{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:fulek-l3-linear-extremal-bound",
  "title": "Fulek's Question on the Extremal Function of $L_3$",
  "canonical_statement": "Fulek defined a weight-five three-row $0$-$1$ matrix $L_3$ and asked whether $\\mathrm{ex}(n, L_3) = O(n)$. It is: every $r \\times s$ matrix avoiding $L_3$ has at most $27r + 2s$ ones, so $6n - 8 \\le \\mathrm{ex}(n,L_3) \\le 29n$ for $n \\ge 5$. The same argument covers an infinite family of light three-row patterns, verifying a conjecture of Pettie and Tardos on linear light patterns for that family.",
  "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:fulek-l3-linear-extremal-bound:event",
      "problem_id": "vibemathed:fulek-l3-linear-extremal-bound",
      "type": "proved",
      "status": "resolved",
      "occurred_at": "2026-07-17T00:00:00.000Z",
      "title": "arXiv:2607.16463 - Linear extremal bounds for a family of forbidden 0-1 matrices",
      "summary": "the companion pattern Fulek proposed alongside L_3 is not covered by this method",
      "ai_contribution": "ai_assisted",
      "attempt_ids": [
        "vibemathed:fulek-l3-linear-extremal-bound:attempt"
      ],
      "method_family_ids": [
        "vibemathed:fulek-l3-linear-extremal-bound:method"
      ],
      "source_assertion_ids": [
        "vibemathed:fulek-l3-linear-extremal-bound:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:fulek-l3-linear-extremal-bound:attempt",
      "problem_id": "vibemathed:fulek-l3-linear-extremal-bound",
      "model": "Codex (GPT-5.6), Claude Code (Fable 5)",
      "provider": "OpenAI / Anthropic",
      "attempted_at": "2026-07-17T00:00:00.000Z",
      "human_collaborators": [
        "Jesse Geneson"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The acknowledgement says the two systems were used for proof exploration, proof criticism, exposition and revision, with no specific step attributed, so the lowest tier applies.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv:2607.16463 - Linear extremal bounds for a family of forbidden 0-1 matrices",
          "url": "https://arxiv.org/abs/2607.16463",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Fulek's Question on the Extremal Function of $L_3$",
          "url": "https://vibemathed.com/problem/fulek-l3-linear-extremal-bound",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:fulek-l3-linear-extremal-bound:verification",
      "problem_id": "vibemathed:fulek-l3-linear-extremal-bound",
      "solution_event_id": "vibemathed:fulek-l3-linear-extremal-bound:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "Single-author arXiv preprint; not yet peer-reviewed.",
      "sources": [
        {
          "label": "VibeMathed: Fulek's Question on the Extremal Function of $L_3$",
          "url": "https://vibemathed.com/problem/fulek-l3-linear-extremal-bound",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv:2607.16463 - Linear extremal bounds for a family of forbidden 0-1 matrices",
          "url": "https://arxiv.org/abs/2607.16463",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "arXiv:2607.16463 - Linear extremal bounds for a family of forbidden 0-1 matrices",
      "url": "https://arxiv.org/abs/2607.16463",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Fulek's Question on the Extremal Function of $L_3$",
      "url": "https://vibemathed.com/problem/fulek-l3-linear-extremal-bound",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:fulek-l3-linear-extremal-bound:signal:watch_only",
      "problem_id": "vibemathed:fulek-l3-linear-extremal-bound",
      "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"
}