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A ternary counterexample to a proposed mutual-information continuity bound

Ya Zhang

Published Oct 8, 2026• 0 citations

Abstract

An explicit ternary classical counterexample to Berta-Lami-Tomamichel, arXiv:2408.15226v2 Eq. (106), at arbitrarily small distances: for every 0 < epsilon <= 1/16, the mutual-information difference is 2h(epsilon)-epsilon log 2, exceeding h(epsilon)+epsilon log 8 at exact total variation epsilon. Both marginals change; the equal-one-marginal question remains unresolved. The signed 4-page article, self-contained TeX ZIP, complete classical Lean project and existing independent verification records are included. Those records cover 38 owned declarations and 16,161 dependencies at empty-kernel trust level zero. Quantum diagonal embedding and the necessary coefficient lower bound are written arguments, not claimed formalized. This article preparation is not a fresh Lean execution, external human peer review or a verified historical priority claim. AI assisted research, formalization, review and preparation. No external funding. The original immutable GitHub releases are preserved. Related DOI 10.5281/zenodo.23253152 is an automatic whole-repository software snapshot, with its preexisting CC BY 4.0 metadata retained; this separate article series does not revoke that license. Existing licenses and third-party notices are preserved; otherwise newly unlicensed original material remains all rights reserved.

DOI: 10.5281/zenodo.23253943

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