Finite-Rank Tensor Correctors for BBGKY Closure in Singular Density-Selected Phase Dynamics

This preprint develops a finite-rank tensor-corrector mechanism for projected BBGKY closure in a two-dimensional regularized logarithmic density-selected phase benchmark on the flat torus. The main construction replaces scalar memory correction by a rank-two tensor-memory response block in an observable-dual topology. The manuscript proves a rank-two closure estimate under response nondegeneracy, angular-tail, memory-lag, amplitude-variation, and scale-admissibility conditions, with a conservative admissible convergence witness omega = 1/12. No trace-norm propagation-of-chaos theorem and no full three-dimensional Coulomb closure are claimed. This record includes the manuscript PDF and the accompanying LaTeX source bundle.