Rank-Unimodality Below Alternating Two-Valued Compositions: A Computer-Assisted Proof for the Infinite Family (a,b)^m

This restricted mathematical preprint proves rank-unimodality for principal ideals below alternating two-valued compositions (a,b)^m, for all integers a>b>=1 and m>=1. A duplicate-free rank-polynomial recurrence, a computer-assisted all-parameter certificate for the log-concavity of Q², and a self-contained middle-rank argument yield the result. The public deposit includes a paper PDF and a reproducibility ZIP with symbolic verifiers, logs, and SHA256 manifests. The mathematical argument underwent independent AI-assisted audit (MODEL, PROOF, COMPUTATION: PASS in the supplied Claude v0.4 report), but has not been human peer-reviewed. Novelty remains INCONCLUSIVE: the full text of the 2026 Chen and Zhang preprints was not available for comparison. No claim is made to prove the conjecture for arbitrary compositions or to establish priority over uninspected work. All rights reserved.