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Preprint in the OpenAI Math release

Mass and covering exponents for fixed-length honeycomb walks

OpenAI

Abstract

For uniform self-avoiding walks of every sufficiently large integer length on the honeycomb lattice, we prove diameter exponent 3/4 and simultaneous local-mass and covering exponent 4/3, with arbitrary positive exponent slack and arbitrary polynomial failure probability.

open until 1 Jan 2028

est. 50% chance this result is independently verified by the end of 2027.

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