What a local encoder cannot see: spectral fibres of the human proteome and the representation of perturbagens

UniPert-G2CP (Li et al., Cell 189, 2026) represents genetic perturbagens by their protein sequences and chemical perturbagens by ECFP4 fingerprints, and shows that its protein encoder outperforms composition-type encoders such as pseudo amino acid composition (PseAAC). We examine this comparison through algebraic genomics, the combinatorics of sequences with prescribed local content. An encoder is local of order k if it depends on a sequence only through its multiset of k-mers. Composition, k-mer composition, PseAAC with lag λ ≤ k−1 and every mean-pooled convolutional encoder of window k are local; so is ECFP, in the molecular-graph sense. A local encoder is constant on the spectral fibre of a sequence, the set of sequences with the same k-mer multiset. The size of the fibre is an Eulerian-trail count, which we compute exactly by the BEST theorem after contracting forced arcs, for all 20,431 reviewed human proteins. Separation is not resolution. No two distinct human proteins share a k-mer spectrum for any k ≥ 2, so every local encoder of order at least 2 separates the reference proteome. Yet the median protein shares its 3-mer spectrum with 2^239 other sequences and its 4-mer spectrum with 2^19. The spectral resolution κ, the least k beyond which the spectrum determines the sequence, has median 5 and exceeds 10 for 854 proteins. The unresolved order lives in duplication-driven families. The largest κ occur in the hominoid-specific segmental-duplication families NBPF (median κ = 46, up to 951), GOLGA6, NPIP and POTE, and in keratin-associated proteins, collagens and mucins. KRAB zinc-finger proteins are 3% of the proteome but 41% of the proteins with κ > 10. Explicit collisions. For 12 human proteins we construct a different sequence, altered at up to 15% of its positions, with the same 25-spectrum; it receives the identical 68-dimensional PseAAC vector (λ = 24, the setting of the UniPert benchmark) and the identical output of a window-25 convolutional encoder. On the DNA side, a strand-agnostic local encoder is constant on the set of double-stranded reconstructions, which for bacteriophage φX174 at k = 10 has 31,925,753,246,212 elements; computing its size is #P-hard in general. The record contains the paper, the code, the UniProt snapshot used, the per-protein results and the figures. All computations are exact except where stated, and the verification script reproduces every exact number in the paper in about five minutes on 16 cores.