[13] COS-CL - Collapsing-Structure Classical Limit: Classical field equations in the variational refinement limit of discrete models (GR, Yang-Mills, Dirac, Higgs/Yukawa)

This manuscript proves the classical continuum limit of coupled discrete actions on COS (Collapsing-Structure) refinement families, combining Regge-type gravity, holonomy-based lattice Yang–Mills, a vertex-based Dirac discretization, and Higgs/Yukawa couplings within a unified variational framework. Under shape regularity and compatibility assumptions (consistent logarithm/branch choices for holonomies and the Lorentz sector; local geometric matching and curvature control; gauge and spin consistency; and coercive norm estimates), any stationary discrete refinement sequence admits a subsequence whose Whitney/FEEC reconstructions converge (in appropriate weak topologies) to a limiting configuration C = (g, A, ψ, Φ). The limit is weakly stationary for the corresponding continuous coupled action and therefore satisfies the Einstein–Yang–Mills–Dirac–Higgs/Yukawa field equations, including an effective mass/source contribution induced by the Yukawa coupling. The proof is modular, relying on DEC/Whitney norm stability, quadrature and moment control, compactness from energy estimates (with local gauge fixing when needed), and sector-wise consistency of the first variation.