Optimal Transport Geometry of Natural Spectral Regime Transitions

Abstract

Empirical optimal transport analysis of natural spectral regime transitions recorded by a 4-node ESP32 mesh network with AS7341 10-channel spectral sensor (7-second sampling, Belgrade 44.82N 20.46E). Dataset: 13 independent logs (10 dawn, 3 dusk), 16,576 total samples. The optimal coupling on boot320 (N=867, M=205) has exactly N+M-1 nonzero entries (transport polytope vertex), with 94.3% Monge concentration. Spearman stability rho=0.995 across 10 dawn logs (45 pairwise comparisons). Dawn transitions accelerate (W2: 399 to 1036); dusk transitions decelerate (W2: 6566 to 550, 92% drop). Lie generator coherence (C20) separates calibration quality: 4/5 post-fix logs pass vs 1/5 pre-fix. Formal verification: 435 PVS theorems (39 theories) and 153 Lean 4 theorems (zero sorry). Runtime certificate framework: 22 certificates validated on all 13 logs in under 2 seconds. Raw spectral logs available upon request.