Evidence for a Functional Proximity Law in Multilayer Networks

We report an empirical regularity in multilayer networks, the Functional Proximity Law: degree-centrality hub scores correlate more strongly between layers encoding functionally similar relationships than between layers encoding dissimilar ones. We test this across 9 independent canonical domains spanning molecular biology, systems neuroscience, computer systems, ecology, and linguistics. Eight domains reach p < 0.05; all nine satisfy the directional inequality between pre-registered similar and dissimilar layer pairs. Three DENIED domains reveal named structural mechanisms bounding the law's scope. A negative control confirms the method does not fire on random structure. Pre-registration artifacts are publicly archived at https://github.com/vladi160/preregistrations