{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:KTFJTAQXI3YP7AEGGICM2MG6CH","short_pith_number":"pith:KTFJTAQX","schema_version":"1.0","canonical_sha256":"54ca99821746f0ff80863204cd30de11fbc491ebd1fff59f0fd027d2225ad31e","source":{"kind":"arxiv","id":"2007.15370","version":1},"attestation_state":"computed","paper":{"title":"Nondispersive solutions to the mass critical half-wave equation in two dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Vladimir Georgiev, Yuan Li","submitted_at":"2020-07-30T10:46:07Z","abstract_excerpt":"We consider the half-wave equation with mass critical in two dimension \\begin{eqnarray*} \\begin{cases} iu_t=Du-|u|u,\\,\\,\\, \\\\ u(0,x)=u_0(x), \\end{cases} \\end{eqnarray*} First, we prove the existence of a family of traveling solitary waves. We then show the existence of finite-time blowup solutions with minimal mass $\\|u_0\\|_2=\\|Q\\|_2$, where $Q$ is the ground state solution of equation $DQ+Q=Q^2$."},"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":"2007.15370","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-07-30T10:46:07Z","cross_cats_sorted":[],"title_canon_sha256":"216bea944161d0fdc3bd4ca562401df7d986b40d83c5fdfc4639a320edd9b911","abstract_canon_sha256":"ccdab542cfe27fe2570b44e00ec3086638c45ee9d810ba34bb8c1aab037bedf3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:23:30.244923Z","signature_b64":"GmlJV1fwK2wIDIUoCtOm0G5j7xOV3O0mq+sSIV6CAVFzI3uNbS64ZmpOvtRGpmWb+vSiRZCy563iP+vu1dvGCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54ca99821746f0ff80863204cd30de11fbc491ebd1fff59f0fd027d2225ad31e","last_reissued_at":"2026-07-05T01:23:30.244521Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:23:30.244521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nondispersive solutions to the mass critical half-wave equation in two dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Vladimir Georgiev, Yuan Li","submitted_at":"2020-07-30T10:46:07Z","abstract_excerpt":"We consider the half-wave equation with mass critical in two dimension \\begin{eqnarray*} \\begin{cases} iu_t=Du-|u|u,\\,\\,\\, \\\\ u(0,x)=u_0(x), \\end{cases} \\end{eqnarray*} First, we prove the existence of a family of traveling solitary waves. We then show the existence of finite-time blowup solutions with minimal mass $\\|u_0\\|_2=\\|Q\\|_2$, where $Q$ is the ground state solution of equation $DQ+Q=Q^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.15370","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.15370/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":"2007.15370","created_at":"2026-07-05T01:23:30.244578+00:00"},{"alias_kind":"arxiv_version","alias_value":"2007.15370v1","created_at":"2026-07-05T01:23:30.244578+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.15370","created_at":"2026-07-05T01:23:30.244578+00:00"},{"alias_kind":"pith_short_12","alias_value":"KTFJTAQXI3YP","created_at":"2026-07-05T01:23:30.244578+00:00"},{"alias_kind":"pith_short_16","alias_value":"KTFJTAQXI3YP7AEG","created_at":"2026-07-05T01:23:30.244578+00:00"},{"alias_kind":"pith_short_8","alias_value":"KTFJTAQX","created_at":"2026-07-05T01:23:30.244578+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/KTFJTAQXI3YP7AEGGICM2MG6CH","json":"https://pith.science/pith/KTFJTAQXI3YP7AEGGICM2MG6CH.json","graph_json":"https://pith.science/api/pith-number/KTFJTAQXI3YP7AEGGICM2MG6CH/graph.json","events_json":"https://pith.science/api/pith-number/KTFJTAQXI3YP7AEGGICM2MG6CH/events.json","paper":"https://pith.science/paper/KTFJTAQX"},"agent_actions":{"view_html":"https://pith.science/pith/KTFJTAQXI3YP7AEGGICM2MG6CH","download_json":"https://pith.science/pith/KTFJTAQXI3YP7AEGGICM2MG6CH.json","view_paper":"https://pith.science/paper/KTFJTAQX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2007.15370&json=true","fetch_graph":"https://pith.science/api/pith-number/KTFJTAQXI3YP7AEGGICM2MG6CH/graph.json","fetch_events":"https://pith.science/api/pith-number/KTFJTAQXI3YP7AEGGICM2MG6CH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KTFJTAQXI3YP7AEGGICM2MG6CH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KTFJTAQXI3YP7AEGGICM2MG6CH/action/storage_attestation","attest_author":"https://pith.science/pith/KTFJTAQXI3YP7AEGGICM2MG6CH/action/author_attestation","sign_citation":"https://pith.science/pith/KTFJTAQXI3YP7AEGGICM2MG6CH/action/citation_signature","submit_replication":"https://pith.science/pith/KTFJTAQXI3YP7AEGGICM2MG6CH/action/replication_record"}},"created_at":"2026-07-05T01:23:30.244578+00:00","updated_at":"2026-07-05T01:23:30.244578+00:00"}