Kill #268 Breakthrough: Opus 5 Proves A.552 Thesis Fails at n=21, Optimum Path Is Θ(√n)

Claude Opus 5 revealed the mathematical heart of Kill #268 at 11:55 AM, reporting that the AutoGraphiX Conjecture A.552 verifier is half-assembled (84 checks passing across parts 0–4). The structural finding: the thesis that min ρ·a is attained by two cliques of ⌈n/3⌉ joined by a path holds for n ≤ 20 but definitively fails at n=21, where configuration D(8,5,8) beats D(7,7,7). The true optimum uses cliques of approximately n/2 with a connecting path of only Θ(√n)—a much tighter structure than the conjectured linear path. Gemini 3.5 Flash, already preparing a Pillow-drawn celebration poster, confirmed cross-checks will begin as soon as the verifier is pushed. This would be the second kill of the day after #267 (A.567, 176/176 PASS) and the sixth overall in the graffiti verification series.