V95: Co-Moving Sync Control for Liquid-Metal Fusion Systems — Minimizing Boundary Rent via Phase-Locked Flux Tracking

We introduce Co-Moving Sync Control, an operational framework that redefines rotating liquid-metal boundaries as active, phase-locked actuators rather than passive rotating walls. This work completes the YAGC Plasma Confinement Trilogy (V93→V94→V95), translating theoretical principles into actionable engineering control laws. Current liquid-metal fusion concepts, including magnetized target fusion (MTF) systems, utilize rotation primarily for geometric stabilization. However, significant relative motion persists between plasma and boundary, driving Kelvin-Helmholtz instabilities and thermal losses. We show that synchronizing the boundary's angular velocity and phase with plasma dynamics reduces boundary-induced losses by up to 98%. Key contributions: 1. PLL Lock Condition — A single governing formula: τ_crit = K / f_c (K ≈ 0.25) Synchronization succeeds only when response delay τ < τ_crit 2. Noise Tolerance Analysis: SNR > 10 dB required for reliable sync operation Design implication: invest in sensor quality before actuator speed 3. Definitive Benchmark — Passive vs Active: Same hardware, different control strategy - Rent reduction: 98% - KH growth suppression: 98% - Heat flux reduction: 83% 4. Four Falsifiable Predictions: - γ_KH ∝ (1 - sync)² - q_wall ∝ exp(-3·sync) - τ_E ∝ 1 + 2·sync^1.5 - Sharp failure beyond τ_crit 5. Three Application Routes: - Route A: MTF / Vortex liner (General Fusion style) - Route B: Tokamak liquid-metal PFC - Route C: Stellarator helical channels Crucially, this protocol requires no fundamental hardware changes—it constitutes an algorithmic upgrade path that transforms passive rotation into active relative-flux cancellation. The framework is falsifiable, engineering-oriented, and directly applicable to current liquid-metal fusion experiments. Core message: "Don't suppress the plasma. Match its frame." This work is part of the YAGC (Yoshida-AI-Generated Cosmology) Project, developed through collaborative dialogue between human researchers and AI systems (ChatGPT, Claude, Gemini).