This paper develops a conditional gate framework for cutoff-regularized Coulomb-type BBGKY defects in an observable-dual topology. It does not claim unconditional cutoff-free BBGKY closure, trace-norm propagation of chaos, or a complete microscopic cancellation theorem. The construction separates the problem into a model gate topology, coupled admissible triples, a scale-consistency meta-contract, macro and adaptive finite-rank budgets, a microscopic correction gate assumption, higher-order residual budgets, and a dictionaryrelative dual-witness obstruction alternative. The main theorem states that verified module estimates imply vanishing of the regularized defect in the selected observable topology. A finite-window toy instantiation is included to show that the algebraic gate is not merely formal: concrete exponent choices can pass all budget inequalities without asserting any physical Coulomb closure. The derivative bookkeeping for the explicit cutoff and the mollified-cutoff variant are stated so that cutoff-loss exponents, projector constants, and micro-correction constants remain visible in later model instantiations. Conversely, failure of the gate identifies precise targets for new short-scale estimates, enlarged dictionaries, radial or angular obstruction witnesses, topology-cost accounting, or a separate compactness-andidentification argument. The purpose is therefore not to finish the Coulomb endpoint, but to state exactly which estimates would be sufficient and which residual channels remain mathematically exposed.
Dmytro Panasenko (Mon,) studied this question.