{
  "project": "ORYNTHRA-H6",
  "version": "1.0.0",
  "date": "2026-10-09",
  "core_scope": "Finite task quotients and phase-registered conserved-spectrum representation implementation",
  "not_a_general_file_compressor": true,
  "formal_statements_with_supplied_proofs": 19,
  "regression_tests": {
    "passed": 44,
    "total": 44,
    "percentage": 100,
    "meaning": "Release test pass rate, not correctness probability"
  },
  "exhaustive_six_label_permutations": {
    "checked": 720,
    "total": 720
  },
  "exact_symbolic_gram_identities": 2,
  "claims": [
    {
      "label": "prop:counting",
      "number": "3.1",
      "type": "proposition",
      "title": "No shortening of every finite string",
      "proof_status": "Proof supplied in manuscript; not independently or formally certified",
      "novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
    },
    {
      "label": "thm:quotient",
      "number": "4.3",
      "type": "theorem",
      "title": "Minimal future-compatible task quotient",
      "proof_status": "Proof supplied in manuscript; not independently or formally certified",
      "novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
    },
    {
      "label": "thm:linear",
      "number": "5.1",
      "type": "theorem",
      "title": "Closure-rank compression",
      "proof_status": "Proof supplied in manuscript; not independently or formally certified",
      "novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
    },
    {
      "label": "thm:sixwing",
      "number": "6.1",
      "type": "theorem",
      "title": "Six-wing activation law",
      "proof_status": "Proof supplied in manuscript; not independently or formally certified",
      "novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
    },
    {
      "label": "cor:nonsubmod",
      "number": "6.2",
      "type": "corollary",
      "title": "Unbounded failure of submodular budgeting",
      "proof_status": "Proof supplied in manuscript; not independently or formally certified",
      "novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
    },
    {
      "label": "prop:storage",
      "number": "7.1",
      "type": "proposition",
      "title": "Storage-only photon cutoff",
      "proof_status": "Proof supplied in manuscript; not independently or formally certified",
      "novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
    },
    {
      "label": "thm:packing",
      "number": "8.2",
      "type": "theorem",
      "title": "Spectral branch packing",
      "proof_status": "Proof supplied in manuscript; not independently or formally certified",
      "novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
    },
    {
      "label": "cor:onemode",
      "number": "8.3",
      "type": "corollary",
      "title": "The one-mode obstruction",
      "proof_status": "Proof supplied in manuscript; not independently or formally certified",
      "novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
    },
    {
      "label": "thm:deficit",
      "number": "9.1",
      "type": "theorem",
      "title": "Exact representation-deficit law",
      "proof_status": "Proof supplied in manuscript; not independently or formally certified",
      "novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
    },
    {
      "label": "prop:gap",
      "number": "10.1",
      "type": "proposition",
      "title": "Generator defect bound",
      "proof_status": "Proof supplied in manuscript; not independently or formally certified",
      "novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
    },
    {
      "label": "prop:robustone",
      "number": "10.2",
      "type": "proposition",
      "title": "One-mode robust obstruction",
      "proof_status": "Proof supplied in manuscript; not independently or formally certified",
      "novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
    },
    {
      "label": "thm:symmetric",
      "number": "11.1",
      "type": "theorem",
      "title": "Full-permutation photon threshold",
      "proof_status": "Proof supplied in manuscript; not independently or formally certified",
      "novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
    },
    {
      "label": "prop:simplex",
      "number": "12.1",
      "type": "proposition",
      "title": "Vacuum-complement orthogonality",
      "proof_status": "Proof supplied in manuscript; not independently or formally certified",
      "novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
    },
    {
      "label": "cor:unitary",
      "number": "13.1",
      "type": "corollary",
      "title": "Universal finite-dimensional coherent control",
      "proof_status": "Proof supplied in manuscript; not independently or formally certified",
      "novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
    },
    {
      "label": "prop:meanstore",
      "number": "14.1",
      "type": "proposition",
      "title": "Minimum uniform storage energy",
      "proof_status": "Proof supplied in manuscript; not independently or formally certified",
      "novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
    },
    {
      "label": "prop:weighted",
      "number": "14.2",
      "type": "proposition",
      "title": "Uniform equivariant mean-energy optimum",
      "proof_status": "Proof supplied in manuscript; not independently or formally certified",
      "novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
    },
    {
      "label": "prop:query-energy",
      "number": "15.1",
      "type": "proposition",
      "title": "Necessary query-energy bound",
      "proof_status": "Proof supplied in manuscript; not independently or formally certified",
      "novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
    },
    {
      "label": "prop:nonresonance",
      "number": "16.1",
      "type": "proposition",
      "title": "Rationally independent frequencies",
      "proof_status": "Proof supplied in manuscript; not independently or formally certified",
      "novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
    },
    {
      "label": "prop:gapenergy",
      "number": "16.2",
      "type": "proposition",
      "title": "Energy-gap stability of the commutator obstruction",
      "proof_status": "Proof supplied in manuscript; not independently or formally certified",
      "novelty_status": "Inherited foundation, standard consequence, or candidate combination; see prior-art audit"
    }
  ],
  "candidate_contributions": [
    "Task-to-spectrum representation packing workflow",
    "Exact optimum 2(1-C/M) for the stated covariance metric",
    "Natural-permutation resource frontier and exact deficit plateau",
    "Six-wing unbounded high-order activation construction"
  ],
  "physical_assumptions": [
    "Degenerate modes for H proportional to total photon number",
    "Arbitrary unitaries within invariant photon-number sectors",
    "Exact physical group representation for the main deficit theorem",
    "Phase-registered logical action, including arbitrary logical superpositions",
    "Ideal preparation and readout; external phase reference not charged",
    "No uncharged correlated side information in memory bounds"
  ],
  "explicit_negative_results": [
    "H6 is not exact arbitrary-state one-photon-loss correcting",
    "Number twirling destroys exact H6 label distinguishability",
    "A nondegenerate register spectrum excludes exact energy-conserving nonabelian logical action"
  ],
  "global_novelty_verified": false,
  "external_peer_review": false,
  "proof_assistant_verified": false,
  "hardware_validated": false,
  "physical_energy_density_record": null,
  "proposed_not_delivered": [
    "Loss-correcting spectral packing characterization",
    "Reference-inclusive optimal code",
    "Learned multimodal compression benchmark",
    "Restricted optical control synthesis and noisy hardware comparison"
  ]
}