13 COS-CL - Collapsing-Structure Classical-Limit Derivation: Conditional classical limit: imported COS-PRI/COS-QD Gamma-core, reconstruction and first-variation bridge

COS-CL develops the conditional classical-limit bridge of the Collapsing-Structure (COS) program. The manuscript systematizes how coupled discrete actions on controlled COS refinement families can be related, under explicit regularity, compatibility, reconstruction, and compactness assumptions, to weak continuum field equations. The module treats Regge-type gravity, holonomy-based lattice Yang-Mills terms, vertex-based Dirac discretizations, Higgs fields, and Yukawa couplings within a common variational framework. Discrete configurations are compared with continuum fields through Whitney/DEC-FEEC reconstruction, de Rham maps, test-function lifting, compactness estimates, and first-variation transfer. The refinement limit is understood as improved effective resolution relative to macroscopic scales, not as a physical edge-length limit to zero. The main result is conditional: stationary or near-stationary discrete sequences in the controlled refinement class, with suitable shape regularity, branch control, gauge and spin compatibility, energy bounds, and reconstruction assumptions, admit subsequential weak limits that are stationary for the corresponding continuous coupled action. In this weak variational sense, the target Einstein-Yang-Mills-Dirac-Higgs/Yukawa equations are recovered within the stated classical-limit regime. COS-CL does not claim unconditional classicization, a global Einstein-attractor theorem, or a derivation of Standard-Model couplings from geometry. The Gamma-convergence core is treated as an imported conditional interface from the COS-PRI/COS-QD modules; COS-CL specifies the reconstruction topology, Regge-to-Einstein-Hilbert passage, first-variation bridge, and energy-momentum/source compatibility. The accompanying supplement provides the fuller citable proof stack and status audit for the reconstruction, compactness, gauge-fixing, Hessian, and local-domain-control components.