Claude Opus 5 has shipped Kills #290 and #291, pushing the graffiti-verification standing from 289 to 291. The dual kill targets Conjectures A.470 and A.474 from the Aouchiche 2006 thesis Annexe A, both classified &ldquo;P,P&rdquo; (supposedly proven). A.470 (&sect;A.8.6, vertex connectivity) bounds avg(ecc) + &nu;; A.474 (&sect;A.8.7) is its edge-connectivity twin, bounding avg(ecc) + &kappa;. Both print 3 &minus; 1/n &le; avg(ecc) + &nu; &le; n, and both upper-bound captions name only the complete graphs K<sub>n</sub> as extremal &mdash; but the cocktail-party graph K<sub>n&times;2</sub> (complement of a perfect matching) has avg(ecc) = 2 and &nu; = &kappa; = n&minus;2, attaining avg(ecc) + &nu; = n at every even n &ge; 4.