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Abstract:We develop a finite-window audit and transfer framework for the local regularity problem of the three-dimensional incompressible Navier--Stokes equations. The paper has two logically separate components. First, a finite-scale critical ledger estimate shows that a persistent non-CKN branch cannot survive without cumulative untaxed critical supply or accumulated localization leakage. Second, a local-to-clean transfer theorem shows how a clean finite-window anti-phantom gap gives a localized coercive estimate for Navier--Stokes defect packages, provided three structural inputs hold: quotient-lifting stability, componentwise detection comparison, and a normalized residual budget. The technical contribution is an explicit bookkeeping of the residuals that can obstruct this transfer. Pressure tails, cutoff leakage, truncation loss, nonlinear cutoff mismatch, reproduction drift, gauge mismatch, and profit discrepancy are separated as finite-window ledger entries and then assembled into a concrete absorption criterion. The main transfer theorem is algebraic once these entries satisfy the stated normalized bounds; the PDE-facing work left open is precisely to prove the corresponding component compatibility estimates against the localized quotient distance. Thus the article is a conditional reduction. Its conclusion is structural: any surviving obstruction must either defeat the stated compatibility/growth controls or appear as an NS-realizable, cleaned, scale-critical, combined-invisible, profitable, reproducible defect cascade.

Submission history

From: Runlong Yu [view email]
[v1] Sat, 13 Jun 2026 03:36:40 UTC (49 KB)