Dimensional Self-Consistency in the Universal Functional Coherence Theory: Criticality, Irreversibility, and the Origin of 3D Reality

Description This article presents a direct advancement in continuity with previous works related to the Universal Functional Coherence Theory (UFCT). It explicitly connects to κ ≈ 0.17: The Universal Threshold of Irreversibility (DOI: 10.5281/zenodo.17109905) and The Fisher–KPP Equation as the Universal Theory of Functional Coherence: Fractal Traveling-Wave Solutions and Ontological Criticality (DOI: 10.5281/zenodo.17110034), expanding and deepening their conclusions. While the first established κ ≈ 0.17 as the universal threshold of irreversibility and the second demonstrated the structural equivalence of the UFCT master equation with the Fisher–KPP equation, the present work advances by showing that the 3+1 dimensionality of the universe emerges as a result of a condition of critical self-consistency. Based on extensive simulations and rigorous mathematical analysis, it demonstrates that only in three spatial dimensions is the UFCT coherence front stable, sustained by a two-dimensional critical surface exhibiting Ising universality (δ = 1/8, η = 1/4). This result provides a causal explanation for the tridimensionality of the universe, unifying κ, δ, and χ² as fundamental invariants of reality. Thus, this article should be read in continuity with the previous works, functioning as an extension and refinement that consolidates UFCT as a predictive framework capable of simultaneously explaining the arrow of time, universal criticality, and the observed dimensionality of reality.