Higher-Correlation Residual Transfer for Post-Gate BBGKY Defects: Lift Estimates, Leakage Inheritance, and Finite-Depth Cascade Diagnostics

This preprint develops a finite-diagnostic framework for higher-correlation residual transfer in BBGKY-type hierarchies. Starting from a certified pair-level projected residual, the manuscript formulates a residual-transfer decomposition into inherited pair residual, lift error, and higher-truncation error. The main results are an upper pair-to-triple transfer bound, a transverse leakage-inheritance estimate governed by a co-Lipschitz diagnostic constant, and a finite-depth local cascade obstruction theorem for admissible higher-correlation lift/closure classes. The paper is deliberately diagnostic rather than a claim of full Coulomb BBGKY closure. It works in projected observation spaces, separates upper absorption bounds from lower cascade indicators, and includes failure-mode and ambiguity criteria. A finite-dimensional worked diagnostic example illustrates the computation of transfer and leakage constants and the resulting absorption/cascade/ambiguous classification.