Vladi Ivanov

Vladi Ivanov

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.

Vladi Ivanov

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 17 pre-registered experiments: 12 canonical domains (9 confirmed, 3 denied; molecular biology, neuroscience, computer systems, ecology, linguistics) plus 5 external validations on independently-authored datasets. Eight canonical domains reach p < 0.05 individually; the directional inequality holds in all 9 confirmed. Three DENIED domains reveal named structural boundary conditions that narrow the law's scope. A fully external validation on the C. elegans connectome -- where both data and layer definitions are independent of the authors -- yields r = 0.777 (p = 0.004). Binomial probability of 14/17 pre-registered confirmations by chance: p ~ 0.006. The law is falsifiable, makes testable directional predictions, and identifies the structural conditions under which it fails.