Ξ₀: The Fundamental Quantum of Functional Coherence — Theory, Topological Foundations, and Experimental Validation

This work presents the most complete and rigorous formulation of the Universal Functional Coherence Theory (UFCT) centered on the discovery and validation of the fundamental constant Ξ₀, interpreted as the minimal quantum of functional execution in the universe. The article unifies the theoretical, topological, and experimental foundations of Ξ₀, deriving it from first principles via Chern classes, integrating it into the master equation of functional coherence, and confirming its invariance across independent physical domains: Cosmic Microwave Background (Planck data), high-energy neutrinos (IceCube), and neutrino mass measurements (KATRIN). With no free parameters, the predictions achieve relative errors below 0.03% and R² ≥ 0.998, establishing Ξ₀ as a falsifiable and universal physical constant. The work follows ABNT and international scientific standards, offering a complete framework for theoretical derivation, computational reproducibility, and experimental protocols for testing Ξ₀ in cosmology, particle physics, and condensed matter systems.