041204443",
"cubature_errors": [
1.021405182655144e-14,
6.8833827526759706e-15
]
},
{
"N": 12,
"M": 12,
"one_minus_cos_theta": "1",
"pair_coefficient": 0.37739675210647,
"uniform_density_probe": 0.2499455223332616,
"exact_pair_coefficient": "1413540859172049778066621327907709600/3745503508661002148471232997041204443",
"cubature_errors": [
1.021405182655144e-14,
6.8833827526759706e-15
]
},
{
"N": 12,
"M": 12,
"one_minus_cos_theta": "2",
"pair_coefficient": 0.003232540034540885,
"uniform_density_probe": 0.005601812600840036,
"exact_pair_coefficient": "12107490041260040893002594545108400/3745503508661002148471232997041204443",
"cubature_errors": [
1.021405182655144e-14,
6.8833827526759706e-15
]
},
{
"N": 12,
"M": 34,
"one_minus_cos_theta": "0",
"pair_coefficient": 0.0,
"uniform_density_probe": 0.0,
"exact_pair_coefficient": "0",
"cubature_errors": [
1.3100631690576847e-14,
8.992806499463768e-15
]
},
{
"N": 12,
"M": 34,
"one_minus_cos_theta": "1/2",
"pair_coefficient": 0.3538425055488899,
"uniform_density_probe": 0.1867589151748412,
"exact_pair_coefficient": "5086638777611558353891567124038460296982700418984060009676350/14375431718473248289958137425398456797432149735501000115068243",
"cubature_errors": [
1.3100631690576847e-14,
8.992806499463768e-15
]
},
{
"N": 12,
"M": 34,
"one_minus_cos_theta": "1",
"pair_coefficient": 0.47201307925880176,
"uniform_density_probe": 0.2499455223332616,
"exact_pair_coefficient": "2261797263703735351773094583112747613965718505872600608727600/4791810572824416096652712475132818932477383245167000038356081",
"cubature_errors": [
1.3100631690576847e-14,
8.992806499463768e-15
]
},
{
"N": 12,
"M": 34,
"one_minus_cos_theta": "2",
"pair_coefficient": 0.0013384311616912576,
"uniform_density_probe": 0.005601812600840036,
"exact_pair_coefficient": "2748646539252785826166500531682096503047107690618697098000/2053633102639035469994019632199779542490307105071571445009749",
"cubature_errors": [
1.3100631690576847e-14,
8.992806499463768e-15
]
},
{
"N": 34,
"M": 12,
"one_minus_cos_theta": "0",
"pair_coefficient": 0.0,
"uniform_density_probe": 0.0,
"exact_pair_coefficient": "0",
"cubature_errors": [
1.3100631690576847e-14,
8.992806499463768e-15
]
},
{
"N": 34,
"M": 12,
"one_minus_cos_theta": "1/2",
"pair_coefficient": 0.3538425055488899,
"uniform_density_probe": 0.18734751068929764,
"exact_pair_coefficient": "5086638777611558353891567124038460296982700418984060009676350/14375431718473248289958137425398456797432149735501000115068243",
"cubature_errors": [
1.3100631690576847e-14,
8.992806499463768e-15
]
},
{
"N": 34,
"M": 12,
"one_minus_cos_theta": "1",
"pair_coefficient": 0.47201307925880176,
"uniform_density_probe": 0.24999746960656172,
"exact_pair_coefficient": "2261797263703735351773094583112747613965718505872600608727600/4791810572824416096652712475132818932477383245167000038356081",
"cubature_errors": [
1.3100631690576847e-14,
8.992806499463768e-15
]
},
{
"N": 34,
"M": 12,
"one_minus_cos_theta": "2",
"pair_coefficient": 0.0013384311616912576,
"uniform_density_probe": 0.0012047321249893425,
"exact_pair_coefficient": "2748646539252785826166500531682096503047107690618697098000/2053633102639035469994019632199779542490307105071571445009749",
"cubature_errors": [
1.3100631690576847e-14,
8.992806499463768e-15
]
},
{
"N": 34,
"M": 34,
"one_minus_cos_theta": "0",
"pair_coefficient": 0.0,
"uniform_density_probe": 0.0,
"exact_pair_coefficient": "0",
"cubature_errors": [
1.3100631690576847e-14,
8.992806499463768e-15
]
},
{
"N": 34,
"M": 34,
"one_minus_cos_theta": "1/2",
"pair_coefficient": 0.5314754593998599,
"uniform_density_probe": 0.18734751068929764,
"exact_pair_coefficient": "15382242193276371425527265891353166922988089353913042935535976732019005403854398094754442036304905550/28942525795350818089062198173705740219033498584475605263255379464381203402073878477858894101309137533",
"cubature_errors": [
1.3100631690576847e-14,
8.992806499463768e-15
]
},
{
"N": 34,
"M": 34,
"one_minus_cos_theta": "1",
"pair_coefficient": 0.7087981270178824,
"uniform_density_probe": 0.24999746960656172,
"exact_pair_coefficient": "20514408074911404324037740318964418768741182501380759278417344957228950702186180474446368581311159200/28942525795350818089062198173705740219033498584475605263255379464381203402073878477858894101309137533",
"cubature_errors": [
1.3100631690576847e-14,
8.992806499463768e-15
]
},
{
"N": 34,
"M": 34,
"one_minus_cos_theta": "2",
"pair_coefficient": 0.0009850869084146894,
"uniform_density_probe": 0.0012047321249893425,
"exact_pair_coefficient": "28510903257454540008314782961177228542380176980212186216255887221660982281898088642675197427710800/28942525795350818089062198173705740219033498584475605263255379464381203402073878477858894101309137533",
"cubature_errors": [
1.3100631690576847e-14,
8.992806499463768e-15
]
}
]
}