Biologically reachable spectral fibres: repeat shuffling, copy ambiguity and the scarcity of cryptic pathogenic missense variants in ClinVar

A protein sequence encoder that depends only on k-mer statistics is blind to the rearrangements that preserve them: the spectral fibre of the protein. Most members of a fibre are not proteins that evolution or disease could produce. We ask which part of the fibre is biologically reachable, and whether human pathogenic variation falls into it. Members of a fibre share length and amino acid composition, so no single substitution, insertion or deletion can stay in it. That includes repeat expansion and contraction by non-allelic homologous recombination. What can stay is a reciprocal exchange of residues between repeat copies whose (2k−1)-residue contexts agree except at the exchanged site. A related ambiguity affects single variants. When the same substitution can occur in either of two repeat copies with identical contexts, the two variant proteins have the same k-spectrum, and no local encoder of order k can tell which copy is mutated (copy-ambiguous twins). Across the 20,431 reviewed human proteins, copy ambiguity at k = 10 concerns 37% of positions in NBPF, GOLGA6, NPIP and POTE proteins and 23% in mucins, against 0.31% outside the repeat families. We intersected this with 2.23 million ClinVar missense variants (release of 24 September 2026) mapped to UniProt. Pathogenic and likely pathogenic variants rarely have a copy-ambiguous twin: 107 of 62,786 at k = 5, 4 at k = 10, and none of 60,519 at k = 25. Against a gene-matched expectation they are depleted (0.79, 0.22 and 0 of the expected counts; p = 0.006, 7·10⁻⁵ and 0.04), more strongly than benign variants (0.91, 0.87, 0.73). All variant classes are depleted at long contexts, consistent with the limits of short-read mapping in identical repeats. The pathogenic variants with twins form 215 (variant, twin) sequence pairs. Local encoders give identical outputs on every one of them, while separating each variant from the wild type. One discordant case is FOXP2 p.Gln168His (likely pathogenic), whose twin p.Gln165His in the same polyglutamine tract is classified likely benign; both assertions have a low review status. We find no evidence of a large class of cryptic pathogenic variants hidden in spectral fibres. The regions where local encoders are order-blind are also the regions that clinical variant databases cover least. This record contains the paper (PDF and LaTeX source), the code, the ClinVar missense extract mapped to UniProt, the UniProt snapshot, all results and the figures. The full ClinVar variant summary is not redistributed; the code downloads it from NCBI. Companion papers: doi:10.5281/zenodo.22950095, doi:10.5281/zenodo.22959211, doi:10.5281/zenodo.22960439, doi:10.5281/zenodo.22963882. Code: https://github.com/Ruqing1963/reachable-fibres