Quadratic Characteristic Control for Charged Infrared Sectors: Selected-Packet Schur Reductions and Wilson–Yukawa Realizations

We develop a finite-regulator verification framework for a second-order infrared condition on charged states in theories with a massless electromagnetic tail. Rather than attempting a full construction of charged infraparticle sectors, the paper isolates the quadratic characteristic-function estimate required at the state level and reduces its verification to explicit microscopic bounds. The first step is a centered quadratic finite-difference criterion for bounded charged characteristics, together with a counterexample showing that first-order characteristic control alone does not imply the required second-order bound. For a retained-light decomposition, the heavy-side problem is then reduced from a full conditional Gram estimate to a single selected packet diagonal. Direct-contact and distinct-root connected contributions are controlled by separate Schur kernels before packet integration. A complementary fermion-first realization converts a background-uniform Wilson singular gap directly into a selected-packet operator bound. This formulation avoids an unnecessary physical-volume Schur summation and yields a normalization-stable estimate proportional to the inverse singular reserve. A selected-Yukawa full-multiplet realization is developed in which a positive reserve \(R_D\) implies\[s_{\min}(D_{\ell,T}^B)\ge R_D,\]and the corresponding selected-packet fermionic contribution is bounded by \(O(R_D^{-1})\) when the source-normalization ratio remains uniformly controlled. Pointwise exponential inverse localization is retained as a separate consequence. The paper also distinguishes several logically independent interfaces: source-coordinate floors, chiral mass orientation, kinetic-multiplet compatibility, packet normalization, and Euclidean-to-Minkowski characteristic identification. In particular, the Wilson realization is restricted to spin-independent or otherwise explicitly skew-accretive hopping structures; a generic chiral gauge discretization is not claimed to satisfy these assumptions automatically. The analytic ingredients—Schur estimates, finite-range inverse localization, Wilson fermions, and gauge-invariant Higgs–fermion composites—have established antecedents. The contribution is their organization into a verification architecture for a charged infrared second-fluctuation hypothesis. To the best of our knowledge, the specific selected-packet/two-Schur/Wilson verification chain developed here has not previously been formulated in this charged-infrared setting. The results are conditional sufficient criteria and microscopic realizations. The paper does not construct the full interacting gauge–Higgs–Yukawa Osterwalder–Schrader theory, prove interacting target/reference OS-Gram stability, establish the Euclidean-to-Minkowski characteristic identification, construct a complete charged infraparticle sector, or prove a final electron-inevitability theorem. Version 1.0. Reserved DOI: 10.5281/zenodo.23758901.