Machinery Space is the Right Coordinate for Biological Coverage: Diagnosing the Compositional Ceiling in Genomic Foundation

Foundation models of protein and genome sequence plateau on function and phenotype prediction: added data yields vanishing returns and simple linear or evolutionary baselines match billion-parameter encoders. A natural diagnosis, advanced by recent work on this exact setting, is that generalization is coverage-limited: held-out lineages fall where no labelled training neighbour exists. We agree coverage binds, but show the field has been measuring coverage in the wrong coordinate system. We ask, for held-out bacterial families, which notion of “closeness to the training set” actually predicts whether a model generalizes: closeness in the foundation model’s own embedding space, in taxonomy, or in machinery space, the space of metabolic pathway content (KEGG modules). On 15,002 genomes we find a sharp trait-class×coordinate interaction. For machinery-localized traits (pathogenicity, biosafety level), machinery-space proximity predicts per-genome generalization at AUROC ≈ 0.652, whereas embedding- space (≈ 0.531) and taxonomy (≈ 0.548) proximity are near chance; for compositional traits no coordinate is strongly predictive. A pre-registered control rules out that machinery space is merely a taxonomy proxy: machinery distance is nearly orthogonal to taxonomy (η2=0.042) and taxonomy coverage is itself near chance. The coordinate is not an artifact of a hand-built ontology: a learned genome-context foundation model (Bacformer) recovers it (coverage-AUROC 0.68 on machinery traits) while mean-pooled ESM-2 is near chance (0.52), localizing the failure to gene-content-destroying pooling rather than to foundation models as such. We further show, via multi-seed learning curves, that (i) on compositional traits every diversity operator saturates at the same plateau, reproducing the published single-cell diversity null in genomes, and (ii) maximizing taxonomic diversity by dereplication specifically harms machinery traits (−0.033 AUROC) while leaving compositional traits untouched (+0.004). The compositional ceiling is thus a statement about which axis one samples. The corrective is not more taxa but coverage measured in machinery space.