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| Format: | Recurso digital |
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Zenodo
2026
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| Matèries: | |
| Accés en línia: | https://doi.org/10.5281/zenodo.18514005 |
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- <p>We present a structural reduction of the global regularity problem for the three–dimensional incompressible Navier–Stokes equations. Building on the geometric formulation of vortex stretching, we show that any finite–time singularity must pass through a unique obstruction: persistent alignment of the vorticity direction with the extremal strain eigenframe across infinitely many scales and turnover intervals.</p> <p>We then exclude this configuration by two independent rigidity mechanisms. First, we prove that any quantitative Lagrangian mixing (anti–congruence) enforces angular leakage incompatible with sustained alignment. Second, even in the absence of mixing, we show that persistent non–algebraic locking induces a finite congruence allocation problem admitting a uniform dual deficit; this deficit propagates across scales via a distinctness principle adapted from odd covering systems.</p> <p>As a consequence, all non–algebraic blow–up scenarios are structurally excluded. Any remaining singularity would have to lie in a finite–dimensional algebraic symmetry class, for which global regularity is already known. The argument is deterministic, finite, and avoids probabilistic, entropy, or genericity assumptions.</p>