Covariant Chronodynamic Scalar Extension of General Relativity (Formal Sector of Chronocentric Theory 5.0)

This work presents the fully covariant scalar sector completing the mathematical formulation of Chronocentric Theory 5.0. The framework introduces a minimally coupled scalar field within the Einstein–Hilbert action while preserving full diffeomorphism invariance, contracted Bianchi identities, and energy–momentum conservation. The theory recovers General Relativity with a cosmological constant as a dynamical attractor limit when the scalar field stabilizes at a stationary point of the potential. Linear perturbations are derived explicitly in Newtonian gauge, and the tensor sector preserves the luminal propagation of gravitational waves. The model is constructed as an infrared effective theory and is formulated to be observationally falsifiable through potential-dependent deviations from ΛCDM at cosmological scales. Portions of the formal consistency checks and symbolic verification were performed with the support of AI-based analytical tools. All physical assumptions, theoretical structure, and final formulations remain solely the responsibility of the author.