Verification code and certificates for The Borodin–Kostochka inequality from degree 750

Verification programs, fixed inputs and numerical certificates accompanying Lizhong Chen’s manuscript, “The Borodin–Kostochka inequality from degree 750”.

Version 3.0.0 supports the degree-750 finite bounds and supersedes the degree-1000 numerical package in earlier versions of this record. The manuscript identifies this supplement as BK750-paper-v009-supplement-20261102.

The selected finite domain contains 772 neighbourhood probability comparisons and 187 clique comparisons: 98 selected reference comparisons, 14 low-deficit endpoint comparisons, and 75 high-deficit comparisons formed from 150 branch averages. The broader 262-comparison reference check is also retained.

The ZIP contains Python and C++ verification programs, fixed inputs, complete probability curves, finite comparison outputs, reproduction instructions and SHA-256 manifests. Begin with DEPOSIT.md and MANIFEST.json, then verification/README.md, verification/PROFILE_MAP.json, verification/data-index.json and verification/REPRODUCE.md. The numerical payload is unchanged from the named v009 supplement. The companion manuscript is distributed separately.

Upload preparation checks file identities and the supplied manifests; it is not a fresh rerun of all numerical jobs or a new independent mathematical audit. The computations establish finite numerical bounds. The graph-theoretic reductions, conditioning and dependency arguments, and the passage to every maximum degree at least 750 are given in the companion paper.

Python 3.9 or later is required; the producer replay and unified-high calculation also require a C++17 compiler. Reproduction instructions specify strict rounding flags, resource limits and expected outputs.