A Unified Covariant Framework for Quantum Dynamics, Electromagnetism and Gravity Using the Deterministic Computation Law

This work develops a covariant modelling framework - the Deterministic Computation Law (DCL) - that introduces a reproducibility scalar field as an additional degree of freedom coupled to spacetime geometry, gauge fields, and quantum dynamics. The framework is constructed entirely within standard relativistic field theory, electromagnetism, and open-quantum-systems theory, and is not presented as a replacement for established physics. Instead, it provides a unified variational structure in which deterministic geometric evolution and probabilistic quantum behavior arise as different limiting regimes of a single action functional. The unified action extends the Einstein–Hilbert and gauge-field-theoretic sectors with a dimensionless reproducibility field, a curvature-coupling function and a GKSL-compatible reproducibility functional governing open-system evolution. Variation yields a coupled set of equations-referred to as the Unified Master Equation (UME)-that reduce to General Relativity and standard Maxwell equations, as well as to Schrödinger–Liouville or GKSL dynamics. The resulting structure also provides a controlled semiclassical interface between quantum dynamics and classical curvature, without making claims about Planck-scale physics or full quantum gravity. Within this framework, the reproducibility field mediates a tunable correspondence between deterministic and probabilistic evolution, enabling analysis of variance suppression in quantum ensembles, weak-field scalar corrections in curved backgrounds, and information-theoretic quantities such as entropy production. These consequences are presented as model-dependent signatures rather than predictions of physical law. At galactic scales, the weak-field limit admits an explicit galaxy-regime closure under which selected realizations of the Unified Master Equation reproduce the gravitational phenomenology typically attributed to dark matter, including flat galaxy rotation curves observed in nearby spiral galaxies, and are consistent with the observed radial acceleration relation, without introducing additional matter species or modifying electromagnetism. The overall contribution is a covariant, EFT-compatible structure that organizes geometric, gauge, quantum, and scalar dynamics under a single unifying mathematical principle while remaining strictly within established theoretical machinery.