The Relativistic Causal-Order Gate

This paper presents a mathematical formulation of the Relativistic Causal-Order Gate (Ferra Gate), extending it from a kinematic representation to a full dynamical theory. Starting from the process matrix formalism in Algebraic Quantum Field Theory (AQFT), we construct the Ferra Gate as a higher-order operator encoding superpositions of causal orders between operations localized in distinct spacetime regions. We then introduce a dynamical evolution law for the process matrix, treating it as an open quantum system in a "super-spacetime" formalism. We prove the existence of a conserved causal charge, derive the master equation governing causal order evolution, and demonstrate how decoherence selects definite causal orders. The theory yields falsifiable predictions including causal oscillations and gravitational phase modulations. A complete computational implementation in Python is provided, revealing unexpected phenomena such as decoherence saturation and sensitivity to the sign of gravitational curvature. All numerical results are reproducible and verify the theoretical predictions.