Integrated Closed-Loop Architecture: Bridging Spatial Field Memory (PHI-OMEGA / M) and Deep-Space Relativistic Communication via Hybrid GPU-Accelerated Quantum Error Correction

This paper establishes a unified theoretical and computational framework that bridges the PHI-OMEGA / M (Sun Cage) spatial field-memory dynamics and the AURA-X deep-space relativistic communication architecture within modern hybrid quantum-classical error correction (QEC) paradigms. Inspired by recent industrial breakthroughs in AI-driven, GPU-accelerated closed-loop decoding—exemplified by high-throughput NVIDIA-Riverlane architectures—we demonstrate that 3D Fibonacci-Halbach spatial tensor dynamics (K_{ij}) and real-time phase-coherence preservation directly mirror adaptive decoding under non-stationary noise environments. Through digital twin simulations and theoretical modeling tested under extreme lunar surface thermal-vacuum profiles and Earth-Moon L_2 orbital equilibrium, we analyze eigenvalue stiffness limits (\approx 168977 \text{ s}^{-1}), high-order numerical integration (RK4), and thermodynamic dissipation boundaries. We propose an integrated closed-loop computational stack (Q \rightarrow \text{AI} \rightarrow \text{GPU} \rightarrow \text{Decoder}) capable of regulating both quantum-state stability and long-range interstellar signal fidelity against cosmic decoherence. Finally, strict empirical falsifiability criteria and hardware roadmap implementations are outlined.