Historical records: Topological Quantization of the Functional Action: An Ontological Principle for Physical Reality

This work establishes that quantization is not an empirical assumption but a topological necessity derived from the functional action of the Theory of Universal Functional Coherence (TUFC). By reformulating the action S[χ,ψ] in terms of the functional metric f = χ²/ψ, it demonstrates that the system admits only discrete values restricted by topological invariants. The resulting condition, S = n·(Dχ·Ξ₀)^(3/2), n ∈ ℤ, provides necessary and sufficient criteria for the existence of coherent reality. The study unifies quantum mechanics, relativity, and thermodynamics under a single ontological closure, reframing quantization as a theorem of existence. The appendices detail the mathematical foundations, numerical simulations, and connections with Planck units, general relativity, thermodynamics, topology, and cobordism, consolidating TUFC as a topological and ontological framework for physical reality.