Published August 29, 2026 | Version 0.1.0-candidate

A Three-Layer Obstruction for Uniformly Popular Differences

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Description

Anonymous unrefereed candidate. This release gives an explicit counterexample in Z/21Z to the strict one-third question in AIM Problem 1.18, an elementary three-layer family, and odd-cyclic counterexamples for every fixed threshold below 2/5.

Producer-side normal and optimized Python replay, a separate JavaScript implementation, four semantic mutation controls, fresh-extraction checks, and internal editorial review pass. Novelty remains only partially assessed. Independent reproduction, formal verification, external specialist review, editorial peer review, and priority are not established. No claim is made that 2/5 is sufficient or sharp or that the C21 witness is minimal.

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