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Given any points $q_1,\\ldots, q_k$ in the domain, we find initial and boundary data so that the solution blows-up preci"},"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":"1702.05801","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-19T21:54:57Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"e6eacbcaa9ebb6b52952e87f19032455306b6309cd5303f8d84610e75ee513c3","abstract_canon_sha256":"9c696c2ee94fc8e20cef75ddd7e05f6ee6e91b49100199df207a7f13a01aece4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:26.939615Z","signature_b64":"eL0BjJXGwlh5tg4T1LGHfPjqHqShBlg44WqKKvrzdbMdJuNFqL5LRCCO1weRVM5w31wbd21pi4iZt3cBJWt2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ca7e9cc943ed503b465505f03aaa5552425cace141476dfb76f20b96effa631","last_reissued_at":"2026-05-17T23:40:26.938821Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:26.938821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Singularity formation for the two-dimensional harmonic map flow into $S^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Juan Davila, Juncheng Wei, Manuel del Pino","submitted_at":"2017-02-19T21:54:57Z","abstract_excerpt":"We construct finite time blow-up solutions to the 2-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 &= \\varphi \\quad \\text{on } \\partial \\Omega\\times(0,T) \\\\ u(\\cdot,0) &= u_0 \\quad \\text{in } \\Omega , \\end{align*} where $\\Omega$ is a bounded, smooth domain in $\\mathbb{R}^2$, $u: \\Omega\\times(0,T)\\to S^2$, $u_0:\\bar\\Omega \\to S^2$ is smooth, and $\\varphi = u_0\\big|_{\\partial\\Omega}$. Given any points $q_1,\\ldots, q_k$ in the domain, we find initial and boundary data so that the solution blows-up preci"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05801","kind":"arxiv","version":2},"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":"1702.05801","created_at":"2026-05-17T23:40:26.938976+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.05801v2","created_at":"2026-05-17T23:40:26.938976+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05801","created_at":"2026-05-17T23:40:26.938976+00:00"},{"alias_kind":"pith_short_12","alias_value":"NST6TTEUH3KQ","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"NST6TTEUH3KQHNDF","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"NST6TTEU","created_at":"2026-05-18T12:31:34.259226+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2112.14255","citing_title":"Strict type-II blowup in harmonic map flow","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NST6TTEUH3KQHNDFKBPQHKVFKU","json":"https://pith.science/pith/NST6TTEUH3KQHNDFKBPQHKVFKU.json","graph_json":"https://pith.science/api/pith-number/NST6TTEUH3KQHNDFKBPQHKVFKU/graph.json","events_json":"https://pith.science/api/pith-number/NST6TTEUH3KQHNDFKBPQHKVFKU/events.json","paper":"https://pith.science/paper/NST6TTEU"},"agent_actions":{"view_html":"https://pith.science/pith/NST6TTEUH3KQHNDFKBPQHKVFKU","download_json":"https://pith.science/pith/NST6TTEUH3KQHNDFKBPQHKVFKU.json","view_paper":"https://pith.science/paper/NST6TTEU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.05801&json=true","fetch_graph":"https://pith.science/api/pith-number/NST6TTEUH3KQHNDFKBPQHKVFKU/graph.json","fetch_events":"https://pith.science/api/pith-number/NST6TTEUH3KQHNDFKBPQHKVFKU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NST6TTEUH3KQHNDFKBPQHKVFKU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NST6TTEUH3KQHNDFKBPQHKVFKU/action/storage_attestation","attest_author":"https://pith.science/pith/NST6TTEUH3KQHNDFKBPQHKVFKU/action/author_attestation","sign_citation":"https://pith.science/pith/NST6TTEUH3KQHNDFKBPQHKVFKU/action/citation_signature","submit_replication":"https://pith.science/pith/NST6TTEUH3KQHNDFKBPQHKVFKU/action/replication_record"}},"created_at":"2026-05-17T23:40:26.938976+00:00","updated_at":"2026-05-17T23:40:26.938976+00:00"}