shahbaaz-devsec/ZARQA-D2D-Non-Terrestrial-Network: ZARQA ZFMSC Core — Phase I Production Release (v1.0.0-phase1)

📌 ZARQA Foundational Mathematics & Standardisation Core (ZFMSC) — Phase I This inaugural production release (v1.0.0-phase1 / build 24.7.13) establishes the foundational mathematical, cryptographic, and architectural framework for 6G Direct-to-Device (D2D) Non-Terrestrial Networks (NTNs) across Low Earth Orbit (LEO) and Medium Earth Orbit (MEO) satellite constellations. 🚀 Key Architectural Breakthroughs in Phase I Hybrid Post-Quantum Cryptography Suite (CryptoManager) Combines NIST-standardized lattice-based ML-KEM-768 (Kyber768) with elliptic-curve X25519 Diffie-Hellman ($IKM = s_{\text{PQ}} \mathbin{\Vert} s_{\text{EC}}$). Implements domain-separated HKDF-SHA256 derivation for independent AEAD (ChaCha20-Poly1305) cipher keys and JWT HMAC authentication keys. Features stateless, lock-free RCU key rotation (3,600-second cycle) and blocking OS entropy hardening (/dev/random / GRND_RANDOM). Constant-Time Vectorized Water-Filling Power Allocation Eliminates branch-prediction timing side-channels during multi-carrier downlink power allocation across inverse gain thresholds ($\gamma_k = \sigma^2 / g_k$). Calculates ergodic Shannon capacity in deterministic $O(N \log N)$ execution time. SPD Riemannian Manifold Covariance Tracking Models channel covariance matrices $C \in \mathcal{S}{++}^n$ via Bures-Wasserstein metrics ($d{\text{BW}}^2(C_1, C_2)$). Utilizes second-order Cholesky retraction maps ($\mathcal{R}C(\eta) = L{\text{new}} L_{\text{new}}^T$) governed by Armijo backtracking line search. Simplicial Topological Data Analysis (TDA) Calculates 0-dimensional ($\beta_0$) and 1-dimensional ($\beta_1$) Betti numbers via simplicial homology (AlphaComplex / landmark-selected Vietoris-Rips). Verifies Euler characteristic ($\chi = V - E + F$) stability across dynamic orbital deformation without relying on GPS/GNSS coordinates. Phase Omega Singularity & Photonic NLSE Propagation Models Orbital Angular Momentum (OAM) spatial multiplexing across orthogonal integer topological charges ($\ell \in [\ell_{\min}, \ell_{\max}]$). Simulates optical pulse propagation through dispersive Kerr-nonlinear waveguides using the Non-Linear Schrödinger Equation (NLSE) solved via the Split-Step Fourier Method (SSFM). Incorporates Time-Reversal Mirror (TRM) spatial beam focusing. Game-Theoretic Anti-Jamming Saddle-Point Equilibrium Resolves zero-sum saddle-point equilibria between legitimate transmitter ($Q_T$) and adversarial jammer ($Q_J$) covariance matrices via iterative extragradient bisection. Asynchronous Zero-Trust Linux Sandboxing Integrated DevOps deployment (--auto-deploy) provisioning unprivileged service accounts (zarqa-zfmsc) and virtual environments. Runs a Gunicorn ASGI master with 4 asynchronous Uvicorn workers, zero-copy shared memory IPC (/dev/shm), and strict cgroup memory ceilings. ✔️ Bare-Metal Verification Benchmarks All 12/12 deterministic self-tests passed (--test-only): ✔ Vectorized Water-Filling Power Allocation ✔ FFT Discrete Fractional Calculus Derivatives ✔ Cholesky SPD Retraction & Positive-Definiteness ✔ Spherical Visibility Coverage Integrals ✔ Hurst Exponent Ergodic Fractional Capacity ✔ Bures-Wasserstein Riemannian Optimization ✔ Simplicial Homology AlphaComplex TDA Invariants ✔ Landmark-Selected Rips Complex Topology Fallback ✔ ML-KEM Kyber768 + X25519 Hybrid Key Exchange ✔ Non-IID Satellite Constellation Convergence Bounds ✔ Game-Theoretic Coalition Exact Potential Partitioning ✔ Laplace Mechanism Differential Privacy Tradeoff