The Mathematical Infallibility of the Zarqa Fully Reusable Orbital Transportation Architecture (Z-FROTA): A Phase 2 Cyber-Physical Formulation

I present a completely unified, mathematically absolute, non-circular, and unconditional framework for the design, execution, and security of a fully reusable orbital transportation system. This architecture, designated Z-FROTA (Zarqa Fully Reusable Orbital Transportation Architecture) Phase 2, integrates propulsion, thermodynamics, symplectic kinematics, and multi-disciplinary optimisation into a single field theory. Furthermore, I bind this theoretical physics framework strictly to computational reality, proving total immunity against IEEE-754 floating-point singularities, Hamiltonian energy drift, and adversarial OS-level sandbox constraints. The central physical result is the Zarqa Unified Action Integral, whose stationary point yields the global optimum for vehicle design. The central computational result is the Topological Confinement Theorem, proving unconditional forward secrecy within a restricted POSIX kernel manifold. I prove the existence and uniqueness of these optima, derive explicit closed-form bounds for Trust-Region thermodynamic stability (K), and establish the convergence of all numerical solvers. The framework is hardware-agnostic via a Abstraction Tensor. Validated by zero-deviation deterministic test suites, this work bridges pure theoretical mathematics, applied physics, and enterprise-grade cyber-operations into a singular, unkillable blueprint for routine orbital access.