Complete Detectable Spacetime Geometry II: A Unified Variational Closure Principle for the spectral reconstruction of the Standard Model and Emergent Gravitational Sectors

This work develops a unified variational formulation of Complete Detectable Spacetime Geometry (CDSG), extending prior results on admissible physical structure to a quantitative reconstruction of the Standard Model and its gravitational and cosmological extensions. The framework is based on the requirement that physically realizable processes correspond to closure-complete spacetime action histories together with detectability and consistency constraints that exclude irreducible hidden defects. A generalized action functional is introduced, I_CDSG = S_loc + Γ_cl , where S_loc recovers local field dynamics and Γ_cl encodes contributions from admissible closure histories. Imposing a unified variational condition over fields, histories, spectral parameters, and fermionic modes provides a common structural origin for dynamics, coupling constants, and flavor mixing. Within this framework, the Standard Model appears as the minimal anomaly-free closure sector. Gauge couplings arise as inverse spectral stiffness of closure operators, with the electromagnetic coupling obtained from a minimal periodic spectrum. Quantum corrections are identified with recirculating closure histories, reproducing the leading anomalous magnetic moment contribution a (1) ℓ = α/(2π). Fermions emerge as spinorial closure eigenmodes, with generation structure corresponding to discrete spectral branches, and CKM/PMNS mixing matrices arising from misalignment of closure eigenbases. Variation with respect to the spacetime metric recovers General Relativity as the leading-order closure geometry, while higher-order closure contributions generate additional stress-energy components. These contributions admit an effective interpretation in which recirculation-induced terms produce dark-matter-like behavior at galactic scales, while a residual closure spectral floor yields a vacuum-energy contribution of the observed order. Detailed quantitative fits are left for subsequent work. The resulting framework organizes quantum field theory, the Standard Model, gravitation, and cosmology as scale-dependent manifestations of a single variational closure principle. The construction provides a unified structural and mechanistic foundation, while precise numerical determination of all parameters and higher-order effects remains an open program.