{"paper":{"title":"A conditional Lagrangian clock barrier at the $C^{1,\\frac{1}{3}}$ threshold for axisymmetric Euler without swirl","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ovidiu-Neculai Avadanei","submitted_at":"2026-05-29T17:54:47Z","abstract_excerpt":"We consider axisymmetric no-swirl solutions to the three-dimensional incompressible Euler equations, with initial velocity in $C^{1,\\alpha}\\cap L^2$, where $\\alpha\\in\\left[\\frac{1}{3},1\\right)$. Motivated by Shkoller's Lagrangian clock-and-driver framework for finite-time blow-up below the $C^{1,\\frac{1}{3}}$ threshold, we introduce coherent Lagrangian classes of initial data and conditional solutions for which the same clock mechanism yields a supercritical/critical barrier when $\\alpha\\geq\\frac{1}{3}$, with a genuinely depleted barrier for $\\alpha>\\frac{1}{3}$ and an exponential bound at the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31587","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/2605.31587/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"}