[Exploratory Version] Relativistic Quantum Formalism in Pure Time Theory (PTT) [Exploratory Version]

We develop a fully relativistic quantum formalism based on the Pure Time Theory (PTT), in which all physical structures and interactions emerge from a single scalar field: the temporal relaxation field Trelax(xμ). The spacetime metric gμν is derived covariantly from the gradients of Trelax, eliminating the need to postulate spacetime as a fundamental backdrop. Using this metric, we reformulate the Klein–Gordon and Dirac equations in a manifestly covariant form. We construct a unified action principle incorporating both the quantum fields and the temporal field. Lorentz covariance is formally proven, and canonical quantization is applied to Trelax, yielding regularized propagators with natural ultraviolet (UV) cutoffs governed by the relaxation exponent β≈1.203 A complete numerical simulation of quantum propagation in a Trelax-based metric confirms the localization and coherence predicted by PTT. The framework is shown to be unitary, divergence-free, and empirically testable via SPARC galactic data and Casimir anomalies. This work closes the unification chapter by deriving the quantum-relativistic structure of nature from time itself.