{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:E7EZ4XSUHQQTYECJXIFD23JAZC","short_pith_number":"pith:E7EZ4XSU","schema_version":"1.0","canonical_sha256":"27c99e5e543c213c1049ba0a3d6d20c8b64413bd90a0c743e46cd59daa05a9ad","source":{"kind":"arxiv","id":"1903.06729","version":1},"attestation_state":"computed","paper":{"title":"Non-uniqueness for an energy-critical heat equation on $\\mathbb{R}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hiroaki Kikuchi, Juncheng Wei, Kenji Nakanishi, Slim Ibrahim","submitted_at":"2019-03-15T18:20:54Z","abstract_excerpt":"We construct a singular solution of a stationary nonlinear Schr\\\"{o}dinger equation on $\\mathbb{R}^2$ with square-exponential nonlinearity having linear behavior around zero. In view of Trudinger-Moser inequality, this type of nonlinearity has an energy-critical growth. We use this singular solution to prove non-uniqueness of strong solutions for the Cauchy problem of the corresponding semilinear heat equation. The proof relies on explicit computation showing a regularizing effect of the heat equation in an appropriate functional space."},"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":"1903.06729","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-15T18:20:54Z","cross_cats_sorted":[],"title_canon_sha256":"7649095c25cb4418817a40642ee2c59f785f5a440054f4edd15c682874cc2fb2","abstract_canon_sha256":"baeb0b6159141103e8a007dc78095489aa5410fade65fe538c901821916ce7c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:09.191959Z","signature_b64":"hohRYdlvr6KSyNPep0NrFt1cJZA0Qww1mL0+K8sPOw6MMXGx3VAETxSCLRmDeZZiVTGsQ9rkTwcyI8vjIZHQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27c99e5e543c213c1049ba0a3d6d20c8b64413bd90a0c743e46cd59daa05a9ad","last_reissued_at":"2026-05-17T23:51:09.191556Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:09.191556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-uniqueness for an energy-critical heat equation on $\\mathbb{R}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hiroaki Kikuchi, Juncheng Wei, Kenji Nakanishi, Slim Ibrahim","submitted_at":"2019-03-15T18:20:54Z","abstract_excerpt":"We construct a singular solution of a stationary nonlinear Schr\\\"{o}dinger equation on $\\mathbb{R}^2$ with square-exponential nonlinearity having linear behavior around zero. In view of Trudinger-Moser inequality, this type of nonlinearity has an energy-critical growth. We use this singular solution to prove non-uniqueness of strong solutions for the Cauchy problem of the corresponding semilinear heat equation. The proof relies on explicit computation showing a regularizing effect of the heat equation in an appropriate functional space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06729","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":"1903.06729","created_at":"2026-05-17T23:51:09.191619+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.06729v1","created_at":"2026-05-17T23:51:09.191619+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06729","created_at":"2026-05-17T23:51:09.191619+00:00"},{"alias_kind":"pith_short_12","alias_value":"E7EZ4XSUHQQT","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"E7EZ4XSUHQQTYECJ","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"E7EZ4XSU","created_at":"2026-05-18T12:33:15.570797+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/E7EZ4XSUHQQTYECJXIFD23JAZC","json":"https://pith.science/pith/E7EZ4XSUHQQTYECJXIFD23JAZC.json","graph_json":"https://pith.science/api/pith-number/E7EZ4XSUHQQTYECJXIFD23JAZC/graph.json","events_json":"https://pith.science/api/pith-number/E7EZ4XSUHQQTYECJXIFD23JAZC/events.json","paper":"https://pith.science/paper/E7EZ4XSU"},"agent_actions":{"view_html":"https://pith.science/pith/E7EZ4XSUHQQTYECJXIFD23JAZC","download_json":"https://pith.science/pith/E7EZ4XSUHQQTYECJXIFD23JAZC.json","view_paper":"https://pith.science/paper/E7EZ4XSU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.06729&json=true","fetch_graph":"https://pith.science/api/pith-number/E7EZ4XSUHQQTYECJXIFD23JAZC/graph.json","fetch_events":"https://pith.science/api/pith-number/E7EZ4XSUHQQTYECJXIFD23JAZC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E7EZ4XSUHQQTYECJXIFD23JAZC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E7EZ4XSUHQQTYECJXIFD23JAZC/action/storage_attestation","attest_author":"https://pith.science/pith/E7EZ4XSUHQQTYECJXIFD23JAZC/action/author_attestation","sign_citation":"https://pith.science/pith/E7EZ4XSUHQQTYECJXIFD23JAZC/action/citation_signature","submit_replication":"https://pith.science/pith/E7EZ4XSUHQQTYECJXIFD23JAZC/action/replication_record"}},"created_at":"2026-05-17T23:51:09.191619+00:00","updated_at":"2026-05-17T23:51:09.191619+00:00"}