{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:graffiti-residue-common-divisor",
  "title": "Graffiti's Residue Problem for Common-Divisor Graphs",
  "canonical_statement": "A problem from Fajtlowicz's Graffiti program, studied by Erdős and Staton, on the Havel-Hakimi residue of common-divisor graphs. The paper resolves the problem and extends it, determining the residue's first-order scale and its nontrivial constant from the degree sequence.",
  "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:graffiti-residue-common-divisor:event",
      "problem_id": "vibemathed:graffiti-residue-common-divisor",
      "type": "proved",
      "status": "resolved",
      "occurred_at": "2026-08-03T00:00:00.000Z",
      "title": "arXiv",
      "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.",
      "ai_contribution": "ai_assisted",
      "attempt_ids": [
        "vibemathed:graffiti-residue-common-divisor:attempt"
      ],
      "method_family_ids": [
        "vibemathed:graffiti-residue-common-divisor:method"
      ],
      "source_assertion_ids": [
        "vibemathed:graffiti-residue-common-divisor:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:graffiti-residue-common-divisor:attempt",
      "problem_id": "vibemathed:graffiti-residue-common-divisor",
      "model": "Theo-Conjecture, OpenAI Codex",
      "provider": null,
      "attempted_at": "2026-08-03T00:00:00.000Z",
      "human_collaborators": [
        "Randy Davila"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The study deliberately retained Graffiti's conjecture-example-proof workflow through the TxGraffiti / Theo-Conjecture line: the systems supported registry construction, conjecture generation, exact stress testing, proof search and proof auditing, with the surviving conjecture selected by discrepancy tracking against a quarter-million-graph registry.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2608.04040",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Graffiti's Residue Problem for Common-Divisor Graphs",
          "url": "https://vibemathed.com/problem/graffiti-residue-common-divisor",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:graffiti-residue-common-divisor:verification",
      "problem_id": "vibemathed:graffiti-residue-common-divisor",
      "solution_event_id": "vibemathed:graffiti-residue-common-divisor:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": null,
      "sources": [
        {
          "label": "VibeMathed: Graffiti's Residue Problem for Common-Divisor Graphs",
          "url": "https://vibemathed.com/problem/graffiti-residue-common-divisor",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2608.04040",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "arXiv",
      "url": "https://arxiv.org/abs/2608.04040",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Graffiti's Residue Problem for Common-Divisor Graphs",
      "url": "https://vibemathed.com/problem/graffiti-residue-common-divisor",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:graffiti-residue-common-divisor:signal:watch_only",
      "problem_id": "vibemathed:graffiti-residue-common-divisor",
      "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"
}