{
  "object": "G_6",
  "form": "G_6 = (S_SRSD, A_Omega, D_quant, D_rat, H_ico, C_fin, C_cub; J_6)",
  "version": "1.0",
  "date": "23 August 2026",
  "author": "Matthew Alan Newman",
  "orcid": "0009-0007-5468-3125",
  "contracts": {
    "foundation": "SRSD",
    "omega": "OMEGA_NAUGHT/1.0",
    "omega_proof": "OMEGA_NAUGHT_PROOF/1.0",
    "cubature": "CLASS_I_CUBATURE/1.0",
    "global": "NEWMAN_GLOBAL_OBJECT/1.0"
  },
  "foundation": {
    "sort": "S_SRSD",
    "paper": "III",
    "doi": "10.5281/zenodo.21927248",
    "law": "E_s(y)=(d, rho), D_s(d, rho)=s*d+rho, D_s E_s = id"
  },
  "sorts": [
    { "id": "srsd", "symbol": "S_SRSD", "paper": "III", "doi": "10.5281/zenodo.21927248" },
    { "id": "omega", "symbol": "A_Omega", "paper": "V", "doi": "10.5281/zenodo.22048540" },
    { "id": "quant", "symbol": "D_quant", "paper": "I", "doi": "10.5281/zenodo.21830285" },
    { "id": "rat", "symbol": "D_rat", "paper": "II", "doi": "10.5281/zenodo.21843485" },
    { "id": "ico", "symbol": "H_ico", "paper": "IV", "doi": "10.5281/zenodo.22033917" },
    { "id": "fin", "symbol": "C_fin", "paper": "V", "doi": "10.5281/zenodo.22048540" },
    { "id": "cub", "symbol": "C_cub", "paper": "VI", "doi": "10.5281/zenodo.22068873" }
  ],
  "omega_contract": {
    "name": "OMEGA_NAUGHT/1.0",
    "status": "frozen",
    "algebra": "Q(T)[lambda]/(lambda^2-T*lambda-T^2)",
    "Q": "339949771344778",
    "S": "1000000000000000",
    "bits": 15,
    "d_star": 42189065,
    "L60": "339949771344778929576702809321279193551009905014259416689444",
    "U60": "339949771344778929576702809321279193551009905014259416689445",
    "role": "Referenced, not modified. Full JPRV lives on the live companion, not in this runner."
  },
  "omega_proof": {
    "contract": "OMEGA_NAUGHT_PROOF/1.0",
    "status": "frozen",
    "manifest_sha256": "56693dd0ea48bc0e4015e984a5c0bd63f82dfd537dda63e638cc7707365e8ec9",
    "proof_evidence_root_sha256": "f3862e793400a0df022da5c67f970b73ba022fb840591e47c9b412a071bb6fd0",
    "verifier": "/proof/omega_proof_verifier.py",
    "certificate": "/proof/OMEGA_NAUGHT_PROOF_1.0_certificate.json",
    "trusted_lemmas": [
      "alternating_atan_series_remainder",
      "machin_identity_with_standard_atan_branch_theorem",
      "continued_fraction_least_denominator_nonprefix_lemma"
    ],
    "role": "Proof-carrying verifier under frozen OMEGA_NAUGHT/1.0. Does not rewrite the interchange contract."
  },
  "omega_channel": {
    "map": "a + b*sqrt(5) |-> (a-b) + (2b/T)*lambda",
    "sqrt5": "2*lambda/T - 1",
    "role": "interoperability representation; not a source of cubature theorems",
    "arrow": "C_cub -> A_Omega is coefficient encoding only; H_ico -> C_cub generates the masses"
  },
  "cubature": {
    "contract": "CLASS_I_CUBATURE/1.0",
    "paper_doi": "10.5281/zenodo.22068873",
    "scope": "1 <= f <= 9",
    "degrees": [5, 9, 11, 15, 17, 21, 23, 27, 29],
    "node_count": "10*f^2 + 2",
    "orbit_csv": "orbit_masses_f1_f9.csv",
    "orbit_csv_sha256": "eed325c55fe183b36b46b591f758935bcf748a91c2427a09a965337895354b98",
    "f9_csv": "f9_affine_family.csv",
    "f9_csv_sha256": "851a5ff03452e21f7839285cd63423385c936907568e852a174056197c20a95f",
    "f9": {
      "rank": 11,
      "orbits": 12,
      "witness": "t = 1/27",
      "positivity": "t_L < t < t_U",
      "affine": "W(t) = W_part + t W_null"
    },
    "status_from_f10": "open",
    "native_field": "Q(sqrt(5))",
    "cubature_pass": "certificate replay for 1 <= f <= 9; the canonical field name remains cubature=PASS to preserve SHA-256 92187a21…; not a proof of the source cubature theorem and not a claim for f >= 10"
  },
  "canonical_record": {
    "json": "{\"contract\":\"NEWMAN_GLOBAL_OBJECT/1.0\",\"srsd\":\"PASS\",\"quantized_dynamics\":\"PASS\",\"rational_floor\":\"PASS\",\"omega\":\"PASS\",\"icosahedral_geometry\":\"PASS\",\"cubature\":\"PASS\",\"finite_replay\":\"PASS\",\"interfaces\":\"PASS\",\"cubature_frequency_max\":9,\"first_mismatch\":42189065,\"result\":\"PASS\"}",
    "sha256": "92187a21a7ad8ecef384eda3a654aaa49daf46a31422e168eb5871d218c949fa",
    "keys": ["contract", "srsd", "quantized_dynamics", "rational_floor", "omega", "icosahedral_geometry", "cubature", "finite_replay", "interfaces", "cubature_frequency_max", "first_mismatch", "result"],
    "wording": "GLOBAL OBJECT CONFORMANCE = PASS",
    "spec": "spec.html"
  },
  "statuses": {
    "theorem_validity": "Mathematical theorem validity — rests on the proofs in the six source works; it is not certified by this conformance system.",
    "certificate_replay": "supplied by exact computation",
    "runtime_conformance": "supplied by pinned Rust/Julia/TypeScript"
  },
  "boundary": [
    "C_cub is independent of Omega; Omega encodes Q(sqrt(5)) coefficients only.",
    "SRSD is the sole frozen foundation.",
    "OMEGA_NAUGHT/1.0 is referenced, never rewritten, by NEWMAN_GLOBAL_OBJECT/1.0.",
    "Floor-map equality is restricted to D_15.",
    "nu_f and mu_f share X_f and are not identified.",
    "All-frequency positivity remains open for f >= 10."
  ]
}