Mossel-Peres Multivariable Bernoulli Factory Claim
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.
- Result
- Disproved(see note)
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Probability
- Posed by
- Elchanan Mossel, Yuval Peres
- Year posed
- 2005
- Years open
- 21y
- Solved
- 2026-06-28
- Model
- Gemini 3.1 Pro (DeepThink)
- Vendor
- Collaborators
- Renato Paes Leme, Jon Schneider
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
the published multivariable claim fails; the single-variable theorem stands
What the AI did
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.
Verification
The refutation is an explicit counterexample, so it is a finite check. arXiv note, not peer-reviewed.
Source
arXiv:2606.29595 - Note on Finite-Automata Bernoulli Factories for Rational Functions