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Moreover, we provide a complete characterization of the limiting behavior of the $C^{1,\\alpha}$ blowup profiles and the associated $C^{1,\\alpha}$ blowup solutions as $\\alpha\\to(1/3)^-$. 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Moreover, we provide a complete characterization of the limiting behavior of the $C^{1,\\alpha}$ blowup profiles and the associated $C^{1,\\alpha}$ blowup solutions as $\\alpha\\to(1/3)^-$. Specifically, as $\\alpha \\to(1/3)^-$, the spatial blowup rate $c_{x,\\alpha}$ diverges to $\\infty$, while the $C^{1,\\alpha"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For any α ∈ (0, 1/3), we construct exact C^{1,α} self-similar blowup profiles for the 3D incompressible Euler equation without swirl, and build on them to prove asymptotically self-similar blowup from C_c^α initial vorticity and C^{1,α}∩L^2 initial velocity. Moreover, as α→(1/3)^-, the spatial blowup rate diverges while the profile converges to a nonzero multiple of r^{1/3} W̄_{1/3}(z).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The fixed-point map defined from the 1D approximate profile is a contraction in the chosen anisotropic weighted space, and the subsequent finite-codimension stability holds in the low-regularity C^{1,α} topology; both rely on the integration-by-parts identity along trajectories that exploits the Euler equation twice.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Constructs C^{1,α} self-similar blowup profiles for 3D Euler without swirl for α<1/3 and proves asymptotically self-similar blowup with limiting factorization to a 1D profile as α approaches 1/3 from below.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The 3D incompressible Euler equations without swirl admit exact C^{1,α} self-similar blowup profiles for every α below 1/3, which are reached asymptotically from C_c^α initial vorticity.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0d727c6e260e59eae91fe838108a40d7a65a2131d2ceccbbed154dc16d383345"},"source":{"id":"2605.15130","kind":"arxiv","version":1},"verdict":{"id":"f18caab9-e257-43f5-9560-5f7ae6720add","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T03:07:51.749800Z","strongest_claim":"For any α ∈ (0, 1/3), we construct exact C^{1,α} self-similar blowup profiles for the 3D incompressible Euler equation without swirl, and build on them to prove asymptotically self-similar blowup from C_c^α initial vorticity and C^{1,α}∩L^2 initial velocity. 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