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.