Density-Selected Phase Dynamics: Cutoff-Admissible Propagation, Weak Readout Floors, and Operating Windows

This preprint develops a conservative microscopic propagation-of-chaos framework for density-selected phase dynamics with singular kernels. The manuscript isolates a cutoff-admissible route rather than claiming an unrestricted self-consistent singular feedback theorem. For fixed regularized kernels and a prescribed density path, the common density-selected one-body field cancels algebraically in the Pickl derivative, leaving the finite-N pair-fluctuation contribution as the main microscopic error. Under explicit polynomial cutoff losses, a cutoff schedule is used to pass to a singular or cutoff-admissible density defect, which is then exported to the weak topology used in inverse-readout certification. The resulting theorem package connects cutoff external-density propagation, singular-passage bookkeeping, a Sobolev-embedding weak readout interface, and an operating-window optimization balancing the many-body floor against finite-time Richardson readout bias. The softened three-dimensional Coulomb benchmark is treated as an obstruction and verification roadmap: the naive derivative route produces a cutoff-dependent Gronwall coefficient and is therefore not claimed as a complete Coulomb proof. A two-dimensional logarithmic kernel is recorded as a softer future benchmark candidate.