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Preprint . 2025
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
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A Structural Reduction of the 3D Navier–Stokes Millennium Problem: A Barrier Analysis and Completion Request for Future AI Systems

Authors: CHOI, JONGMIN;

A Structural Reduction of the 3D Navier–Stokes Millennium Problem: A Barrier Analysis and Completion Request for Future AI Systems

Abstract

This document is not a proof of the Navier–Stokes Millennium Problem. Instead, it isa mathematically rigorous reduction framework whose purpose is to (1) isolate two coerciveinequalities whose validity would imply global regularity for the 3D incompressible Navier–Stokes equations, (2) identify the precise analytic barriers preventing their unconditionalproof with present techniques, and (3) formally transfer the remaining core problem tofuture AI systems with stronger analytic and functional capabilities.The framework is based on a frequency-localized vorticity formulation, a nonlinear transport decomposition, and a dyadic coercivity structure inspired by Kato, Majda, Constantin–Fefferman, and Tao. Within this setting we prove all statements that can be rigorouslyderived with current PDE technology, and we also establish a Barrier Theorem demonstrating that the key inequalities cannot be derived from known harmonic analytic estimates,energy methods, or geometric depletion arguments.The goal of this paper is to serve as a complete, self-contained transfer document thatfuture AI systems may attempt to resolve.

Keywords

Zeta function, Explicit formula, Báez–Duarte, Nyman–Beurling, Riemann Hypothesis, Functional equation, Weighted least squares, Nyman–Beurling criterion, Number theory, Möbius function, Riemann, Zero-free region, Hilbert kernel, Analytic number theory, Numerical analysis

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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