Abstract
<title>Abstract</title> <p>Armosis is the progressive reduction in the fraction of theoretically possible entities observed across successive steps of biological organization. Biological organization occupies only a small fraction of theoretically possible configurations, yet no general quantitative framework exists for measuring this progressive organizational constraint across successive levels of assembly. Quantitative demonstration requires preservation of biological provenance across organizational steps together with sufficient observations to estimate the saturation of the observed repertoire at each organizational step. Armosis is quantified as the logarithm of the ratio of theoretically possible to observed entities. When the organizational framework is defined and provenance preserved, armosis is independent of biological mechanism, classification, entity identity, and the particular assembly being examined. A provenance-aware knowledge graph constructed from 53,166 complete GenBank human mitochondrial genomes enabled direct measurement of theoretical and observed organization from codons through protein-gene templates, respiratory chain complexes, and the complete electron transport chain. Armosis increased progressively across this path, from 1.5 for codon-to-protein-gene relationships to 10.7 for Complex I assembly and 30.9 for the complete electron transport chain. Saturation analyses indicated that observed biological organization approaches a finite repertoire rather than expanding indefinitely with additional genomes. The repertoire has a dominant motif and a set of less common motifs for each entity. Each individual has one instance of each entity from the repertoire that is traceable through assembly steps in a provenance-aware ecosystem. The provenance-aware platform provides a flexible and scalable foundation for extending these analyses by adding other provenance-aware graphs and connecting them to the existing graph. This opens new analytic path traversals across observed entities while preserving provenance throughout the expanded graph.</p>