Evidence for a Functional Proximity Law in Multilayer Networks

Hub importance scores in multilayer networks persist more strongly between functionally similar layers than dissimilar ones. We call this the Functional Proximity Law and test it across 31 pre-registered experiments: 13 canonical domains (10 confirmed, 3 denied; molecular biology, neuroscience, computer systems, ecology, linguistics, AI architecture) plus 18 pre-registered external and replication validations (15 confirmed, 1 denied, 2 partial). Nine canonical domains reach p < 0.05 individually. Six DENIED results reveal six named structural boundary conditions (BC1-BC6), including the newly named BC_INVERSION mechanism in which fan-out leaf clustering inverts the hub correlation. The law extends to particle physics: the first pre-registered Standard Model experiment confirms all 5 hypotheses (r = 0.569, p = 0.010; photon confirmed as hub shadow). COBOL legacy banking software confirms 4/4 hypotheses (r = 0.807, Delta r = 0.688; topological dormancy signatures). A cross-species replication across approx. 600 million years of evolution confirms the law in the Drosophila melanogaster larval connectome (n = 2952 neurons, Spearman rho = 0.663, Pearson r = 0.363, p = 0.002). A hub dominance structural pattern is discovered in the antidepressant evidence chain: the founding assumption ranks #1 hub in all three epistemological layers simultaneously, detectable from graph topology alone. A quantitative precondition predictor, Var(d2) < 0.714, predicts BC_RADIAL failure before experiments run. Binomial probability of 25/31 pre-registered confirmations by chance: p approx. 0.000439 (p < 0.001). The law now spans eight scientific fields.