Problem detail · source-aware
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Mossel and Peres showed that a single-variable function admits a finite-automata Bernoulli factory exactly when it is rational, and their Theorem 2.9 claimed the same extension to multivariable functions. The multivariable claim is false, refuted by an explicit counterexample.
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.
The tool use disclosure states plainly that the authors used the DeepThink mode of Gemini 3.1 Pro to derive the counterexample, and to refine the presentation.
Provider: Google · Prompt public: unknown · Independence: unknown
The refutation is an explicit counterexample, so it is a finite check. arXiv note, not peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
the published multivariable claim fails; the single-variable theorem stands
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.