Abstract
<title>Abstract</title> <p>A companion paper introduced the conservation–divergence spectrum, a sequence-level instrument for finding specificity-determining positions in protein families, and showed that it works. This paper asks when it can be trusted to work, and whether that can be known in advance. Across seven protein families spanning four recognition chemistries, the spectrum's four-corner geometry is universal (the two axes are negatively correlated in all seven, Spearman ρ from −0.07 to −0.98), but recovery of the known specificity code is not. We formalize a two-dimensional criterion — phylogenetic independence of the functional grouping (checkable a priori) and locality of the specificity code (checkable only after the fact) — and validate it prospectively in both directions: a pre-registered predicted hit (aminoacyl-tRNA synthetases) is confirmed blind (6/6 discrimination residues in the top 15% of anomaly, structural enrichment p = 7×10⁻⁹), and a pre-registered predicted miss (nuclear-receptor ligand-binding domains) returns a diagnostic split — recall fails (1/3 anchors recovered) while a structural-proximity test still passes (p = 9×10⁻⁸) — isolating grouping locality as an independent failure mode. A benchmark against three standard methods shows all of them hit and miss together on the two families tested — supporting, in this panel, that the applicability limit tracks the family rather than any one detector.</p>