Unified Dimension Diffusion Model (UDDM v2.5): A Complete Cosmological Framework Based on Energy Ontology, Global Relaxation, and Local Self-Constraint

Abstract Based on three core axioms of energy ontology, global relaxation, and local self-constraint without prior assumptions or circular definitions, this paper constructs a logically closed, mathematically rigorous, and dimensionally self-consistent Unified Dimension Diffusion Model (UDDM v2.5). Starting from energy primitives in a pre-geometric spacetime-free background, the model strictly derives the endogenous emergence process from a discrete topological network to 3 + 1-dimensional continuous spacetime. Based on the non-equilibrium directed active percolation theory[16], we deduce the micro-macro unified dynamic equation and the galaxy-scale effective diffusion coefficient, and modify the Einstein field equations to distinguish local baryonic matter, self-constraint effects, and the global relaxation background. This framework completely eliminates the circular definitions, phenomenological assumptions, and fine-tuning problems in traditional cosmology. Based on topological quantum field theory[13], this paper clarifies the general macroscopic expression of the quantum dissipation term, and strictly deduces that the steady-state self-constraint parameter ξ0​≈1.3 is a three-dimensional topological invariant. The corrected core formula for galactic rotation curves achieves full dimensional self-consistency, positive sign definiteness, and a physical magnitude that fully matches SPARC observations[9]. We provide an analytical solution for galactic dynamics with no free fitting parameters, which naturally resolves the core difficulties of the Λ-CDM model, including the cusp-core crisis, dark matter, dark energy, and Hubble tension. This paper supplements the operational definition of core concepts, the corresponding limit of general relativity, a strictly compatible framework for quantum mechanics, the emergence mechanism of particle properties, and a test scheme for the SPARC galaxy database. All predictions of the model are quantitatively testable, with galactic rotation curves as the preferred decisive test scenario, forming a complete cosmological research program fully consistent with Popper's scientific methodology[7].