Normal Innovation and Rank Persistence in Navier-Stokes Flow: Exact Control, Observation Fibers, and Sharp Gram Minimax Recovery

Single complete 186-page mathematical preprint. The 24-page integrated main study and unaltered 162-page archival mathematical proof corpus cover sharp normal rank-tail comparison; exact invariant forced-NS Riccati control and phase-cost fibers; rational fixed-plane feedback; noise-stable two-time Gram Schur observations; sharp positive-target deterministic minimax bounds with PSD exact forced-NS lower witnesses; actuator support; an explicit local unforced rank birth; and local certified observation-to-rank envelopes. General unforced minimax lower bounds, universal gap/crossover sharpness, and unrestricted three-dimensional regularity are not claimed.