The Benchmark Number Is Not the Deployment Number: Rank Collapse and Base-Rate Collapse, Measured Across Four Domains

A leaderboard reports one number per model. Two things that number silently discards are how many independent axes of skill it collapses into a single scalar, and what population its accuracy was measured on versus where the model is used. This paper measures both, on public data, with every figure independently re-verified through a second code path before inclusion. Rank collapse: on ProteinGym, the standard variant-effect-prediction benchmark, a null-gated decomposition of the 217x97 assay x model matrix shows the single ranking hides at least three specialization axes (singular values 7.87/6.60/5.88 against a permutation null of 4.46/4.32/4.22). The sharpest axis, structure-vs-sequence models on protein stability, is powered across all 64 Tsuboyama stability assays (64/64, median gap +0.346) and traced to a chemistry x exposure mechanism: structure-aware models win on surface aromatic substitutions (p=8e-8) and lose on surface charge substitutions, converging in the buried core, after two competing hypotheses (buried-core packing; general hydrophobicity) were tested and killed. The same null-gated test applied to three unrelated benchmarks (MTEB embeddings, SWE-bench code-agent evaluation, LMArena chat preference) finds a hidden axis in every one that resolves at all. Base-rate collapse: ten clinical variant-pathogenicity predictors report AUCs of 0.81-0.98 on a benchmark that is 65% pathogenic; reprojected by Bayes to the 0.1-1% prevalence a real screening population presents, the best predictor's flag precision falls from 93% to 12% (1.3% at 0.1%). The identical arithmetic, applied to AI-generated-text detection on GPT-4 output, takes the strongest detector's benchmark precision of 79% to 16% at a 5% real-world machine-text rate -- about five false accusations per genuine catch -- and shows the classifier lineage behind many commercial "AI checkers" scores AUC=0.545 on GPT-4, indistinguishable from a coin flip. Genomics and generated text share the identical failure shape because the underlying arithmetic is the same theorem; only the base rate changes. The paper releases two reusable, self-tested primitives -- a rank-dimensionality auditor and a Bayes recalibrator -- and the full analysis pipeline.