Conditional Reconstruction Closure C: Pre-Metric Closure: Integrability, Externally Sourced Compatibility, and Gauge Reconnection

This paper studies, without introducing a metric, the Hodge star operator, ora specific gauge group, which electromagnetic equations a local constraint closurecan strictly translate, and where the claimed upper bound of the translation lies.The core construction is a partial translation map from certified local constraintconfigurations to cochains; the map is required only to preserve three structures—restriction, exterior differentiation, and source coupling—and does not presupposefullness, faithfulness, or essential surjectivity. On this interface, the flagship theorem C-CT2 yields the equation content of the translation image: if the closureforces the integrability residual and the source residual to vanish, then dF = 0 anddH =J hold, andthe complex axiom immediately gives dJ = 0. This paper furthergives a complete account of Abelian gauge reconnection: the curvature is invariantunder additive gauge transformations, and on a contractible complex the gaugeequivalence classes are uniquely labeled by the curvature; the systematic classification of the non-Abelian case is registered as an external debt and is not pre-spentat this layer. Explicit witnesses of three-account separation falsify the two statements the information loss coefficient is the dissipation coefficient” and informationconservation is equivalent to the sourced equation.” Six registered machine-checkeditems pass verification under the given inputs, cell orderings, Appendix B conventions, and Appendix C registrations, using exact integer and rational arithmetic;their exact arithmetic readings provide the underlying ledger for the numerical assertions in the later text. The claimed upper bound of this paper is explicit: onlythe pre-metric system is obtained; the vacuum Maxwell equations, constitutive relations, the Lorentz force, and energy conservation are not obtained; J is an externalinput, and the material structure lies outside the scope of the construction.