In a previous open letter to CERN (Oct 2025), we conjectured a continuity law coupling 4D Maxwell theory to a higher-dimensional bulk via a symmetry-constrained leakage current. This manuscript provides the rigorous sheaf-theoretic derivation of that phenomenological claim. We demonstrate that the apparent dimensional mismatch in the naive continuity equation d(⋆F − Js) = 0 resolves when treated within the derived category of constructible sheaves. Specifically, we identify the bulk-induced "current" not as a differential form of fixed degree, but as a hypercohomology class ω(η) ∈ H3(X,Rπ∗Jbulk). The projection of this class onto the physical vacuum induces a topological polarization 2-form Σbulk. We derive the exact scaling of the interferometric visibility floor, 1 − V ∼ Λ−2k, as a consequence of the spectral gap in the Leray-Serre spectral sequence of the compactification fibration. This establishes the theoretical consistency of the De Ceuster-Maxwell deformation.