We propose that optimal sequential memory compression and the biological measurement of interpersonal coherence are instances of the same underlying geometric problem. Drawing on the Barteau framework's mathematical proof that any homogeneous, isotropically suppressing dynamical system must converge to φ-wound orbital structure, we establish that (1) the golden ratio φ is the uniquely optimal compression base for bounded sequential memory by Hurwitz's theorem on Diophantine approximation; (2) the Biometric Coherence Friction coefficient (BCF) measures the degree to which biological systems instantiate this geometry during interpersonal transmission; and (3) the compression-transmission duality — the conjecture that memory and transmission are the same operation viewed from opposite directions — follows naturally from the shared mathematical skeleton. We situate these claims within existing neuroscience, signal processing, and AI memory compression literature, distinguish what is proven from what remains conjectural, and propose testable experimental predictions for both the AI and biological cases.
Stewart Barteau (2026) studied this question.