[Exploratory Version] Pure Time Theory: Dynamical Derivation and Cosmological Stabilization of the Fundamental Constants [Exploratory Version]

This paper presents a comprehensive derivation of the five fundamental physical constants — c, G, h-bar, alpha, and k_B — within the framework of the Pure Time Theory (PTT), a novel paradigm where spacetime, matter, and all physical interactions emerge from a single scalar temporal field, T_relax. Through a logically sequenced approach, these constants arise dynamically from the structure and local gradients of T_relax, without assuming any pre-existing geometry, quantum structure, or arbitrary parameters. The central field equation, ∇² T_relax = beta × sqrt(rho), links time relaxation with energy density via a single dimensionless constant beta. Each physical constant is derived through a successive stabilization process, from wavefront propagation and curvature emergence to charge quantization and thermal fluctuations, forming a logically unified chain. The article also introduces a Lagrangian formulation of the theory, a preliminary quantization of the temporal field, and presents numerical predictions that can be tested through cold atom interferometry and cosmic data. A topological vortex-based mechanism for electric charge is validated through lattice simulations, suggesting robust stability under perturbations. By rooting all derivations in a single scalar field, PTT offers a new framework that unifies classical and quantum physics, gravity, and thermodynamics. The theory aligns with the Principle of Logical Unicity (PLU), offering a conceptually complete alternative to current models of unification.