{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:factorial-conjecture-two-variables",
  "title": "Two-Variable Factorial Conjecture",
  "canonical_statement": "Let $\\mathcal{L}(x^{a}y^{b})=a!\\,b!$ on $\\mathbb{C}[x,y]$. The Factorial Conjecture asks whether $\\mathcal{L}(f^{m})=0$ for every $m\\geq 1$ forces $f=0$. The homogeneous two-variable case was settled by Liu and Sun; the inhomogeneous problem does not reduce to it, because radial integration couples the homogeneous layers through Gamma factors. A claimed proof settles the full two-variable case affirmatively.",
  "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:factorial-conjecture-two-variables:event",
      "problem_id": "vibemathed:factorial-conjecture-two-variables",
      "type": "proved",
      "status": "candidate",
      "occurred_at": "2026-08-01T00:00:00.000Z",
      "title": "Factorial conjecture manuscript (GitHub)",
      "summary": "Claimed in a self-published research draft; a standalone by-product is the transcendence of the integral of exp(q) between distinct algebraic endpoints for nonconstant algebraic q",
      "ai_contribution": "ai_co_developed",
      "attempt_ids": [
        "vibemathed:factorial-conjecture-two-variables:attempt"
      ],
      "method_family_ids": [
        "vibemathed:factorial-conjecture-two-variables:method"
      ],
      "source_assertion_ids": [
        "vibemathed:factorial-conjecture-two-variables:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:factorial-conjecture-two-variables:attempt",
      "problem_id": "vibemathed:factorial-conjecture-two-variables",
      "model": "GPT-5.6 Sol, Claude Opus 5",
      "provider": "OpenAI, Anthropic",
      "attempted_at": "2026-08-01T00:00:00.000Z",
      "human_collaborators": [
        "Christopher D. Long"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "Per the author's disclosure, the manuscript was developed through interactive work with ChatGPT 5.6 Sol, which assisted in proof discovery, organization, symbolic checking, reference verification, adversarial auditing and drafting; Claude Opus 5 contributed the semisimple-projector strategy, the reduction to phase-polynomial moments, and further adversarial audits. The AI systems are not authors and the human author takes full responsibility.",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "Liu-Sun, homogeneous two-variable case",
          "url": "https://doi.org/10.1017/S0004972719000546",
          "kind": "paper",
          "license": null
        }
      ],
      "sources": [
        {
          "label": "Factorial conjecture manuscript (GitHub)",
          "url": "https://github.com/octonion/mathematics/tree/master/fc",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Two-Variable Factorial Conjecture",
          "url": "https://vibemathed.com/problem/factorial-conjecture-two-variables",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:factorial-conjecture-two-variables:verification",
      "problem_id": "vibemathed:factorial-conjecture-two-variables",
      "solution_event_id": "vibemathed:factorial-conjecture-two-variables:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "The author marks the 37-page draft explicitly as not yet peer reviewed and not formally verified. Published as a PDF and LaTeX source in a personal GitHub repository, with no independent check on record.",
      "sources": [
        {
          "label": "VibeMathed: Two-Variable Factorial Conjecture",
          "url": "https://vibemathed.com/problem/factorial-conjecture-two-variables",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "Factorial conjecture manuscript (GitHub)",
          "url": "https://github.com/octonion/mathematics/tree/master/fc",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "Factorial conjecture manuscript (GitHub)",
      "url": "https://github.com/octonion/mathematics/tree/master/fc",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Two-Variable Factorial Conjecture",
      "url": "https://vibemathed.com/problem/factorial-conjecture-two-variables",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:factorial-conjecture-two-variables:signal:verify_now",
      "problem_id": "vibemathed:factorial-conjecture-two-variables",
      "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"
}