{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:wowii-graph-conjecture-144",
  "title": "Written on the Wall II, Graph Conjecture 144",
  "canonical_statement": "For every finite connected simple graph $G$, is the order of the largest induced tree at least $\\mathrm{girth}(G) - 1 + \\mathrm{ecc}(G, \\mathrm{center}(G))$, where the last term is the eccentricity of the centre set? Answered affirmatively, with a Lean proof.",
  "plain_summary": "VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "candidate",
  "solution_events": [
    {
      "id": "vibemathed:wowii-graph-conjecture-144:event",
      "problem_id": "vibemathed:wowii-graph-conjecture-144",
      "type": "proved",
      "status": "candidate",
      "occurred_at": "2026-08-03T00:00:00.000Z",
      "title": "Formal Conjectures PR #4696",
      "summary": "The Formal Conjectures pull request flipping this from open to solved is still open rather than merged, so the canonical repository has not yet accepted it.",
      "ai_contribution": "ai_assisted",
      "attempt_ids": [
        "vibemathed:wowii-graph-conjecture-144:attempt"
      ],
      "method_family_ids": [
        "vibemathed:wowii-graph-conjecture-144:method"
      ],
      "source_assertion_ids": [
        "vibemathed:wowii-graph-conjecture-144:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:wowii-graph-conjecture-144:attempt",
      "problem_id": "vibemathed:wowii-graph-conjecture-144",
      "model": "ChatGPT + Codex",
      "provider": "OpenAI",
      "attempted_at": "2026-08-03T00:00:00.000Z",
      "human_collaborators": [
        "Chris Maki"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The author states that ChatGPT and Codex assisted with computational exploration, proof analysis, Lean API discovery and proof engineering, and that he reviewed the work thoroughly and takes full responsibility for it.",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "Lean proof at the pinned commit",
          "url": "https://github.com/beowulf127/wowii144-lean/blob/046429d509b28c90ee2ec38ae27c1ad377c6a5fc/WOWII144/Main.lean",
          "kind": "lean-proof",
          "license": null
        },
        {
          "label": "Upstream statement (Formal Conjectures)",
          "url": "https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/WrittenOnTheWallII/GraphConjecture144.lean",
          "kind": "lean-statement",
          "license": null
        }
      ],
      "sources": [
        {
          "label": "Formal Conjectures PR #4696",
          "url": "https://github.com/google-deepmind/formal-conjectures/pull/4696",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Written on the Wall II, Graph Conjecture 144",
          "url": "https://vibemathed.com/problem/wowii-graph-conjecture-144",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:wowii-graph-conjecture-144:verification",
      "problem_id": "vibemathed:wowii-graph-conjecture-144",
      "solution_event_id": "vibemathed:wowii-graph-conjecture-144:event",
      "level": "lean_verified_statement_audited",
      "mathematical_correctness": "supported",
      "statement_fidelity": "audited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "Checked here on 2026-08-03, statically rather than by rebuilding. The theorem statement was diffed against the upstream Formal Conjectures statement and is identical apart from a hypothesis binder name, which is the fidelity check that matters. All 16 Lean files at the pinned commit (5,873 lines) contain no sorry, no admit, no axiom declarations and no native_decide. The author reports lake build --wfail and axiom checks passing; that build was NOT reproduced here.",
      "sources": [
        {
          "label": "VibeMathed: Written on the Wall II, Graph Conjecture 144",
          "url": "https://vibemathed.com/problem/wowii-graph-conjecture-144",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "Formal Conjectures PR #4696",
          "url": "https://github.com/google-deepmind/formal-conjectures/pull/4696",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "Formal Conjectures PR #4696",
      "url": "https://github.com/google-deepmind/formal-conjectures/pull/4696",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Written on the Wall II, Graph Conjecture 144",
      "url": "https://vibemathed.com/problem/wowii-graph-conjecture-144",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:wowii-graph-conjecture-144:signal:verify_now",
      "problem_id": "vibemathed:wowii-graph-conjecture-144",
      "kind": "verify_now",
      "reason": "The source labels this result as a candidate; verification should precede reuse.",
      "generated_at": "2026-09-13T16:28:40.178Z"
    }
  ],
  "uncertainties": [
    "The source status is candidate and must not be represented as solved.",
    "VibeMath has not independently verified the mathematical claim.",
    "AI-attempt independence and training-data exposure are unknown unless explicitly documented.",
    "VibeMath has not independently audited the mathematical statement, proof, or novelty claim."
  ],
  "generated_at": "2026-09-13T16:28:40.178Z"
}