Vacuum as Dense Fabric: Phase-Governed Gravity, Kernel K, and the Dual Projection Unification of α_EM and α_lam

This work presents a unified theoretical framework in which the quantum vacuum is modeled as a structured higher-dimensional coherence fabric rather than empty spacetime. The framework integrates Phase-Governed Gravity (PGG) with the Information Scale Lattice (ISL) constraint geometry programme. A 120×120 Cayley graph Laplacian kernel K constructed from the symmetric group S5 (η = 9 generators, Φ = 120 closure states) is explicitly derived and spectrally computed. Two physically motivated projection operators acting on K produce: • The electromagnetic fine-structure constant • The gravitational coherence constant Both emerge without free parameters as projections of the same kernel. The model further derives a Planck-scale natural vacuum viscosity, defines a dimensionless gravitational Reynolds number, explains the SPARC dwarf-galaxy alpha plateau, resolves the ultra-diffuse galaxy bifurcation, and predicts a hysteresis signature distinguishing the framework from MOND and ΛCDM. Seven quantitative, falsifiable predictions are provided for JWST, DESI, and galaxy kinematic datasets. All mathematical constructions, spectral properties, and falsification criteria are explicitly stated.