Candidate Generation, Not Acceptance Strictness: Diagnosing Failure Modes in Self-Evolving Structure Search

Adaptive structure search can fail for three distinct reasons: the candidate generator may never propose the required structure, the selection rule's effective strictness may drift with problem size, or the evaluation signal may fail to distinguish valid from spurious structure. End-of-run performance alone cannot tell these failure modes apart. We examine all three in a birth-move search over the number of components in a high-dimensional feature-gated mixture, where ground truth is known. Across thirty independently generated datasets per cell, perturbation-based candidates achieve at most $23/30$ correct recoveries over a sweep of trigger and tolerance settings, whereas candidates initialized from relevance-informed subclusters achieve $30/30$. Candidate generation, rather than selection, is therefore the first bottleneck. We further identify three constants, introduced at different stages, that share the same scale mismatch; correcting their scale improves recovery from $0/30$ to $30/30$, $0/30$ to $15/30$, and $10/30$ to $30/30$. After these corrections, positive gains among known-spurious candidates become more frequent as the nominal ratio $p/n$ approaches one; a matched-ratio comparison suggests this relationship may not transfer unchanged across dimensions. Proposal-level diagnostics attribute the remaining failures to candidate generation rather than to acceptance strictness.