Parte III - Matemática da Unificação com MBs. v3

This article is Part III of a series on hylomorphic unification based on topological coherence. It proposes a formulation that integrates geometry, energy, and structure, where spacetime is interpreted as an emergent manifestation of a deeper topological coherence. The approach preserves the mathematical rigor of General Relativity while introducing an additional descriptive level — the effective topological level, represented by a symbolic coherence tensor that mediates curvature and energy without revealing its technological mechanism. The Axiom of Mathematical Hylomorphism provides the ontological foundation for the unity of form and matter, and the topological glue acts as the operator of continuity between domains, enabling space and time to emerge from a quantum–topological flow of coherence. The formalism leads naturally to the Equation of Emergence (Einstein–Jos), where relativity arises as the hydrodynamic limit of a discrete mesh of coherences. In cosmology, a functional coherence term behaves as a negative-pressure fluid (functional Λ), accounting for the universe’s accelerated expansion without invoking an inert vacuum. The formulation is self-testable, since the internal consistency between the physical and topological levels ensures correspondence with empirical observations. In summary, the universe is portrayed as a self-coherent hylomorphic structure in which micro- and macroscopic phenomena are complementary expressions of the same topological continuity; space, time, and energy emerge as rhythmic manifestations of coherence — the true “glue” that keeps being in act. Keywords: topological coherence; hylomorphism; unification; relativity; emergent cosmology; functional spacetime.