{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:UMQEJPA3IU32A3OKEZHVIGCRVS","short_pith_number":"pith:UMQEJPA3","schema_version":"1.0","canonical_sha256":"a32044bc1b4537a06dca264f541851acba9be3f5931aeace329ce78f8ccf5a6c","source":{"kind":"arxiv","id":"1711.05387","version":1},"attestation_state":"computed","paper":{"title":"Infinite time blow-up for half-harmonic map flow from $\\mathbb{R}$ into $\\mathbb{S}^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Yannick Sire, Youquan Zheng","submitted_at":"2017-11-15T02:52:26Z","abstract_excerpt":"We study infinite time blow-up phenomenon for the half-harmonic map flow \\begin{equation}\\label{e:main00} \\left\\{\\begin{array}{ll}\n  u_t = -(-\\Delta)^{\\frac{1}{2}}u + \\left(\\frac{1}{2\\pi}\\int_{\\mathbb{R}}\\frac{|u(x)-u(s)|^2}{|x-s|^2}ds\\right)u\\quad\\text{ in }\\mathbb{R}\\times (0, \\infty),\n  u(\\cdot, 0) = u_0\\quad\\text{ in }\\mathbb{R},\n  \\end{array} \\right. \\end{equation} with a function $u:\\mathbb{R}\\times [0, \\infty)\\to \\mathbb{S}^1$. Let $q_1,\\cdots, q_k$ be distinct points in $\\mathbb{R}$, there exist an initial datum $u_0$ and smooth functions $\\xi_j(t)\\to q_j$, $0<\\mu_j(t)\\to 0$, as $t\\to "},"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":"1711.05387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-15T02:52:26Z","cross_cats_sorted":[],"title_canon_sha256":"f4066375a7abf03d14ba9a9f32746e341a945df07ce647625baed41313c0157c","abstract_canon_sha256":"c1430e660e1e73f1ccc9cc4a958c72696afc85ee89ab6f5aa3a71c279bde08b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:33.419880Z","signature_b64":"eWgMTogNdgep7SyvgtsWmDPyTcSJaigTFL/T49XWzeFEWPVCTUGqEqaANoMc6rwW3BllF94a6zuAifwOutJDBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a32044bc1b4537a06dca264f541851acba9be3f5931aeace329ce78f8ccf5a6c","last_reissued_at":"2026-05-18T00:30:33.419333Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:33.419333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinite time blow-up for half-harmonic map flow from $\\mathbb{R}$ into $\\mathbb{S}^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Yannick Sire, Youquan Zheng","submitted_at":"2017-11-15T02:52:26Z","abstract_excerpt":"We study infinite time blow-up phenomenon for the half-harmonic map flow \\begin{equation}\\label{e:main00} \\left\\{\\begin{array}{ll}\n  u_t = -(-\\Delta)^{\\frac{1}{2}}u + \\left(\\frac{1}{2\\pi}\\int_{\\mathbb{R}}\\frac{|u(x)-u(s)|^2}{|x-s|^2}ds\\right)u\\quad\\text{ in }\\mathbb{R}\\times (0, \\infty),\n  u(\\cdot, 0) = u_0\\quad\\text{ in }\\mathbb{R},\n  \\end{array} \\right. \\end{equation} with a function $u:\\mathbb{R}\\times [0, \\infty)\\to \\mathbb{S}^1$. Let $q_1,\\cdots, q_k$ be distinct points in $\\mathbb{R}$, there exist an initial datum $u_0$ and smooth functions $\\xi_j(t)\\to q_j$, $0<\\mu_j(t)\\to 0$, as $t\\to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05387","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":"1711.05387","created_at":"2026-05-18T00:30:33.419419+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.05387v1","created_at":"2026-05-18T00:30:33.419419+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05387","created_at":"2026-05-18T00:30:33.419419+00:00"},{"alias_kind":"pith_short_12","alias_value":"UMQEJPA3IU32","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"UMQEJPA3IU32A3OK","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"UMQEJPA3","created_at":"2026-05-18T12:31:46.661854+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/UMQEJPA3IU32A3OKEZHVIGCRVS","json":"https://pith.science/pith/UMQEJPA3IU32A3OKEZHVIGCRVS.json","graph_json":"https://pith.science/api/pith-number/UMQEJPA3IU32A3OKEZHVIGCRVS/graph.json","events_json":"https://pith.science/api/pith-number/UMQEJPA3IU32A3OKEZHVIGCRVS/events.json","paper":"https://pith.science/paper/UMQEJPA3"},"agent_actions":{"view_html":"https://pith.science/pith/UMQEJPA3IU32A3OKEZHVIGCRVS","download_json":"https://pith.science/pith/UMQEJPA3IU32A3OKEZHVIGCRVS.json","view_paper":"https://pith.science/paper/UMQEJPA3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.05387&json=true","fetch_graph":"https://pith.science/api/pith-number/UMQEJPA3IU32A3OKEZHVIGCRVS/graph.json","fetch_events":"https://pith.science/api/pith-number/UMQEJPA3IU32A3OKEZHVIGCRVS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UMQEJPA3IU32A3OKEZHVIGCRVS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UMQEJPA3IU32A3OKEZHVIGCRVS/action/storage_attestation","attest_author":"https://pith.science/pith/UMQEJPA3IU32A3OKEZHVIGCRVS/action/author_attestation","sign_citation":"https://pith.science/pith/UMQEJPA3IU32A3OKEZHVIGCRVS/action/citation_signature","submit_replication":"https://pith.science/pith/UMQEJPA3IU32A3OKEZHVIGCRVS/action/replication_record"}},"created_at":"2026-05-18T00:30:33.419419+00:00","updated_at":"2026-05-18T00:30:33.419419+00:00"}