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Finite uniform Bernoulli shifts with unequal base entropy

Peter Burton

Palomar Registrypalomar/PALOMAR-2026-10-27-000030Oct 27, 2026math.DSscore 0

There exist a countable group G and a nontrivial finite alphabet A such that the ordinary left Bernoulli shifts on A and A times A, equipped with their uniform product probability measures, are equivariantly measure-preservingly isomorphic on invariant conull measurable sets. The inverse is measurable. The finite alphabets have different cardinalities and therefore different uniform base Shannon entropies. The algebraic existence input is supplied by the pinned OpenAI proofs. This formalization does not certify all-base collapse, finitary continuity, the integer coding inputs, or the…

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