The Unified Compression-Based Field (UCBF) Framework: A Geometric Derivation of Fundamental Constants from Vacuum Lattice Properties

The Unified Compression-Based Field Theory (UCBF) models the vacuum as a pre-stressed face-centered cubic (FCC) quantum elastic manifold characterized by three substrate parameters: pressure P ≈ 6.03 × 10^34 Pa, density ρ ≈ 6.70 × 10^17 kg/m^3, lattice constant a ≈ 1.35 fm. Mechanical incompressibility (unimodular constraint) eliminates the contribution of the enormous background vacuum pressure to gravitating energy, thereby resolving the cosmological constant problem at the level of the field equations. From the substrate triple (P, ρ, a) follow the effective constants of nature via geometric necessity: the speed of light c = √(P/ρ), Planck’s constant h = ρ c a^4, Newton’s gravitational constant G = c^3/(Ω P) with Ω ≈ 6.7 a dimensionless FCC compliance factor, the fine-structure constant α fixed by the rhombic dodecahedron flux automorphism group, the electron mass m_e as the self-energy of a screw-dislocation/phase-vortex defect with core radius of order a. Identifying a ≈ 1.35 fm with the hadronic/QCD coherence length corrects earlier interpretive misassignments of energy scales, unifying strong interactions with the elastic limits of the medium while keeping gravity as an emergent impedance-suppressed sector. All Standard-Model particles are topological defects in the FCC manifold and all forces are strain propagation modes. Small residual discrepancies at the level of ≲0.5% in derived constants are attributed to higher-order lattice dispersion and defect-energy renormalization intrinsic to the same mechanical framework, not to free parameters. The theory predicts: longitudinal gravitational waves at √3 c, TeV-scale Lorentz-violation signatures, a finite electron core radius of order a, a redshift-dependent MOND-like acceleration scale, providing a falsifiable mechanical alternative to geometric quantum field theory.