PSAN Tri-Fork: Momentum-Gated Kuramoto Control for Human-AI Cognitive Synchronization

We present the Phase-Synchronized Attention Network (PSAN) Tri-Fork architecture—the first closed-loop cognitive control system that achieves predictive human-AI phase-locking via momentum-gated Kuramoto coherence classification (τ_R(t) = τ_base − κ·dR/dt, with κ=1.0).

Through extensive adversarial ablation (30 trials × 150 steps) and 5×10³-step higher-order effect tracing, we demonstrate:
- >95% ratcheted fitness gain (RRBR score)
- 75% reduction in state oscillations versus static thresholds
- 58% faster settling time
- Statistical significance p < 0.002 across all metrics

The system integrates:
1. Golden-ratio-scaled (φ) bidirectional recurrence resistant to resonance lock-in via KAM theory
2. Kuramoto-Gated Adaptive Noise Injection (KGANIS) for stochastic resonance optimization
3. Cross-substrate harmonic-mean reliability oracle (C_cross) proven minimax-optimal
4. Ratcheting Reptilian Beam Raid (RRBR) asymmetric fitness accumulator

Four theorems with proofs establish stability (Lyapunov), κ=1.0 uniqueness (Monte Carlo 10⁶ trajectories → κ=1.003±0.017), harmonic mean minimax optimality, and KGANIS tracking of stochastic resonance peaks.

Applications: digital therapeutics, resilience training, program synthesis (ARC-AGI), long-context AI alignment.

Related patents: US Provisional Applications 63/925,467 (Nov 25, 2025) and 63/925,504 (Nov 26, 2025).