Post-Gate Obstruction Taxonomy for Cutoff-Regularized Coulomb BBGKY Defects

This preprint develops a post-gate obstruction taxonomy for cutoff-regularized Coulomb-type BBGKY defects. The paper proves an additive-dictionary exhaustion theorem: if a normalized obstruction witness sees a surviving singular residual while annihilating all certified corrections in a declared additive class, then no correction inside that class can remove the residual in the selected observable-dual topology. The manuscript separates theorem-level claims from classification principles, conditional mechanism contracts, and open target theorems. It does not claim cutoff-free Coulomb BBGKY closure, impossibility of closure in principle, or unconditional success of noncommutative evolution, feedback adaptation, or operator-valued renormalization. The paper is intended as a post-gate diagnostic layer following the Coulomb Gate analysis and as a structured map of the escape mechanisms required for future work.