Develops a recursive finite-window audit chain framework with anti-phantom certificates and propagation theorems for Navier-Stokes generated packages.
Schur Visibility and Anti-Phantom Reduction in One-Component Navier-Stokes Degeneration
3 Pith papers cite this work. Polarity classification is still indexing.
abstract
We study the finite-scale one-component degeneration problem for suitable weak solutions of the three-dimensional incompressible Navier--Stokes equations under a scale-invariant bound and smallness of the vertical component. Qualitative compactness gives convergence, in the harmonic-pressure quotient, toward the strict two-and-a-half-dimensional boundary, but it does not provide a quantitative rate. This paper proves, in an explicitly abstract trace-obstruction skeleton associated with the old observable closure, that the standard old observable package is insufficient to force a logarithmic or power selected-trace rate. The negative result is an envelope/skeleton theorem, not a Navier--Stokes counterexample. After excluding elementary high-frequency escape by parabolic trace drop and fixed-window analytic obstruction by finite-dimensional Lojasiewicz control, the remaining obstruction is an all-order finite-mode flat branch. We identify the Navier--Stokes-specific mechanism needed to control this branch: strict Schur trace-projectability may fail, but the resulting defect can be visible through the relaxed vertical-pressure channel. In active finite-window models, strict Schur phantoms are relaxed-visible. The final theorem is a conditional dichotomy: either relaxed anti-phantom closure holds and yields conditional logarithmic strict-shadow selection, or there exists an NS-realizable, cleaned, relaxed-invisible, unaligned left-singular cascade.
fields
math.AP 3years
2026 3verdicts
UNVERDICTED 3representative citing papers
Proves a finite-chain CKN-bad scale counting theorem for 3D Navier-Stokes via standard PDE closure with one-component compactness and an amended canonical detector realization.
Audit of Navier-Stokes obstruction calculus shows existing decompositions locate CKN badness transport but lack coercive estimates, proving a resolution lemma and identifying the need for a filtered stretching-diffusion estimate with subgrid terms.
citing papers explorer
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Finite-Window Recursive Audit Chains for Navier-Stokes Generated Packages
Develops a recursive finite-window audit chain framework with anti-phantom certificates and propagation theorems for Navier-Stokes generated packages.
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Finite-Chain CKN-Bad Scale Counting for Navier-Stokes: Standard PDE Closure and Canonical Detector Realization
Proves a finite-chain CKN-bad scale counting theorem for 3D Navier-Stokes via standard PDE closure with one-component compactness and an amended canonical detector realization.
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A Structural Audit of Navier-Stokes Obstruction Calculus
Audit of Navier-Stokes obstruction calculus shows existing decompositions locate CKN badness transport but lack coercive estimates, proving a resolution lemma and identifying the need for a filtered stretching-diffusion estimate with subgrid terms.