Verification artifact: A certified lower bound on the quantum-capacity threshold of the depolarizing channel

Verification artifact: A certified lower bound on the quantum-capacity threshold of the depolarizing channel Artus Krohn-Grimberghe (Percivio Ltd.), 2026. Companion deposit to the arXiv preprint of the same title (arXiv ID in this record's related identifiers). This deposit lets anyone verify, with no dependencies beyond a standard Python 3 installation, that two explicit 45-qubit rank-two states have one-shot coherent information of certified sign at four exact rational noise values of the qubit depolarizing channel D_p(rho) = (1-3p) rho + p (X rho X + Y rho Y + Z rho Z) — in particular, positive coherent information at p = 16239/250000 = 0.064956, hence quantum capacity Q > 0 for all p <= 0.064956. Contents • artifact/payloads/ — the two states as raw 1472-byte payloads (184 little-endian IEEE-754 binary64 values = 92 complex amplitudes, two purification rows over the 46-dimensional n = 45 Dicke basis), plus notebook/ copies in the torch-native format of the states published with arXiv:2605.09138 (the R payload is byte-identical to the tensor storage of that repository's published n_45_ens.pt).• artifact/certificates/ — four ~17.4 MB JSON certificates, one per (state, p) endpoint.• artifact/verifier/verify.py — single-file, standard-library-only verifier (no NumPy, no floats, no asserts). One command per endpoint: python3 artifact/verifier/verify.py artifact/certificates/<endpoint>.json <payload_sha256> <p_num>/<p_den> Each run recomputes the permutation-symmetric block decomposition of the channel output from the raw payload bytes in exact rational arithmetic, replays every eigenvalue- and entropy-enclosure step as cleared-denominator big-integer comparisons, and prints one ACCEPT line with the certified enclosure (exit 0) or one REJECT line (exit 1). About half an hour per endpoint on an Apple M4 Pro.• artifact/evaluator/ — the exact evaluator source (not needed for verification; included for inspection).• artifact/MANIFEST.txt — SHA-256 of every artifact file.• main.pdf — the paper (also on arXiv).• REPRODUCTION-NOTE.md — one-page quick start with the four (payload hash, p) pairs and a five-minute floating-point cross-check. The four endpoints R.c128 | 9a94606d28cb787e | 4057/62500 | positiveR.c128 | 9a94606d28cb787e | 16229/250000 | negativeA.c128 | 1df2e00c06b2614c | 16239/250000 | positiveA.c128 | 1df2e00c06b2614c | 203/3125 | negative Full hashes are in REPRODUCTION-NOTE.md and artifact/MANIFEST.txt. Provenance and license State A was found by AI-driven numerical optimization initialized from the public states of arXiv:2605.09138; verification is independent of the discovery pipeline (see the paper's contribution statement). License: CC BY 4.0. A browsable, manifest-verified copy of this artifact is maintained at https://github.com/percivio-ltd/certified-science (results/depolarizing-threshold-n45/).