VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise 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.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement
fidelity, correctness, priority, or novelty.
What AI did
GPT-5.6 Sol, Claude Opus 5
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.
The author marks the 37-page draft explicitly as not yet peer reviewed and not formally verified.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.
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
Known method families
argument (source-reported)
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
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.