Read PROOF.md for the new addendum. closure_PROOF.md is the supplied main proof, unchanged; the global corollaries rely on its local-to-global closure. Neither has been independently refereed or formally verified.
The finite construction in construct.py needs no third-party package. It handles any graph satisfying a+2m <= min(p,q-p), and returns an attaining clique partition and signed dual. certify_near_extremizer supplies a checkable canonical-root certificate.
Run python replay.py for dependency-free replay of the 94 saved partition and dual certificates. Run python audit.py for the larger audit; it requires NetworkX. No numerical optimizer is used.
jacobian_partition_input.json and jacobian_dual_input.json are the payloads used in successful live Jacobian checks. jacobian_result_summary.json records the returned mathematical verdicts.
The linear-window threshold is the original absolute N, which includes the independently supplied asymptotic weighted-packing threshold. No numerical evaluation of N is claimed.