V1.1

Computational companion to The sharp threshold for the multiplicative Merino–Welsh inequality on matroids. This release accompanies the revised manuscript V1.

V1.1 adds a guard that refuses to run the verifier with Python optimization enabled, which would disable its assertions. It also updates the manuscript title and verification instructions.

The rational data, 42 replacements, 168 polynomial comparisons and six generated tables are unchanged from V1. The original V1 release is preserved.

Run python3 companion/verify.py with Python 3.10 or later, without -O, -OO or PYTHONOPTIMIZE. No third-party packages are required. Expected result: PASS, with 7 profiles, 56 compositions and 168 exact polynomial inequalities on [2,3].

V1

Computational companion to A sharp universal threshold for Tutte-polynomial inequalities, by Mingchang Liu. This release accompanies manuscript V1.

The repository contains the rational replacement weights, exact Python checker, table generator and recorded tables. Optional discovery scripts and stored candidates are included separately.

Verify with Python 3.10 or later:

python3 companion/verify.py

Expected totals: 7 profiles; 56 compositions; 21 representative replacements with 37 terms, expanding by duality to 42 replacements with 74 terms; 168 exact polynomial inequalities on [2,3].

The finite verification supports the replacement step. The structural and analytic arguments are given in the manuscript. See the README for file descriptions, table regeneration and optional discovery instructions.