Finite-Window Computational Anti-Phantom Theorems for Scale-Critical Navier-Stokes Defects

Abstract

We prove a finite-window anti-phantom principle for scale-critical Navier--Stokes defect packages and develop a conditional localized transfer framework around it. In a fixed clean quotient, the main compactness theorem shows that if the only defect that is simultaneously invisible, exactly reproducible, and tax-free is a gauge artifact, then observation, reproduction failure, and tax control the clean quotient distance by a positive finite-window gap. We then isolate the additional localized inputs needed to use this clean gap for Navier--Stokes packages: pressure-source observability, enhanced pressure-tail geometry, chart visibility, and residual sub-budgets for localization, reproduction, and gate/tax mismatch. The localized results are conditional finite-window reductions with explicit error constants, including a comparison theorem between the enhanced-tail geometry and the original intrinsic geometry under stated projection and harmonic tail approximation assumptions. The paper should be read as a rigorous finite-window obstruction framework, not as a proof of Navier--Stokes regularity, a construction of a singular solution, or a scale-uniform regularity criterion.