The Unified Compression-Based Field Theory (UCBF): Complete Geometric Version with Coherence Dynamics

This manuscript presents a complete and fully geometric formulation of the Unified Compression-Based Field Theory (UCBF), incorporating coherence dynamics and resolving the prior epistemic ambiguity between parameter fitting and genuine prediction. UCBF proposes that fundamental physical constants emerge from the ground-state structure of a discrete, compression-optimized spacetime lattice coupled to coherence dynamics, rather than being free parameters. The theory is reformulated here to achieve explicit identifiability closure through three independent mechanisms: (i) the derivation of scale-free, dimensionless predictions independent of arbitrary normalizations; (ii) a mathematical proof of structural uniqueness excluding nearby lattice configurations and interaction kernels; and (iii) the identification of novel, model-independent experimental observables with sharp falsification boundaries. The framework is developed with full mathematical rigor, including explicit axioms, definitions, theorems, and step-by-step derivations. All derived quantities are systematically classified as Derived, Anchored, or Test-separating, providing transparent epistemic status for each prediction. The theory predicts a discrete spectrum of coherence modes, a lattice-induced correction to gravitational coupling at short distances, and explicit relationships linking the fine-structure constant, lattice geometry, and electroweak symmetry breaking. Importantly, the manuscript explicitly identifies where the current formulation is falsified by existing experimental data—most notably in its predictions for the running of the fine-structure constant and the electroweak scale—thereby demonstrating that UCBF is a predictively distinct and falsifiable theoretical framework rather than a phenomenological fitting model. This work should be understood as a proof-of-concept for constructing highly constrained physical theories with minimal free parameters, explicit identifiability, and sharp falsification criteria, while clearly delineating the limitations that must be resolved in future developments.