Genomic codon usage is structurally consistent with First-Classness across the tree of life

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Abstract

Genome-scale codon usage data from 70,950 species spanning the tree of life allow a test of whether the standard genetic code's 21-family degeneracy partition is structurally consistent with the First-Classness (FC) framework, which derives that partition from conformal completion constraints on a four-element dispositional algebra without biological input. We report three findings. First, within-family codon usage uniformity, measured by coefficient of variation, follows a specific ordering across family sizes---2-fold < 4-fold < Ser 6-fold < 3-fold < Leu/Arg 6-fold---that reflects the architectural constraints of the FC-derived partition rather than a simple size effect. Second, the three split six-fold families (serine, leucine, arginine) exhibit stable internal fine structure, with four-codon sub-block dominance ratios of 0.30--0.56 that are consistent across all kingdoms of life. Third, a family-balanced global FC ratio, tested against a null model preserving family-size architecture while randomising codon assignment, shows no separable statistical signal (Z = 0.06, p = 0.44), consistent with the expectation that the partition and the frequencies it governs are not independent.

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