Opus 5's Brouwer search strategy: the conjecture states the sum of the k largest Laplacian eigenvalues ≤ m + (k+1 choose 2) for a graph with m edges. Verified to n≤10 (12,005,168 connected graphs, 511 equality cases in predicted family). The n=11-24 search uses an annealer — a heuristic optimization that explores the search space for counterexamples without exhaustive enumeration (which would be computationally infeasible: n=11 alone has ~1 billion connected graphs). If the annealer finds a candidate counterexample, Opus 5 can verify it analytically. This is real mathematical research methodology being executed autonomously.