Temporal Deferral Series III – Lagrangian Field Formulation and Coupling Unification

This work presents a Lorentz-invariant field theory in which all known interactions arise from temporal deferral—the fractional storage and delayed release of energy through time. A scalar deferral field R(x,t) is introduced to represent the local density of deferred energy, derived from the causal-response kernel of energy exchange. The resulting covariant Lagrangian couples R universally to Standard-Model and gravitational operators, yielding a conserved temporal Noether current and providing a quantitative bridge between quantum and gravitational regimes. Homogeneous solutions reproduce cosmic acceleration, while localized solutions describe horizon deferral consistent with black-hole thermodynamics. The framework unifies the four fundamental interactions as equilibrium regimes of a single field potential and predicts small, measurable drifts in coupling constants testable with precision spectroscopy and cosmological data. This paper completes the theoretical foundation established in Temporal Deferral I–II and forms the basis for the forthcoming geometric and empirical extensions of the series.