The Pure Time Theory - Canonical Refoundation Based on Scalar Temporal Ontology

This revision (v25) establishes the complete axiomatic foundation of the Pure Time Theory (PTT), formally articulating its minimal postulates, derived quantities, and logical closure. Axioms A1-A4 define the ontological status of the scalar field T_relax, its canonical spectral decomposition, and the Principle of Logical Unicity (PLU). From this basis, all core results--emergent geometry, fundamental constants, canonical field equations, and quantum structure--are derived as theorems within a self-contained formal system. This version provides a fully rigorous mathematical framework, allowing direct verification and critical evaluation by the broader scientific community. This document presents the first fully canonical formalization of the Pure Time Theory (PTT), a framework in which all physical phenomena emerge solely from the local relaxation dynamics of a scalar temporal field, T_relax. The theory is developed without invoking any predefined geometry, physical constant, or external equation. Instead, all structures, metric tensors, matter densities, field equations, quantum behavior, and gravitational coupling, are derived step by step from the internal behavior of T_relax, in strict accordance with the Principle of Logical Unicity (PLU). The derivation begins with a minimal ontological postulate: that pure time constitutes the sole generative substrate of reality, and that its local relaxation is the only observable projection. From this scalar trace, the theory reconstructs geometry, action principles, causal structure, particle spectra, and Planck-scale constants through a progressive chain of formal derivations. The present version consolidates previous results and introduces several new elements, including: (1) the emergence of a canonical scalar measure for integration, (2) the full derivation of the canonical field equation for T_relax, (3) the construction of an emergent stress-energy tensor without postulating matter, and (4) the canonical quantization of the scalar field, leading to discrete excitations indexed by the nontrivial zeros of the Riemann zeta function. This text is intended as a self-contained reference for researchers seeking a logically unified and ontologically minimal reconstruction of physics from a single scalar origin.