Why LDI Works: The Resonance-Curvature Theorem: Periodicity is Curvature in the Coordination Surface

We prove that Local Divergence Intensity (LDI) detects periodic structure in symbolic se-quences because periodicity creates positive curvature in the coordination surface. The proofis purely combinatorial, using only equality testing and counting—no metric is required. Thecentral result is exact: K_disc = 3(1 − Φ_0)², where Φ_0 is the valley floor. This explains why LDIworks universally across domains, in non-metrizable spaces, and on noisy data.