{
  "schema": "MC-CIVIC-ASSIGNMENT/2.0",
  "policy": "research/e47/CITY_CONSTITUTION_EVIDENCE_DETERMINED_PROMOTION_20261008.md",
  "source": "research/e47/evidence_ledger.json",
  "source_sha256": "8dcb8c4a8fa1c3a4a5df5aae36cb3c038eac5bd67a142533a3ffaa652a4dc854",
  "claims": [
    {
      "id": "census.decomposition",
      "statement": "V2⊗V2⊗V2 = V0 + 3V1 + 5V2 + 4V3 + 3V4 + 2V5 + V6",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_CASIMIR_CENSUS_CERTIFICATE.json",
      "certificate_sha256": "35a540d21756f13398ed0800b6fbcaaeff2daf8a0e0b05db4701c6387c23288a",
      "verified_check": "census_1_3_5_4_3_2_1",
      "depends_on": [],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "census.e47_unique_quadratic_selector",
      "statement": "{2,5} is the only two-sector Casimir selection of dimension 47",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_CASIMIR_CENSUS_CERTIFICATE.json",
      "certificate_sha256": "35a540d21756f13398ed0800b6fbcaaeff2daf8a0e0b05db4701c6387c23288a",
      "verified_check": "e47_unique_quadratic_selector",
      "depends_on": [
        "census.decomposition"
      ],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "einstein.unmarked_moduli_embedding",
      "statement": "E47 (n = 47) injects into Ricci-flat Lorentzian metrics modulo diffeomorphism",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_INTRINSIC_SPACETIME_UNMARKED_CERTIFICATE.json",
      "certificate_sha256": "a26042f6d6604ec777f909f77f0e1f2e7932f11df309825833fa543cdcd5c2cb",
      "verified_check": "unmarked_affine_rigidity",
      "depends_on": [
        "profile.injectivity",
        "profile.vacuum"
      ],
      "conditional_on": [
        "plane-wave-equivalence-group-exhausts-isometries"
      ],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "lock.chebyshev_rate",
      "statement": "Chebyshev bound 1/T_n(17/15) = 2/((5/3)^n + (3/5)^n); rate 3/5",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_CONDITION_LOCK_CERTIFICATE.json",
      "certificate_sha256": "322cbaea147344334d012d327e028f118f3d3e27d79dc085abf7eec26889caed",
      "verified_check": "chebyshev_closed_form",
      "depends_on": [
        "census.decomposition",
        "lock.condition_4"
      ],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "lock.condition_4",
      "statement": "|K| on the complement of E47 is {108,112,140,180,432}; condition number 4",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_CONDITION_LOCK_CERTIFICATE.json",
      "certificate_sha256": "322cbaea147344334d012d327e028f118f3d3e27d79dc085abf7eec26889caed",
      "verified_check": "condition_K_4",
      "depends_on": [
        "census.decomposition"
      ],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "lock.equioscillation",
      "statement": "Gamma* takes the values -15/17 and +15/17 on the complement; step 1/99144 is optimal",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_CONDITION_LOCK_CERTIFICATE.json",
      "certificate_sha256": "322cbaea147344334d012d327e028f118f3d3e27d79dc085abf7eec26889caed",
      "verified_check": "equioscillation_exact",
      "depends_on": [
        "census.decomposition",
        "lock.condition_4"
      ],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "lock.five_factor_identity",
      "statement": "prod (1 - x/lambda) over the five nonzero K^2 eigenvalues is 1 at 0 and vanishes on the complement spectrum",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_CONDITION_LOCK_CERTIFICATE.json",
      "certificate_sha256": "322cbaea147344334d012d327e028f118f3d3e27d79dc085abf7eec26889caed",
      "verified_check": "five_factor_scalar_identity",
      "depends_on": [
        "census.decomposition",
        "lock.condition_4"
      ],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "lock.five_step_termination",
      "statement": "Krylov dimension of the complement is 5; five Richardson steps reach P exactly",
      "evidence": "E1",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_CONDITION_LOCK_CERTIFICATE.json",
      "certificate_sha256": "322cbaea147344334d012d327e028f118f3d3e27d79dc085abf7eec26889caed",
      "verified_check": "krylov_dimension_5",
      "depends_on": [
        "census.decomposition",
        "lock.condition_4",
        "lock.five_factor_identity"
      ],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "moment.cube_best_conditioned",
      "statement": "The cube is the best-conditioned moment carrier: ||K||/gap = 4, optimal rate 15/17, Chebyshev rate 3/5",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_MOMENT_DYNAMICS_CERTIFICATE.json",
      "certificate_sha256": "eb433fe1a554564c1229d2bfe547d5dd9704c708f45ce93d0073d572cd306786",
      "verified_check": "cube_best_conditioned_in_family",
      "depends_on": [
        "census.decomposition",
        "moment.cube_first_proper_carrier",
        "moment.dynamics_closed_forms",
        "moment.fibonacci_lucas_carriers",
        "moment.triple_roots"
      ],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "moment.cube_first_proper_carrier",
      "statement": "V2⊗V2⊗V2 is the first triple product on which the moment selector cuts a proper kernel; there it is (C-6I)(C-30I) with dim ker 47",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_MOMENT_SELECTOR_CERTIFICATE.json",
      "certificate_sha256": "d6a9fc021290b9aec0bdd1fcc3e15dc5fd6de9e9a4a2fd7ddd33167aa894fbdb",
      "verified_check": "first_proper_member_is_e47",
      "depends_on": [
        "census.decomposition",
        "moment.fibonacci_lucas_carriers",
        "moment.triple_roots"
      ],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "moment.cube_flow_replay",
      "statement": "On the 125x125 carrier ||e^{-tK^2} - P|| = e^{-11664 t}, ||(I - K^2/99144)^n - P|| = (15/17)^n, and the five-factor product is the exact projector",
      "evidence": "E1",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_MOMENT_DYNAMICS_CERTIFICATE.json",
      "certificate_sha256": "eb433fe1a554564c1229d2bfe547d5dd9704c708f45ce93d0073d572cd306786",
      "verified_check": "machine_flow_and_iteration_rates",
      "depends_on": [
        "moment.dynamics_closed_forms",
        "moment.fibonacci_lucas_carriers",
        "moment.triple_roots"
      ],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "moment.dynamics_closed_forms",
      "statement": "On every Fibonacci–Lucas carrier the moment selector's gap is at J = j+1 and its top at J = 3j, so sqrt(kappa) = j^2(4j+1)/(j+1)^2 (proved in the note; exact for k = 5..13)",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_MOMENT_DYNAMICS_CERTIFICATE.json",
      "certificate_sha256": "eb433fe1a554564c1229d2bfe547d5dd9704c708f45ce93d0073d572cd306786",
      "verified_check": "root_kappa_closed_form",
      "depends_on": [
        "moment.fibonacci_lucas_carriers",
        "moment.triple_roots"
      ],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "moment.fibonacci_lucas_carriers",
      "statement": "Both moment roots are Casimir values on V_j⊗V_j⊗V_j iff (2J+1, 2j+1) = (L_k, F_k) with k odd (proved in the note; exhaustively checked for 2j ≤ 400)",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_MOMENT_SELECTOR_CERTIFICATE.json",
      "certificate_sha256": "d6a9fc021290b9aec0bdd1fcc3e15dc5fd6de9e9a4a2fd7ddd33167aa894fbdb",
      "verified_check": "upper_root_iff_fibonacci_to_j200",
      "depends_on": [
        "moment.triple_roots"
      ],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "moment.triple_roots",
      "statement": "On V_j⊗V_j⊗V_j the Casimir has mean 3j(j+1) and standard deviation 2j(j+1), so the moment roots are j(j+1) and 5j(j+1)",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_MOMENT_SELECTOR_CERTIFICATE.json",
      "certificate_sha256": "d6a9fc021290b9aec0bdd1fcc3e15dc5fd6de9e9a4a2fd7ddd33167aa894fbdb",
      "verified_check": "triple_mu_3jj1_sigma_2jj1",
      "depends_on": [],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "profile.injectivity",
      "statement": "For odd n and even N >= n+3, q -> [g_q] is injective modulo plane-wave equivalence",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_PROFILE_INJECTION_CERTIFICATE.json",
      "certificate_sha256": "ac2e914189e11bb2851ed5913158570c3dc7aa169696d5de1696f1da71ea7178",
      "verified_check": "odd_n_injective",
      "depends_on": [
        "profile.vacuum"
      ],
      "conditional_on": [
        "plane-wave-equivalence-group-exhausts-isometries"
      ],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "profile.parity_obstruction",
      "statement": "For even n, a = -1 identifies distinct profiles",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_PROFILE_INJECTION_CERTIFICATE.json",
      "certificate_sha256": "ac2e914189e11bb2851ed5913158570c3dc7aa169696d5de1696f1da71ea7178",
      "verified_check": "even_n_counterexample",
      "depends_on": [],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "profile.vacuum",
      "statement": "Every Brinkmann plane wave g_q with H = F(u)(x^2 - y^2) is Ricci-flat",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_PROFILE_INJECTION_CERTIFICATE.json",
      "certificate_sha256": "ac2e914189e11bb2851ed5913158570c3dc7aa169696d5de1696f1da71ea7178",
      "verified_check": "every_profile_vacuum",
      "depends_on": [],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "symmetry.bosonic_slice",
      "statement": "E47 ∩ Sym³V2 is a single V2",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_SIGNATURE_SYMMETRY_CERTIFICATE.json",
      "certificate_sha256": "88bd3d1d7813c499ad1bdde7eeed16571b75999c3756004c4900a69d62258828",
      "verified_check": "bosonic_slice_exact",
      "depends_on": [
        "census.decomposition",
        "symmetry.su2_s3_table"
      ],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "symmetry.fermion_exclusion",
      "statement": "E47 ∩ Λ³V2 = 0",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_SIGNATURE_SYMMETRY_CERTIFICATE.json",
      "certificate_sha256": "88bd3d1d7813c499ad1bdde7eeed16571b75999c3756004c4900a69d62258828",
      "verified_check": "fermion_exclusion_exact",
      "depends_on": [
        "census.decomposition",
        "symmetry.su2_s3_table"
      ],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "symmetry.gamma_not_isometry",
      "statement": "||Gamma* eta Gamma* - eta|| = 12800/23409; Gamma* is not a Krein isometry",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_SIGNATURE_SYMMETRY_CERTIFICATE.json",
      "certificate_sha256": "88bd3d1d7813c499ad1bdde7eeed16571b75999c3756004c4900a69d62258828",
      "verified_check": "gamma_not_krein_isometry_exact",
      "depends_on": [
        "census.decomposition",
        "lock.condition_4"
      ],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "symmetry.k_inertia",
      "statement": "In(K) = (23, 55, 47)",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_SIGNATURE_SYMMETRY_CERTIFICATE.json",
      "certificate_sha256": "88bd3d1d7813c499ad1bdde7eeed16571b75999c3756004c4900a69d62258828",
      "verified_check": "K_inertia_exact_23_55_47",
      "depends_on": [
        "census.decomposition"
      ],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "symmetry.krein_isometries",
      "statement": "SU(2) rotations and S3 permutations satisfy U^dagger eta U = eta (checked on sampled rotations)",
      "evidence": "E1",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_SIGNATURE_SYMMETRY_CERTIFICATE.json",
      "certificate_sha256": "88bd3d1d7813c499ad1bdde7eeed16571b75999c3756004c4900a69d62258828",
      "verified_check": "krein_isometry_su2_rotations",
      "depends_on": [],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "symmetry.mixed_core",
      "statement": "47 = 5 + 42 + 0 (symmetric, mixed, antisymmetric)",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_SIGNATURE_SYMMETRY_CERTIFICATE.json",
      "certificate_sha256": "88bd3d1d7813c499ad1bdde7eeed16571b75999c3756004c4900a69d62258828",
      "verified_check": "mixed_core_exact",
      "depends_on": [
        "census.decomposition",
        "symmetry.su2_s3_table"
      ],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    },
    {
      "id": "symmetry.su2_s3_table",
      "statement": "Exact SU(2) x S3 multiplicity table of V2⊗V2⊗V2",
      "evidence": "E0",
      "civic_state": "PRIMA_FACIE",
      "certificate": "artifacts/E47_SIGNATURE_SYMMETRY_CERTIFICATE.json",
      "certificate_sha256": "88bd3d1d7813c499ad1bdde7eeed16571b75999c3756004c4900a69d62258828",
      "verified_check": "su2_s3_table",
      "depends_on": [
        "census.decomposition"
      ],
      "conditional_on": [],
      "empirical": [],
      "scope": "as-stated-in-ledger",
      "supersession": "not_assessed"
    }
  ],
  "claim_count": 24,
  "assignment_sha256": "4e1c44dd49bf5b76686e2ac6e932d0ed2c920c850022f79ce80fbc67c7dbfa2c",
  "surfaces": {
    "citadel": {
      "assignment_sha256": "4e1c44dd49bf5b76686e2ac6e932d0ed2c920c850022f79ce80fbc67c7dbfa2c",
      "url": "/E47-Kartekeya/data/city-assignment.json"
    },
    "citizenship_bureau": {
      "assignment_sha256": "4e1c44dd49bf5b76686e2ac6e932d0ed2c920c850022f79ce80fbc67c7dbfa2c",
      "url": "/E47-Kartekeya/data/city-assignment.json"
    },
    "proof_forge": {
      "assignment_sha256": "4e1c44dd49bf5b76686e2ac6e932d0ed2c920c850022f79ce80fbc67c7dbfa2c",
      "url": "/E47-Kartekeya/data/city-assignment.json"
    },
    "publication": {
      "assignment_sha256": "4e1c44dd49bf5b76686e2ac6e932d0ed2c920c850022f79ce80fbc67c7dbfa2c",
      "url": "/E47-Kartekeya/data/city-assignment.json"
    }
  }
}