Frustrated Synchronization in Doubt-Modulated FitzHugh-Nagumo Networks: Attractor Diversity and Topological Phase Transitions

POST-AUDIT CORRECTIONS (2026-04-26 — v3.2.1):- Preprint : équation du doute corrigée (ε_u adaptatif, alpha_s=2.0, C_cap=5.0)- Statistiques n=5 seeds : ΔH_cog = 0.0027 bits (0.115%)- Nouveau draft paper_2 ajouté : "The Doubt Variable as Anti-Synchronization Filter"- Nouvelles figures : p2_sigma_social_ablation, p2_tau_u_bifurcation Mem4ristor v3.2.0 — Adaptive Coupling & Frustration-Driven Diversity We present a modified FitzHugh-Nagumo oscillator network with a third state variable, doubt (u), that modulates coupling polarity via a Levitating Sigmoid kernel tanh(π(0.5−u)) + δ. Combined with heretic nodes (inverted stimulus polarity) and Gaussian noise, this mechanism sustains multi-state attractors from homogeneous initial conditions. KEY RESULTS:- Regular lattices (2D periodic, N=100): sustained attractor entropy H_cog ≈ 0 with current KIMI bins (±0.4/1.2) under default parameters (I_stim=0). Historical H_stable ≈ 0.92 reported with pre-KIMI bins (±0.8/1.5); see limitations.md for reconciliation.- Scale-free networks (Barabási-Albert): phase transition at m ≈ 5 where ALL coupling normalizations converge to consensus (dead zone). Degree-linear normalization recovers diversity for m ≤ 3.- Hardware validation: SPICE RMS error <1% vs Python (lattice 4×4, ngspice 46).- Escape mechanism: thermal noise + capacitive mismatch enable partial recovery from dead zone (H≈1.61 bits at σ_noise=0.5, σ_C=0.5 on BA m=5). CRITICAL AUDIT CORRECTIONS (2026-04-22):- §3.1: Fixed false stability claim. Isolated unit at α=0.15 is stable spiral, not unstable. Hopf bifurcation at α_crit≈0.296.- §3.3: Entropy bound (Eq. 9) valid only when I_stim≠0; heretic mechanism is vacuous under zero stimulus.- Eq. 2: Documented always-active plasticity decay term −w/τ_plast.- Verilog-A v2.6: Fully synchronized to dynamics.py v3.2 with Levitating Sigmoid kernel, τ_u=10.0, adaptive ε_u, and corrected heretic polarity application. CONTENTS:✓ Restructured preprint (11 pages, 0 LaTeX errors)✓ Full source code (dynamics.py v3.2.0-audited, mem4ristor_v26.va synchronized)✓ Scientific regression tests (74 tests passing)✓ Experimental scripts & figures (SPICE validation, ablation studies, coordination metrics)✓ Truth table of scientific claims (docs/limitations.md)