Relational Clocks, Complete Simplices, and Phase Structure in Organized Causal Networks: An Exploratory Investigation

We investigate whether organized relational dynamics can generate intrinsic temporal
structures. Complete graphs Kn possess exact degenerate vibrational spectra ωn =p nD/τr
(proved). Triadic closure dynamicsspontaneously generates large cliques, which inherit this exact spectrum. A population picture replaces the single-clock hypothesis: evolved networks contain O(103) maximal cliques forming a temporal medium with collective spectrum P(ω).
A competing organization–fragmentation dynamics reveals three relational phases (dispersed, organized, condensed) with a candidate order parameter R = p/q. Whether this constitutes a genuine critical phenomenon, and whether it connects to the SR temporal sector, remains open. All results are exploratory; no SR prediction is claimed.