{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:bellman-lost-in-forest-golden-gnomon",
  "title": "Bellman's Lost-in-a-Forest Problem for the Golden Gnomon",
  "canonical_statement": "What is the shortest curve guaranteed to reach the boundary of the golden gnomon - the isosceles triangle with equal sides $1$ and apex angle $108^\\circ$ - from an unknown starting position and heading? The optimum is a symmetric seven-piece path of segments, circular shoulders and tangents, of exactly determined transcendental length $C = 1.282676\\ldots$ - the first proved exact optimum for an isosceles triangle with base angle below $45^\\circ$.",
  "plain_summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "resolved",
  "solution_events": [
    {
      "id": "vibemathed:bellman-lost-in-forest-golden-gnomon:event",
      "problem_id": "vibemathed:bellman-lost-in-forest-golden-gnomon",
      "type": "proved",
      "status": "resolved",
      "occurred_at": "2026-07-27T00:00:00.000Z",
      "title": "arXiv:2607.24483 - The exact solution of Bellman's lost-in-a-forest problem for the golden gnomon",
      "summary": "Bellman's problem for general regions remains open",
      "ai_contribution": "ai_discovered",
      "attempt_ids": [
        "vibemathed:bellman-lost-in-forest-golden-gnomon:attempt"
      ],
      "method_family_ids": [
        "vibemathed:bellman-lost-in-forest-golden-gnomon:method"
      ],
      "source_assertion_ids": [
        "vibemathed:bellman-lost-in-forest-golden-gnomon:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:bellman-lost-in-forest-golden-gnomon:attempt",
      "problem_id": "vibemathed:bellman-lost-in-forest-golden-gnomon",
      "model": "Claude Fable 5, GPT-5.6 Sol, Claude Opus 5",
      "provider": "Anthropic / OpenAI",
      "attempted_at": "2026-07-27T00:00:00.000Z",
      "human_collaborators": [
        "Alexander Temerev",
        "Alessio Doria"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The models were used throughout: to search out the extremal curve, to draft the arguments, and to write the accompanying Lean 4 development. The paper states precisely which steps are machine-checked, and notes those checks hold regardless of how the statements were found.",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "Lean verification development",
          "url": "https://github.com/atemerev/gnomon",
          "kind": "lean-proof",
          "license": null
        }
      ],
      "sources": [
        {
          "label": "arXiv:2607.24483 - The exact solution of Bellman's lost-in-a-forest problem for the golden gnomon",
          "url": "https://arxiv.org/abs/2607.24483",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Bellman's Lost-in-a-Forest Problem for the Golden Gnomon",
          "url": "https://vibemathed.com/problem/bellman-lost-in-forest-golden-gnomon",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:bellman-lost-in-forest-golden-gnomon:verification",
      "problem_id": "vibemathed:bellman-lost-in-forest-golden-gnomon",
      "solution_event_id": "vibemathed:bellman-lost-in-forest-golden-gnomon:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "Lean 4 verifies the two finite algebraic certificate families and the discrete ledger identities, but not the full argument end to end; the paper's appendix states exactly which steps are machine-checked. arXiv preprint, not yet peer-reviewed.",
      "sources": [
        {
          "label": "VibeMathed: Bellman's Lost-in-a-Forest Problem for the Golden Gnomon",
          "url": "https://vibemathed.com/problem/bellman-lost-in-forest-golden-gnomon",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv:2607.24483 - The exact solution of Bellman's lost-in-a-forest problem for the golden gnomon",
          "url": "https://arxiv.org/abs/2607.24483",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "arXiv:2607.24483 - The exact solution of Bellman's lost-in-a-forest problem for the golden gnomon",
      "url": "https://arxiv.org/abs/2607.24483",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Bellman's Lost-in-a-Forest Problem for the Golden Gnomon",
      "url": "https://vibemathed.com/problem/bellman-lost-in-forest-golden-gnomon",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:bellman-lost-in-forest-golden-gnomon:signal:watch_only",
      "problem_id": "vibemathed:bellman-lost-in-forest-golden-gnomon",
      "kind": "watch_only",
      "reason": "Current public evidence does not meet the default replay threshold.",
      "generated_at": "2026-09-13T16:28:40.178Z"
    }
  ],
  "uncertainties": [
    "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"
}