Anticipation Series — Paper III: Collective Coherence: Scaling and Synchronization in N3 Networks

Paper III of the Anticipation Series within the Radial Coherential Dynamics (RCD) research program. ABSTRACT:Papers I and II established anticipation as thermodynamically costly counterfactual simulation, with individual dynamics governed by driven-dissipative Langevin equations. Here we address the COLLECTIVE problem: what happens when N anticipatory agents couple into a network? We introduce the Synchronization Index Ψ as the collective order parameter, analogous to the Kuramoto model for coupled oscillators. The central hypothesis is that synchronized networks (Ψ → 1) exhibit SUPERLINEAR scaling of anticipation leverage: L_A^{collective} ~ N^β with β > 1. This "network advantage" arises because simulation costs (S_sim) are shared while avoided costs (S_avoided) multiply across the network. We derive pseudo-critical density ρ_c below which collective coherence collapses, and show that misinformation acts as correlated noise that drives desynchronization. The framework provides quantitative predictions for when collective intelligence emerges and when it breaks down. Explicit falsification conditions are provided. KEYWORDS: Collective intelligence, Network dynamics, Synchronization, Kuramoto model, Superlinear scaling, Anticipatory systems, Information networks, AI-human collaboration This paper was developed using a collaborative human-AI panel methodology, with technical review provided by Claude (Anthropic), ChatGPT (OpenAI), Gemini (Google DeepMind), Grok (xAI), and Perplexity. Part of a trilogy:- Paper I: Physical Foundations (DOI: 10.5281/zenodo.18420495)- Paper II: Thermodynamic Dynamics (DOI: 10.5281/zenodo.18421010)- Paper III: Collective Coherence (this paper)