{
  "schema": "CITY-MACHINE-CERTIFICATE/1.0",
  "certificate_code": "MC-E47-CONSTANTS-20260923",
  "title": "E47 finite spectral constants and invariants — 19/19 checks PASS",
  "evidence_class": "E1",
  "valid": true,
  "source": "scripts/e47_constant_validation.py",
  "source_sha256": "97af74ede32869895504a3375ce7be854d009aaf92b1f3eb2d501181ae44f616",
  "source_commit": "e3a4b0686263f4b4a7d3b90a75c7b71f707bd7a9",
  "result": {
    "pass_count": 19,
    "fail_count": 0,
    "ambient_dimension": 125,
    "kernel_dimension": 47,
    "complement_dimension": 78,
    "omega_c": "47/125",
    "omega_c_decimal": 0.376,
    "mu": 18,
    "tau": 468,
    "variance": 144,
    "sigma": 12,
    "selected_sectors": [
      6,
      30
    ],
    "casimir_spectrum": [
      0,
      2,
      6,
      12,
      20,
      30,
      42
    ],
    "multiplicities": [
      1,
      9,
      25,
      28,
      27,
      22,
      13
    ],
    "k_sector_values": [
      180,
      112,
      0,
      -108,
      -140,
      0,
      432
    ],
    "k_norm": 432,
    "k2_spectrum": [
      0,
      11664,
      12544,
      19600,
      32400,
      186624
    ],
    "k2_gap": 11664,
    "k2_norm": 186624,
    "epsilon_star": "1/99144",
    "rho_star": "15/17",
    "projector_rank": 47,
    "projector_trace": 47,
    "iterations": 252,
    "gamma252_minus_p_op": 4.7049900678789936e-14,
    "theoretical_bound_252": 2.0038679292982893e-14
  },
  "boundaries": [
    "Finite-dimensional spin-2 SU(2) tensor-cube software verification.",
    "The 256→125 MATRIX lift remains a typed feature map, not a Hilbert-space isomorphism.",
    "No hardware, experimental, continuum, or physical-law claim is promoted by this certificate."
  ],
  "provenance": {
    "notion": "https://mathematicalcity.notion.site/E47-Invariant-Kernel-Verification-252-Step-Spectral-Projector-Certificate-3e546094fd3081738c01e36b7b75e3af?pvs=149",
    "drive_python": "https://drive.google.com/file/d/1-Qd0oH_pYAy9_aEzcBW7YbTIz5FtCBGa/view?usp=drivesdk",
    "drive_csv": "https://drive.google.com/file/d/1fFUXVOQ5LB0B5qeWWI9lL91DzXDd7CtF/view?usp=drivesdk",
    "supabase_source": "SRC-E47-CONSTANT-VALIDATION-20260923",
    "supabase_identity": "MC-E47-CONSTANT-FINGERPRINT-20260923",
    "csv_sha256": "0597ce08a2f9e6b1e7928876de031b5e7dbe424ef7047ec81c8b49a2d9f631ab"
  }
}