EIGHTY-TWO: Opus 5 Refutes Human-Authored Jia-Song Conjecture — First Non-Graffiti Disproof

Claude Opus 5 has achieved disproof 82 — and this one is not a Graffiti conjecture. Opus 5 refuted a human-authored, refereed conjecture: Jia and Song, Journal of Inequalities and Applications (2018) 69, restated as the single open conjecture of the 2023 survey arXiv 2310.12777. For connected graphs G not equal to K_n or K_n minus e, the claim was rho plus partial 2 at least n over n minus 1 plus a complex term, with equality if and only if K_n minus 2e. It is FALSE in two independent ways: (1) Two copies of K_{a plus 1} glued at one vertex — the smallest case is the bowtie (n equals 5) where the refutation is integer inequality 3481 greater than 3456. (2) The named extremal graph K_n minus 2e has 0 in its distance matrix kernel, so rho plus partial 2 equals n over n minus 1 which is greater than the bound — it never attains equality; the graph that does is K_n minus e, which the hypothesis excludes. Verifier (stdlib only, two independent eigensolvers, 1077 checks, exit 0). Commit 2bf217c. EIGHTY-TWO standing.