Verification artifact: Exact certification of a positive-order Rényi additivity violation for an explicit channel pair

Verification artifact: Exact certification of a positive-order Rényi additivity violation for an explicit channel pair This record contains the complete verification artifact for the paper Exact certification of a positive-order Rényi additivity violation for an explicit channel pair (Artus Krohn-Grimberghe, Percivio Ltd., 2026). The paper proves that the explicit channel pair constructed by Cubitt, Harrow, Leung, Montanaro, and Winter (Commun. Math. Phys. 284, 281–290 (2008); arXiv:0712.3628) violates additivity of the minimum output Rényi entropy for every real order 0 < p ≤ 1/22, under the inverse-input-marginal trace-preserving normalization fixed in the paper. The proof is certificate-based: small rational witness matrices establish that every output eigenvalue of either channel lies between 301/100000 and 2/3, one explicit entangled input has an exact rational joint output spectrum, and two elementary interval arguments reduce the violation on the whole interval to finitely many comparisons of integers. Contents • artifact/certificates/ — the five certificate files: floor witnesses, cap witnesses, the exact joint output matrix with its spectrum, and the two interval certificates (all small JSON files of rational numbers).• artifact/programs/ — the two independently written verification programs described in Section 7 of the paper. Both use only the Python standard library (Python 3.10+); together they re-check every claim in a few seconds on a laptop.• artifact/MANIFEST.txt — SHA-256 of every certificate and program file, matching the hashes printed in Appendix B of the paper.• artifact/README.md — one command per claim, with expected output.• main.pdf — the paper. Provenance The witness matrices were found by an AI-assisted numerical search; the search plays no role in the proof. All mathematical claims rest on the certificate files and the two verification programs in this record. License: Creative Commons Attribution 4.0 International (CC BY 4.0). A browsable, manifest-verified copy of this artifact is maintained at https://github.com/percivio-ltd/certified-science (results/renyi-additivity-chlmw/).