{
  "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"
  }
}