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For nontrivial compactly supported data that are odd in \\(z\\), nonpositive for \\(z>0\\), and satisfy the hypotheses of the main theorem, we prove \\[\n  \\lim_{t\\to\\infty}\n  \\frac{P(t)[\\log(2+t)]^{5/2}}{(1+t)^{3/2}}=+\\infty,\n  \\qquad\n  P(t):=\\iint_{\\Pi_+}r^"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2511.03171","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-11-05T04:39:20Z","cross_cats_sorted":[],"title_canon_sha256":"940a11231c9d3291999105d64f1e063d47f73dd2a22cf22a5009128398601732","abstract_canon_sha256":"64c1a761ef7df60ed78e42d29c720ebd541159c560d3e58171f4289bde534df9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-29T01:25:31.146236Z","signature_b64":"izuGMkFqSdoV/GAqKt9uXHTUpFmbs3FH8/9KuHmlBHRKVzreiaaQ+NW/pVYbvGIIL1zQbK610MXA0izTi5YUDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31c11ec6d64dc90c7b7b7e57aa538efb186e35e2a6ec2bc3f94800464b438a64","last_reissued_at":"2026-07-29T01:25:31.145260Z","signature_status":"signed_v1","first_computed_at":"2026-07-29T01:25:31.145260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vortex Stretching for Axisymmetric Euler Flows Without Swirl: Three-Halves Radial-Moment Growth and Near-Linear Growth of the Vorticity Maximum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daomin Cao, Guolin Qin, Junhong Fan","submitted_at":"2025-11-05T04:39:20Z","abstract_excerpt":"We study long-time vortex stretching for three-dimensional axisymmetric Euler flows without swirl in the head-on collision geometry of anti-parallel vortex rings that motivated Childress's \\(t^{4/3}\\) conjecture [S.~Childress, \\emph{Physica D} \\textbf{237} (2008), 1921--1925] for optimal vorticity growth in the full axisymmetric no-swirl class. For nontrivial compactly supported data that are odd in \\(z\\), nonpositive for \\(z>0\\), and satisfy the hypotheses of the main theorem, we prove \\[\n  \\lim_{t\\to\\infty}\n  \\frac{P(t)[\\log(2+t)]^{5/2}}{(1+t)^{3/2}}=+\\infty,\n  \\qquad\n  P(t):=\\iint_{\\Pi_+}r^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.03171","kind":"arxiv","version":3},"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/2511.03171/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2511.03171","created_at":"2026-07-29T01:25:31.145711+00:00"},{"alias_kind":"arxiv_version","alias_value":"2511.03171v3","created_at":"2026-07-29T01:25:31.145711+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.03171","created_at":"2026-07-29T01:25:31.145711+00:00"},{"alias_kind":"pith_short_12","alias_value":"GHAR5RWWJXEQ","created_at":"2026-07-29T01:25:31.145711+00:00"},{"alias_kind":"pith_short_16","alias_value":"GHAR5RWWJXEQY633","created_at":"2026-07-29T01:25:31.145711+00:00"},{"alias_kind":"pith_short_8","alias_value":"GHAR5RWW","created_at":"2026-07-29T01:25:31.145711+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GHAR5RWWJXEQY633PZL2UU4O7M","json":"https://pith.science/pith/GHAR5RWWJXEQY633PZL2UU4O7M.json","graph_json":"https://pith.science/api/pith-number/GHAR5RWWJXEQY633PZL2UU4O7M/graph.json","events_json":"https://pith.science/api/pith-number/GHAR5RWWJXEQY633PZL2UU4O7M/events.json","paper":"https://pith.science/paper/GHAR5RWW"},"agent_actions":{"view_html":"https://pith.science/pith/GHAR5RWWJXEQY633PZL2UU4O7M","download_json":"https://pith.science/pith/GHAR5RWWJXEQY633PZL2UU4O7M.json","view_paper":"https://pith.science/paper/GHAR5RWW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2511.03171&json=true","fetch_graph":"https://pith.science/api/pith-number/GHAR5RWWJXEQY633PZL2UU4O7M/graph.json","fetch_events":"https://pith.science/api/pith-number/GHAR5RWWJXEQY633PZL2UU4O7M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GHAR5RWWJXEQY633PZL2UU4O7M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GHAR5RWWJXEQY633PZL2UU4O7M/action/storage_attestation","attest_author":"https://pith.science/pith/GHAR5RWWJXEQY633PZL2UU4O7M/action/author_attestation","sign_citation":"https://pith.science/pith/GHAR5RWWJXEQY633PZL2UU4O7M/action/citation_signature","submit_replication":"https://pith.science/pith/GHAR5RWWJXEQY633PZL2UU4O7M/action/replication_record"}},"created_at":"2026-07-29T01:25:31.145711+00:00","updated_at":"2026-07-29T01:25:31.145711+00:00"}