Mossel-Peres Multivariable Bernoulli Factory Claim
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Statement
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.
Context
the published multivariable claim fails; the single-variable theorem stands
A named theorem in the Bernoulli factory literature that had been cited as settled for twenty years.
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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.
the published multivariable claim fails; the single-variable theorem stands
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