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Here $\\Omega$ is a bounded, smooth axially symmetric domain in $\\mathbb{R}^3$. We prove that for any circle $\\Gamma \\subset \\Omega$ with the same axial symmetry, and any sufficiently small $T>0$ there exist initial and boundary conditions such tha"},"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":"1902.03995","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-11T16:53:31Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"38160066f9d9297573bb6d2731be8c84be522b26eeccce6bbcadbf4afd9ec8f9","abstract_canon_sha256":"4861dd145fa2d38c88997c0923a4f6cfcd50f377be31e8538ed74ee87ee230ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:17.417742Z","signature_b64":"3unLdLtJcM3IgihAljOsMFOpK2cz+q8XZF6Z45c34deIcg0Hy28SloWZwSM67YgakwMsrOyIud8HsuEtQuZaCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b27c7ee95b271618007dc9de3f7bf34d755f979b900f428b3e453cbff3d0efee","last_reissued_at":"2026-05-17T23:54:17.417077Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:17.417077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Blow-up for the 3-dimensional axially symmetric harmonic map flow into S2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Catalina Pesce, Juan Davila, Juncheng Wei, Manuel del Pino","submitted_at":"2019-02-11T16:53:31Z","abstract_excerpt":"We construct finite time blow-up solutions to the 3-dimensional harmonic map flow into the sphere $S^2$, \\begin{align*} u_t & = \\Delta u + |\\nabla u|^2 u \\quad \\text{in } \\Omega\\times(0,T) \\\\ u &= u_b \\quad \\text{on } \\partial \\Omega\\times(0,T) \\\\ u(\\cdot,0) &= u_0 \\quad \\text{in } \\Omega , \\end{align*} with $u(x,t): \\bar \\Omega\\times [0,T) \\to S^2$. Here $\\Omega$ is a bounded, smooth axially symmetric domain in $\\mathbb{R}^3$. We prove that for any circle $\\Gamma \\subset \\Omega$ with the same axial symmetry, and any sufficiently small $T>0$ there exist initial and boundary conditions such tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03995","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":""},"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":"1902.03995","created_at":"2026-05-17T23:54:17.417174+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.03995v1","created_at":"2026-05-17T23:54:17.417174+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03995","created_at":"2026-05-17T23:54:17.417174+00:00"},{"alias_kind":"pith_short_12","alias_value":"WJ6H52K3E4LB","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"WJ6H52K3E4LBQAD5","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"WJ6H52K3","created_at":"2026-05-18T12:33:30.264802+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/WJ6H52K3E4LBQAD5ZHPD667TJV","json":"https://pith.science/pith/WJ6H52K3E4LBQAD5ZHPD667TJV.json","graph_json":"https://pith.science/api/pith-number/WJ6H52K3E4LBQAD5ZHPD667TJV/graph.json","events_json":"https://pith.science/api/pith-number/WJ6H52K3E4LBQAD5ZHPD667TJV/events.json","paper":"https://pith.science/paper/WJ6H52K3"},"agent_actions":{"view_html":"https://pith.science/pith/WJ6H52K3E4LBQAD5ZHPD667TJV","download_json":"https://pith.science/pith/WJ6H52K3E4LBQAD5ZHPD667TJV.json","view_paper":"https://pith.science/paper/WJ6H52K3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.03995&json=true","fetch_graph":"https://pith.science/api/pith-number/WJ6H52K3E4LBQAD5ZHPD667TJV/graph.json","fetch_events":"https://pith.science/api/pith-number/WJ6H52K3E4LBQAD5ZHPD667TJV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WJ6H52K3E4LBQAD5ZHPD667TJV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WJ6H52K3E4LBQAD5ZHPD667TJV/action/storage_attestation","attest_author":"https://pith.science/pith/WJ6H52K3E4LBQAD5ZHPD667TJV/action/author_attestation","sign_citation":"https://pith.science/pith/WJ6H52K3E4LBQAD5ZHPD667TJV/action/citation_signature","submit_replication":"https://pith.science/pith/WJ6H52K3E4LBQAD5ZHPD667TJV/action/replication_record"}},"created_at":"2026-05-17T23:54:17.417174+00:00","updated_at":"2026-05-17T23:54:17.417174+00:00"}