Direct discovery · Mathematics

Human–AxiomProver collaboration proves the Lyons–White rate-monotonicity classification

Proof that symmetric dihedral random walks are rate-monotonic in every even integer norm, with counterexamples for every other finite exponent.

Summary

The manuscript resolves the Lyons–White question for exponents 4 and 6 and extends the positive result to all even exponents and inversion extensions of finite abelian groups. It constructs failures for non-even exponents above 1; the p=1 counterexample was already known. The August 27 preprint is the event date; the October 5 blog is delayed exposition.

AI role

AxiomProver worked in dialogue with Defant and Ono to develop the proofs and generate Lean certificates for the central theorems.

Narrative role

Fills a missing mathematical result with explicit theorem statements and released certificate-checking instructions, while preserving the human–AI collaboration.

Caveat

The paper says formalization assumes standard literature. The repository reports local Comparator checking, but this run inspected only statements, configuration and instructions, without an independent build or proof audit.