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This work aims to develop a finite-rank tensor-corrector mechanism for BBGKY closure in phase dynamics.

May 24, 2026Open Access

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

Key Points

This work aims to develop a finite-rank tensor-corrector mechanism for BBGKY closure in phase dynamics.
Constructed a rank-two tensor-memory response block in a two-dimensional regularized logarithmic density framework.
Proved a rank-two closure estimate under specific conditions including angular-tail and amplitude-variation.
Outlined convergence conditions with a witness value of omega = 1/12.
Demonstrated closure estimate validity under nondegeneracy and memory-lag conditions.
Showed that scalar correction can be replaced by a tensor-corrector mechanism.
Established conservative admissible conditions for convergence without claiming trace-norm propagation.

Abstract

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.

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