Certified Rank-Selective Tensor Correctors for a Three-Dimensional Density-Selected BBGKY Benchmark

This preprint develops a certified rank-selective finite-rank tensor correction mechanism for a three-dimensional cutoff-regularized BBGKY benchmark with density-selected phase response. The construction uses an observable-dual topology matched to selected response/readout channels and a finite response menu with outcomes 3, 8, or fail. The main constructive branch is a rank-three dipole closure theorem under explicit dipole-admissibility and scale-safety gates; the rank-eight quadrupole branch is retained as a conditional diagnostic extension. The manuscript includes manufactured diagnostics and a reproducibility scaffold for the finite-dimensional response matrices and conservative exponent witness.