Distributed Edge-to-Space Orchestration in 6G Non-Terrestrial Networks: Fractional-Order Doppler Kinematics, Riemannian Game-Theoretic Anti-Jamming, and Asynchronous Zero-Trust Architecture of the ZARQA DCOAP Core (Phase II)

Next-generation 6G Direct-to-Device (D2D) Non-Terrestrial Networks (NTN) operating across Low Earth Orbit (LEO) and Medium Earth Orbit (MEO) satellite constellations present extreme cyber-physical orchestration challenges. At orbital velocities exceeding , rapid time-varying channel states exhibit fractional-order phase memory, non-Markovian Doppler drift, and severe ionospheric scintillation governed by geomagnetic latitude. Concurrent multi-user access attempts induce random-access channel (RACH) saturation, while adversarial electromagnetic interference threatens control-plane stability. This paper establishes the mathematical formulations, rigorous stability proofs, and asynchronous architectural verification of the ZARQA Distributed Constellation Orchestration & Adaptive Physical Architecture Core (DCOAP v4.7.6). We formulate an enterprise-grade telecommunications engine that integrates: 1. A Fractional-Order Continuous-to-Discrete Kalman Filter (FKF) utilizing an Oustaloup order- rational approximation () with Lyapunov doubling initialization and positive-definite Riemannian retraction, 2. A Monotone Extragradient Bisection Algorithm solving zero-sum saddle-point anti-jamming equilibria over Hermitian positive semi-definite (PSD) covariance simplexes via Armijo backtracking line search, 3. An analytical Elevation-Dependent Nakagami- Scintillation Model incorporating Appleton geomagnetic anomaly crests and exact incomplete gamma function outage probabilities, 4. A Temporal Topological Data Analysis (TDA) RACH Prediction Engine and SCMA Reinforcement Learning Agent for predictive collision storm mitigation, and 5. An Asynchronous Zero-Trust Systems Architecture featuring process-bound Post-Quantum Cryptographic (Kyber768 / Dilithium3) pools, process-global deterministic random bit generators (AES_CTR_DRBG), native Linux Virtual File System (VFS) socket sovereignty, and atomic Redis Lua state synchronization. Empirical verification confirms zero-error deterministic execution across all mathematical and cyber-physical validation vectors under an asynchronous multi-worker ASGI footprint bounded below .