{"paper":{"title":"Strict 2.5D Shadows for One-Component Navier-Stokes Regularity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Runlong Yu","submitted_at":"2026-06-10T06:50:04Z","abstract_excerpt":"We formulate and prove a conditional finite-scale reduction theorem for the local one-component regularity problem for suitable weak solutions of the three-dimensional Navier--Stokes equations. Starting from a scale-invariant bound Phi(1) <= M and smallness of the critical vertical component C_3(1) = delta, the argument compares the solution with a strict two-and-a-half-dimensional shadow class. The comparison is made in the harmonic-pressure quotient, which is the natural local topology for pressure compactness. The Reynolds commutator produced by coarse graining is treated as a positive cova"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11720","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.11720/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}