ZARQA Phase I Precursor Core: A Unified Mathematical Framework for Autonomous Electromagnetic Topology Characterization via Fractional Calculus and Riemannian Geometry

I present the complete mathematical formalization and proof of stability for Phase I of the ZARQA Electromagnetic (EM) Topology Precursor Core, designed for autonomous lunar South Pole deployment. By resolving fundamental singularities in stochastic process modeling and eigen-spectrum analysis, I have achieved absolute enterprise idempotency. This paper details the exact derivations of the Fractional Poisson Sequential Probability Ratio Test (SPRT), the power-domain Nakagami- robust M-estimator, the Marčenko-Pastur spectral veracity threshold, and the lock-free Riemannian projection of the Grand Unification Tensor. I prove that under these formalized constraints, the autonomous daemon is mathematically invulnerable to orchestration deadlocks, topological spoofing, and floating-point singularities. Validation against live hardware-in-the-loop execution logs demonstrates asymptotic convergence to theoretical Cramér-Rao lower bounds and mathematical self-test compliances.