Vladi Ivanov | Searcharxiv

arXiv2026

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.

cs.SI↗

arXiv2026

Topology as Logic: Structural Role Geometry Across Formal, Software, Biological, and Prebiotic Systems

We ask whether dependency topology correlates with functional load-bearing organization as recoverable geometry -- not as a metaphor, but as a measurable structural property detectable by multilayer network analysis. Across seven independent substrates, we show that hub persistence and rank divergence under the Functional Proximity Law recover operational organization that domain experts describe as logic: axiomatic load-bearing structure in formal mathematics, control and contract structure in legacy software, conserved hub grammar across approx. 600 million years of neural evolution, catalytic role organization in a published prebiotic autocatalytic network, carry-path dominance in a 4-bit digital circuit, betweenness persistence in the ISCAS85 c432 standard benchmark (n=196), and a directional formal-systems replication in the Coq Corelib (n=17). A key methodological finding: degree-based hub persistence is weak between physical wiring and simulation state-correlation layers (r=0.21 in c432), while betweenness-based persistence is stronger (r=0.77 in the 4-bit ALU post-hoc; r=0.34 in c432). The ISCAS85 pre-registered primary hypothesis was CONFIRMED (degree r=0.426, p=0.002, Spearman r=0.551). The formal-systems claim is supported by two proof-assistant corpora: Lean 4 mathlib4 (CONFIRMED, r=0.777, p=0.004) and Coq Corelib (PARTIAL, direction confirmed, r=0.288, p=0.287, n=17, underpowered). All seven experiments were pre-registered before analysis.

cs.SI↗