{
  "schema": "OMEGA_NAUGHT_LEAN_RUN/1.0",
  "generated": "2026-09-13",
  "package": "omega_provenance",
  "package_version": "0.1",
  "status": "pass_on_this_archive",
  "not": [
    "independent third-party reproduction of Papers I\u2013VII",
    "peer review of Papers I\u2013VII",
    "joining theorem",
    "eighth source paper",
    "cubature package for 10 \u2264 f \u2264 21",
    "exact 117 a+b\u221a5 coefficient pairs for f=23 and f=24",
    "hosted Lean toolchain",
    "hosted .lake build cache"
  ],
  "runtime": {
    "os": "Linux-6.12.8+-x86_64-with-glibc2.35",
    "uname": "Linux 6.12.8+ x86_64",
    "kernel": "6.12.8+",
    "machine": "x86_64",
    "lean": "Lean (version 4.19.0, x86_64-unknown-linux-gnu, commit 6caaee842e94, Release)",
    "lean_version": "4.19.0",
    "lean_commit": "6caaee842e94",
    "lake": "Lake version 5.0.0-6caaee8",
    "python": "Python 3.10.21",
    "mathlib": "v4.19.0",
    "mathlib_commit": "c44e0c8ee63ca166450922a373c7409c5d26b00b",
    "ld_preload": "self_exe.so compiled from hosted /formal/scripts/self_exe.c; changes executable discovery only, not arithmetic or the kernel",
    "toolchain_hosted": false,
    "lake_cache_hosted": false,
    "cwd_of_run": "/tmp/omega-provenance (byte copy of hosted /formal sources matching SHA256SUMS)"
  },
  "commands": [
    {
      "cmd": "lake update && lake exe cache get",
      "exit": 0,
      "note": "Mathlib v4.19.0 plus eight inherited packages; cache 6641/6641 files. Author setup_lake_update.log recorded a ProofWidgets fetch failure; this run succeeded. The lake-update transcript itself was not captured as a separate hosted file."
    },
    {
      "cmd": "lake build",
      "exit": 0,
      "transcript": "/formal/evidence/current/build.log",
      "note": "Fresh Built modules (not Replayed). Ends with 'Build completed successfully.'"
    },
    {
      "cmd": "lake env lean Omega/AxiomAudit.lean",
      "exit": 0,
      "transcript": "/formal/evidence/current/axioms.log"
    },
    {
      "cmd": "python3 scripts/check_axioms.py evidence/current/axioms.log",
      "exit": 0,
      "expected": "Checked 147 theorem reports; axioms: Classical.choice, Quot.sound, propext",
      "transcript": "/formal/evidence/current/check_axioms.runtime.txt"
    },
    {
      "cmd": "Python regex scan of hosted Omega.lean and Omega/*.lean for sorry, admit, native_decide",
      "exit": 0,
      "transcript": "/formal/evidence/current/sorry_scan.txt"
    }
  ],
  "axioms_used": [
    "Classical.choice",
    "Quot.sound",
    "propext"
  ],
  "axiom_set_counts": {
    "[Classical.choice, Quot.sound, propext]": 123,
    "[propext]": 16,
    "[]": 4,
    "[Quot.sound, propext]": 4
  },
  "theorem_count": 147,
  "theorems": [
    "Omega.weighted_mean",
    "Omega.displacement_conjugacy",
    "Omega.affine_iterate",
    "Omega.homothety_comp",
    "Omega.homothety_one",
    "Omega.observation_commutes",
    "Omega.observation_iterate",
    "Omega.real_time_semigroup",
    "Omega.arbitrary_intercept_defect",
    "Omega.grid_interface",
    "Omega.phi_pos",
    "Omega.phi_sq",
    "Omega.phi_bounds",
    "Omega.denominator_pos",
    "Omega.lam_pos",
    "Omega.lam_lt_one",
    "Omega.shares_sum",
    "Omega.mu_eq_one_sub",
    "Omega.lam_bounds",
    "Omega.q_lt_lam",
    "Omega.lam_lt_q_plus",
    "Omega.delta_pos",
    "Omega.delta_lt_half_pi",
    "Omega.s_pos",
    "Omega.c_pos",
    "Omega.sc_identity",
    "Omega.one_arcsecond",
    "Omega.seeds_distinct",
    "Omega.marks_collinear",
    "Omega.marks_affine_dimension",
    "Omega.seed_linear_combination",
    "Omega.centered_span",
    "Omega.center_relative_rank",
    "Omega.center_adjoined_affine_dimension",
    "Omega.moment_matrix",
    "Omega.coordinates_rank",
    "Omega.gram_rank",
    "Omega.gram_entries",
    "Omega.embedded_center_relative_rank",
    "Omega.step_threshold",
    "Omega.extinction_threshold",
    "Omega.threshold_values",
    "Omega.extinction_by_ten",
    "Omega.deepest_seeds",
    "Omega.all_twenty_three_steps",
    "Omega.gcd_constants",
    "Omega.inverse_identity",
    "Omega.remainder_halved",
    "Omega.first_remainder_reconstruction",
    "Omega.first_remainder_injective",
    "Omega.first_remainder_injective_domain",
    "Omega.finite_gap_certificate",
    "Omega.certified_gap",
    "Omega.minimum_gap_attained",
    "Omega.finite_certificate_inequality",
    "Omega.S_pos",
    "Omega.Q_pos",
    "Omega.Q_lt_S",
    "Omega.division_identity",
    "Omega.remainder_bound",
    "Omega.step_zero",
    "Omega.step_lt",
    "Omega.step_le",
    "Omega.forward_invariant",
    "Omega.step_monotone",
    "Omega.q_in_interval",
    "Omega.lam_in_interval",
    "Omega.floor_q",
    "Omega.no_interior_boundary",
    "Omega.floor_agreement_of_interval",
    "Omega.exact_parameter_interval",
    "Omega.certified_floor_equality",
    "Omega.trajectory_equality",
    "Omega.truncation_le",
    "Omega.truncation_succ",
    "Omega.truncation_monotone",
    "Omega.truncation_seven",
    "Omega.truncation_eight",
    "Omega.precision_threshold",
    "Omega.arc_length",
    "Omega.semicircle_retained",
    "Omega.semicircle_in_outline",
    "Omega.major_arc_no_retracing",
    "Omega.upper_seed_endpoint",
    "Omega.lower_seed_endpoint",
    "Omega.mark_re",
    "Omega.mark_im",
    "Omega.bilateral_reflection",
    "Omega.mark_distance",
    "Omega.inner_extension_length",
    "Omega.outer_extension_length",
    "Omega.negative_outer_extension_length",
    "Omega.total_extension_length",
    "Omega.chord_length",
    "Omega.outer_segment_retained",
    "Omega.G_eq",
    "Omega.C_eq",
    "Omega.W_eq",
    "Omega.geometric_provenance",
    "Omega.outline_length",
    "Omega.reference_not_outline",
    "Omega.marked_coordinate_uniqueness",
    "Omega.heights_strictly_ordered",
    "Omega.sequential_extensions",
    "Omega.scalar_roundtrip",
    "Omega.scalar_bounds",
    "Omega.scalar_canonical",
    "Omega.rational_residual",
    "Omega.real_residual",
    "Omega.positive_residual_difference",
    "Omega.grid_finite_interface",
    "Omega.grid_trajectory",
    "Omega.repeated_rounding_counterexample",
    "Omega.ledger_interface",
    "Omega.external_factorization",
    "Omega.predecessor_inequalities",
    "Omega.point_reconstruction",
    "Omega.Ledger.euclidean_identity",
    "Omega.Ledger.remainder_bounds",
    "Omega.Ledger.one_step_inverse",
    "Omega.Ledger.roundtrip",
    "Omega.Ledger.encode_length",
    "Omega.Ledger.generated_admissible",
    "Omega.Ledger.canonical_division",
    "Omega.Ledger.admissible_roundtrip",
    "Omega.Ledger.encoding_injective",
    "Omega.Ledger.admissibility_iff",
    "Omega.Ledger.weighted_identity",
    "Omega.Ledger.encoded_weighted_identity",
    "Omega.Ledger.trajectory_reconstruction",
    "Omega.central_provenance_theorem",
    "Omega.mark_dot",
    "Omega.mark_radius",
    "Omega.mark_angle_cosine",
    "Omega.seed_angle",
    "Omega.triangle_area",
    "Omega.placed_distance",
    "Omega.placed_arc_derivative",
    "Omega.placed_G",
    "Omega.placed_C",
    "Omega.provenance_all_placements",
    "Omega.mark_scale",
    "Omega.circle_scale",
    "Omega.outline_scale",
    "Omega.placed_homothety",
    "Omega.readout_scale",
    "Omega.curve_reconstruction"
  ],
  "axiom_free_theorems": [
    "Omega.threshold_values",
    "Omega.inverse_identity",
    "Omega.finite_gap_certificate",
    "Omega.finite_certificate_inequality"
  ],
  "main_theorem": "Omega.central_provenance_theorem",
  "main_theorem_axioms": [
    "propext",
    "Classical.choice",
    "Quot.sound"
  ],
  "source_inventory": {
    "sha256sums_members": 28,
    "sha256sums_ok": true,
    "mismatches": [],
    "package_sha256sums": "/formal/SHA256SUMS"
  },
  "transcripts": {
    "current_build_log": {
      "path": "/formal/evidence/current/build.log",
      "bytes": 1960,
      "sha256": "ddc10580b76d0dd4ec8d9012bf91a78338fc43c003c4f7dbab2421f3c2b760b9",
      "note": "Fresh lake build on this archive, 2026-09-13. Distinct from the author transcript."
    },
    "current_axioms_log": {
      "path": "/formal/evidence/current/axioms.log",
      "bytes": 11804,
      "sha256": "82dae0644b5ce591c3e4af7bf9fdbfa6aeec11591560cb785ab0727a65d8eda1",
      "byte_identical_to_author": true
    },
    "author_build_log": {
      "path": "/formal/evidence/build.log",
      "bytes": 1791,
      "sha256": "b34aef23107d7eb168cf4b1b3642791ab8a49bc7b5848843481e3a01e3be1ae6",
      "note": "Prior author transcript (Replayed). Kept. Not generated on this archive."
    },
    "author_axioms_log": {
      "path": "/formal/evidence/axioms.log",
      "bytes": 11804,
      "sha256": "82dae0644b5ce591c3e4af7bf9fdbfa6aeec11591560cb785ab0727a65d8eda1"
    },
    "sorry_scan": {
      "path": "/formal/evidence/current/sorry_scan.txt",
      "bytes": 1610,
      "sha256": "58b5ac839405753ff6df9434f716cf12b9f4f9d61f59f8e7333fa2577523ed69"
    },
    "check_axioms_runtime": {
      "path": "/formal/evidence/current/check_axioms.runtime.txt",
      "bytes": 1226,
      "sha256": "e10e6ea8c8bdd6c78a82a5b734359126e96e8e60106425f418943b6ba25af884"
    }
  },
  "cubature_payloads": {
    "f10_to_f21": "not_supplied",
    "f23_f24_117_pairs": "not_supplied",
    "note": "This Lean run does not create cubature certificates. CLASS_I_CUBATURE/1.1 still lists 10\u201321 as not_publicly_fixed_in_this_release. The 117 exact a+b\u221a5 pairs, runnable verifier, and 109-residual ledger for f=23,24 remain unhosted."
  },
  "claims_not_made": [
    "peer review of Papers I\u2013VII",
    "joining theorem of Papers I\u2013VII",
    "independent third-party reproduction of Papers I\u2013VII",
    "uniqueness of the measurement rule among all measurements of an unmarked outline",
    "eighth source paper"
  ]
}