{
  "audit": {
    "auditor": "Mathematical Frontier Network independent verifier",
    "completed_at": "2026-08-30T01:17:51Z",
    "verdict": "independently_reproduced_under_frozen_statement",
    "priority_verdict": "not_established",
    "peer_reviewed": false
  },
  "claim": {
    "problem": "Written on the Wall II Conjecture 200",
    "frozen_statement": "Every finite connected simple graph on more than one vertex whose largest induced-tree order equals the ceiling of one plus its average open-neighborhood independence number has a Hamiltonian path.",
    "counterexample": "K_{6,8} with two disjoint alternating six-cycles removed from its edge set",
    "graph6": "M??B]g{~FwT_u?{??",
    "result": "The 14-vertex graph is connected, has largest induced-tree order 7, has average open-neighborhood independence 36/7 and ceiling 7, and has no Hamiltonian path."
  },
  "source": {
    "repository": "https://github.com/OpenMikasa/wowii-conjecture-200",
    "commit": "48d1f5c8ca13ba0b6872b87b9c6a5fb193303568",
    "tree": "142868c6d615d29bd6478fbdf74a3c8d89c113b4",
    "tag": "v1.0.0",
    "author": "OpenMikasa",
    "license": "MIT",
    "primary_problem_url": "http://cms.uhd.edu/faculty/delavinae/research/wowII/all.html",
    "formal_snapshot": "https://github.com/google-deepmind/formal-conjectures/blob/8eda3cc8ebd281bf7efa1c435a19ca6b87c6f4ff/FormalConjectures/WrittenOnTheWallII/GraphConjecture200.lean"
  },
  "source_file_hashes": {
    "counterexample.graph6": "5747cf095550d9d2885f51e8b5c203f5f50ea63b66f5608f3187114c8e911a5d",
    "verification/verify_stdlib.py": "1cbddef373348c03126110e07082fcf50cb9eec4ebd0301dc51ece5760c81815",
    "verification/verify_networkx.py": "5455008949b2bbca06bfbf787d19781cd056a1011c9063a1ed266d74bc177acb",
    "verification/compare_certificates.py": "c9cf4d0dbc982139a883876813c2b76f634ff10a1700a1b417e5ca409001afe3",
    "lean/Counterexample200.lean": "0bd3afe6244557a7935bca84a0466fbb1329432d76681ca70c768a1265dd1244",
    "proof/SPEC.md": "1317f0094ebec60a16bd014d38440d9448ec55ebc8a85d3c29d51550fac126c1",
    "proof/PROOF.md": "88c2980a31d6fc38dd50fe14b931919dd7d819501f253a4c8147366b24b4fe8c",
    "provenance/PRIMARY_SOURCE.md": "d33b88e774bd549da4c39fdfc6a6ca57c1b1f939d96e5e45b23673522141d981"
  },
  "executions": [
    {
      "name": "upstream_standard_library_verifier",
      "implementation_relation": "candidate_supplied",
      "environment": "CPython 3.13.7 container sha256:9ba6d8cbebf0fb6546ae71f2a1c14f6ffd2fdab83af7fa5669734ef30ad48844",
      "isolation": "network disabled; read-only root and source; all capabilities dropped; no-new-privileges; CPU, memory, PID, and temporary-storage limits",
      "output_sha256": "3a8b3c0db021af2fac25bd52ae89ee2dc524c1b0e2b9ff667c6228e3c2feb821",
      "passed": true
    },
    {
      "name": "upstream_networkx_verifier",
      "implementation_relation": "candidate_supplied_independent_implementation",
      "environment": "CPython 3.13.7; NetworkX 3.2.1 wheel sha256:f18c69adc97877c42332c170849c96cefa91881c99a7cb3e95b7c659ebdc1ec2",
      "isolation": "dependencies downloaded before execution; verifier ran network-disabled with read-only root and source, all capabilities dropped, no-new-privileges, and resource limits",
      "output_sha256": "7b45da238057ad261b377e4d6a8c4c36116c1dd59eec87137298bd9af75ba692",
      "passed": true
    },
    {
      "name": "mfn_independent_exact_audit",
      "implementation_relation": "independent implementation from the published edge-deletion specification; no candidate verifier code imported",
      "verifier_url": "https://frontier.datastreamssolutions.com/artifacts/public-reproductions/wowii-200-independent-verifier.py",
      "verifier_sha256": "b4fcf8792fddda8ea25895e5f07876714e6e28dd5fa1b99d5d147b0445566f04",
      "environment": "CPython 3.13.7 standard library only; same pinned container",
      "isolation": "network disabled; read-only root and verifier; all capabilities dropped; no-new-privileges; CPU, memory, PID, and temporary-storage limits",
      "output_sha256": "7373dfc9cd0b1678e0ed0b8214e353c74e522e622921873fd227e03511122213",
      "passed": true,
      "canary": "Replacing the candidate by K_{6,8} produced induced-tree order 9 and ceiling 8, correctly failing the premise equality."
    }
  ],
  "agreed_exact_results": {
    "vertices": 14,
    "edges": 36,
    "degrees": [6, 6, 6, 6, 6, 6, 4, 4, 4, 6, 6, 4, 4, 4],
    "local_independence_sum": 72,
    "local_independence_average": "36/7",
    "ceil_one_plus_average": 7,
    "largest_induced_tree_order": 7,
    "maximum_induced_tree_witnesses": 78,
    "hamiltonian_path": false,
    "enumerated_nonempty_induced_vertex_subsets": 16383
  },
  "limitations": [
    "The original WOWII host timed out during this audit. Source fidelity relies on the pinned repository's hashed July 2026 capture record and the independent Formal Conjectures snapshot; a fresh maintainer or archive confirmation remains desirable.",
    "The negative prior-art search does not establish originality or first-discovery priority.",
    "The repository's Lean formalization was inspected but not compiled in this audit, so formal-proof evidence is not promoted.",
    "The result has not been peer reviewed or accepted by a journal."
  ]
}