The Frustration Zone as Semantic Substrate: Geometric Curvature, Multi-Stability, and Semantic Capacity in Delay-Coupled Complex Networks

ESCT Research Framework — Phases 33–36 Integrated Report Author: Jhang, Rong Jhou | Independent Researcher Date: 2026-05-11 | Version: v4.0 (Post-Correction Integrated) DOI: 10.5281/zenodo.20050420 | License: CC-BY-4.0 Abstract We report the results of a four-phase experimental program (Phases 33–36) within the ESCT (Entropy-Signaling Convergence Theory) framework, establishing a predictive bridge between geometric network structure and semantic capacity in delay-coupled complex networks. Phase 33 discovered an unexpected dynamical regime — the “Frustration Zone” — in which anti-physical (inward-spiraling) curvature geometry combined with delay- induced coupling (κ ≥ 2.0, τ _delay ≥ 0.5) induces robust multi-stability (N_ attr ≈ 3–4) rather than the predicted fast convergence. Phase 34 validated this finding at N = 200 agents, revealing 11 distinct attractors with fractal basin boundaries (Shannon entropy H = 3.18 bits) and confirmed the system operates at the edge of chaos. Phase 35 established the ESCT- CSI (Convergence-Semantic Interface) bridge: basin entropy quantifies semantic capacity, delay time τ _delay is a programmable tuning knob, and anti-physical curvature (C = 3) is the necessary geometric substrate. Phase 36 tested this geometry against synthetic natural- language embedding spaces, confirming that polysemous (ambiguous) words occupy rare basins (100% of tested cases), semantic distance correlates with basin distance (Pearson r = 0.443), and topic hierarchy is encoded in basin hierarchy. Three of four pre-experiment predictions were confirmed; one (fuzzy boundary routing) was disconfirmed, yielding a novel discovery of a Slow-Decision Zone at interpolation parameter α ≈ 0.70–0.75. Honest experimental boundaries and falsified hypotheses are documented in full compliance with Popperian methodology. Keywords: ESCT, Frustration Zone, delay-coupled networks, basin entropy, semantic capacity, multi-stability, anti-physical curvature, semantic embedding, polysemy, edge of chaos, attractor basins, complex networks, AI alignment