Evidence for a Functional Proximity Law in Multilayer Networks

Hub importance scores in multilayer networks persist more strongly betweenfunctionally similar layers than dissimilar ones. This paper introduces theFunctional Proximity Law (FPL) and tests it across 23 pre-registeredexperiments: 13 canonical domains (10 confirmed, 3 denied; molecular biology,neuroscience, computer systems, ecology, linguistics, AI architecture) plus10 pre-registered external validations (9 confirmed, 1 denied). Four DENIEDdomains reveal named structural boundary conditions (BC1–BC6). Binomialprobability of 19/23 confirmations by chance: p ≈ 0.0013. Pre-registrationrecords: https://github.com/vladi160/preregistrations. arXiv: 2604.23639. --- Version 7 — Submission-ready corrections (2026-05-23) Fixes two presentation issues. No experimental data, statistics, orpre-registration records were changed. - Abstract: "independently-authored datasets" → "pre-registered external validations" (M_GEOM_CSG_1 uses an author-constructed graph, so the blanket qualifier was inaccurate for that entry).- Discussion — H_PRIMITIVITY paragraph: restructured to lead with h1 DENIED (BC4 boundary condition) rather than the secondary h4 PARTIAL finding. Result tally unchanged: 1 CONFIRMED / 2 DENIED / 1 PARTIAL. Selected version history: v4 https://doi.org/10.5281/zenodo.19756407 — added WordPress, Next.js, Flask↔Express v5 https://doi.org/10.5281/zenodo.19784776 — added AI Architecture, mathlib4, C. elegans 302 v6 https://doi.org/10.5281/zenodo.19786469 — pre-registration and metadata corrections v7 https://doi.org/10.5281/zenodo.20349791 — this version (presentation corrections)