Finite-Window Recursive Audit Chains for Navier-Stokes Generated Packages

We develop a finite-window recursive audit framework for Navier–Stokes-generated packages. On a fixed window, the underlying anti-phantom certificate asserts that a baseline-visible package is either detected locally or charged to an explicit residual ledger. The first component of the framework is a broad one-step admissibility criterion for pressure-admissible finite-energy Navier–Stokes-generated audit packages under an explicit ledger of synchronization, localization, projection, harmonic-tail, chart, clean-gap, gate/slack, and detector mismatches. The second component is a finite-chain propagation theorem: once one-step admissibility supplies a finite renormalized chain of packages and a static finite-window audit certificate is available at each scale, variable-coefficient error recursion and weighted summation yield a recursive finite-window anti-phantom lower bound. We also give compact/effective pressure projection criteria, reduced quotient chart visibility, clean detector gaps, a pressure–flux–energy matrix kernel condition, a smooth reduced NS-generated verification class, and a conditional Caffarelli–Kohn–Nirenberg compatible defect-extraction criterion.