Advances, Extensions, and Validations of the Universal Functional Coherence Theory: New Corollaries on Recursivity, Arrow of Time, and Minimal Functional Constant

This work presents rigorous advances, extensions, and validations of the Universal Functional Coherence Theory (UFCT), an innovative framework aiming to unify fundamental physics based on the concept of functional coherence of the universe. The research formalizes new mathematical corollaries on the recursivity of the scalar functional field χ(x), elucidates the topological origin of the arrow of time, and confirms the universal conservation of the minimal functional constant Ξ₀, which is fundamental for the stability and evolution of the cosmos. Additionally, quantum-topological self-correction mechanisms, such as the κ-Gaussian filter, and evidence of fractal structures and modular quantization in global coherence are introduced. The work combines theoretical formulations, advanced computational simulations, and confrontations with observational data (CMB, IceCube, KATRIN), demonstrating high precision and falsifiability. This document represents a decisive step towards consolidating the UFCT as a testable, comprehensive, and unifying physical theory with potential impact across physics, cosmology, and information theory.