Recorded data and provenance for the associated calculation.
| checks_passed | 1532 |
|---|---|
| created_utc | 2026-10-10T23:30:28.965559+00:00 |
| exact_arithmetic | SymPy integers and rational numbers; no numerical rank tolerance |
| projected_curvature | Fhat=P_h(F)-[K_mu,K_nu]/4 |
| projected_metric_connection | Ahat=A-J(DJ)/2 |
| scope | local geometric identities and explicit comparison action; no graph evolution or particle simulation |
| title | Retained Ordinary Normal Complex Structure: Exact Geometric Response |
View complete data
{
"checks_passed": 1532,
"created_utc": "2026-10-10T23:30:28.965559+00:00",
"depth_four_real_wave": {
"W2_norm_squared": 2,
"commutator_norm_squared": 4,
"complement_projection_norm_squared": 1,
"first_order_parallel_J_continuation": "obstructed: background F0i is zero",
"unitary_projection_norm_squared": 1
},
"exact_arithmetic": "SymPy integers and rational numbers; no numerical rank tolerance",
"occupied_depths": [
{
"depth": 2,
"even_carrier": 2,
"hodge_coefficient": 0,
"orientation_dimension": 12,
"q": 4,
"su_dimension": 15,
"u_dimension": 16
},
{
"depth": 3,
"even_carrier": 4,
"hodge_coefficient": 1,
"orientation_dimension": 6,
"q": 3,
"su_dimension": 8,
"u_dimension": 9
},
{
"depth": 4,
"even_carrier": 4,
"hodge_coefficient": 1,
"orientation_dimension": 6,
"q": 3,
"su_dimension": 8,
"u_dimension": 9
},
{
"depth": 5,
"even_carrier": 6,
"hodge_coefficient": 0,
"orientation_dimension": 2,
"q": 2,
"su_dimension": 3,
"u_dimension": 4
},
{
"depth": 6,
"even_carrier": 6,
"hodge_coefficient": 0,
"orientation_dimension": 2,
"q": 2,
"su_dimension": 3,
"u_dimension": 4
},
{
"depth": 10,
"even_carrier": 10,
"hodge_coefficient": 0,
"orientation_dimension": 0,
"q": 0,
"su_dimension": 0,
"u_dimension": 0
}
],
"projected_curvature": "Fhat=P_h(F)-[K_mu,K_nu]/4",
"projected_metric_connection": "Ahat=A-J(DJ)/2",
"rank_cases": [
{
"central_dimension": 1,
"commutator_quadratic_eigenvalues": {
"0": 16,
"4": 12
},
"orientation_dimension": 12,
"q": 4,
"real_normal_rank": 8,
"so_dimension": 28,
"su_dimension": 15,
"u_dimension": 16
},
{
"central_dimension": 1,
"commutator_quadratic_eigenvalues": {
"0": 9,
"4": 6
},
"orientation_dimension": 6,
"q": 3,
"real_normal_rank": 6,
"so_dimension": 15,
"su_dimension": 8,
"u_dimension": 9
},
{
"central_dimension": 1,
"commutator_quadratic_eigenvalues": {
"0": 4,
"4": 2
},
"orientation_dimension": 2,
"q": 2,
"real_normal_rank": 4,
"so_dimension": 6,
"su_dimension": 3,
"u_dimension": 4
},
{
"central_dimension": 0,
"commutator_quadratic_eigenvalues": {},
"orientation_dimension": 0,
"q": 0,
"real_normal_rank": 0,
"so_dimension": 0,
"su_dimension": 0,
"u_dimension": 0
}
],
"scope": "local geometric identities and explicit comparison action; no graph evolution or particle simulation",
"sources": {
"experiments/normal-structure-response-checks.py": "42b0350ff80c267d0a25c564fd28ad5b1c57ad702ea8c129de0dd30e18f882fe"
},
"title": "Retained Ordinary Normal Complex Structure: Exact Geometric Response",
"vacuum_cartan_history": {
"A2": "b(t)*x1*T",
"DJ": "0",
"generator": "(j_1-j_2)/2",
"generator_algebra": "su3, hence also u3",
"generator_norm_squared": 1,
"independent_connection_vacuum_ambiguity": "survives",
"vacuum_energy": "0"
}
}