{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:YA3E3NJJ6JSITACLTEDPI26T2Q","short_pith_number":"pith:YA3E3NJJ","schema_version":"1.0","canonical_sha256":"c0364db529f26489804b9906f46bd3d4269bf452a53a2c51fbbca442b611ae62","source":{"kind":"arxiv","id":"1307.6482","version":1},"attestation_state":"computed","paper":{"title":"Parabolic power concavity and parabolic boundary value problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kazuhiro Ishige, Paolo Salani","submitted_at":"2013-07-24T16:41:27Z","abstract_excerpt":"This paper is concerned with power concavity properties of the solution to the parabolic boundary value problem \\begin{equation} \\tag{$P$} \\left\\{\\begin{array}{ll} \\partial_t u=\\Delta u +f(x,t,u,\\nabla u) & \\mbox{in}\\quad\\Omega\\times(0,\\infty),\\vspace{3pt}\\\\ u(x,t)=0 & \\mbox{on}\\quad\\partial \\Omega\\times(0,\\infty),\\vspace{3pt}\\\\ u(x,0)=0 & \\mbox{in}\\quad\\Omega, \\end{array} \\right. \\end{equation} where $\\Omega$ is a bounded convex domain in ${\\bf R}^n$ and $f$ is a nonnegative continuous function in $\\Omega\\times(0,\\infty)\\times{\\bf R}\\times{\\bf R}^n$. We give a sufficient condition for the sol"},"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":"1307.6482","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-24T16:41:27Z","cross_cats_sorted":[],"title_canon_sha256":"4211623ed94d41eaf9174c1e392cedf8cfe4912b0ae103e73f380d62cc21ccfb","abstract_canon_sha256":"9d6e6ce0d758884a53b559ab4c25a80f8271ca6eadb450d820cb5fc847fd921c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:36.385399Z","signature_b64":"XoE7MCmyHmJLYBGN9jtDUud1op0XoxZMigCxVx2CcPkKv+C/VUBJluPuFoap5xhDswwqV+dqTW+suek4TkEtBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0364db529f26489804b9906f46bd3d4269bf452a53a2c51fbbca442b611ae62","last_reissued_at":"2026-05-18T03:17:36.384824Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:36.384824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parabolic power concavity and parabolic boundary value problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kazuhiro Ishige, Paolo Salani","submitted_at":"2013-07-24T16:41:27Z","abstract_excerpt":"This paper is concerned with power concavity properties of the solution to the parabolic boundary value problem \\begin{equation} \\tag{$P$} \\left\\{\\begin{array}{ll} \\partial_t u=\\Delta u +f(x,t,u,\\nabla u) & \\mbox{in}\\quad\\Omega\\times(0,\\infty),\\vspace{3pt}\\\\ u(x,t)=0 & \\mbox{on}\\quad\\partial \\Omega\\times(0,\\infty),\\vspace{3pt}\\\\ u(x,0)=0 & \\mbox{in}\\quad\\Omega, \\end{array} \\right. \\end{equation} where $\\Omega$ is a bounded convex domain in ${\\bf R}^n$ and $f$ is a nonnegative continuous function in $\\Omega\\times(0,\\infty)\\times{\\bf R}\\times{\\bf R}^n$. We give a sufficient condition for the sol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6482","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":"1307.6482","created_at":"2026-05-18T03:17:36.384927+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.6482v1","created_at":"2026-05-18T03:17:36.384927+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6482","created_at":"2026-05-18T03:17:36.384927+00:00"},{"alias_kind":"pith_short_12","alias_value":"YA3E3NJJ6JSI","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"YA3E3NJJ6JSITACL","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"YA3E3NJJ","created_at":"2026-05-18T12:28:06.772260+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/YA3E3NJJ6JSITACLTEDPI26T2Q","json":"https://pith.science/pith/YA3E3NJJ6JSITACLTEDPI26T2Q.json","graph_json":"https://pith.science/api/pith-number/YA3E3NJJ6JSITACLTEDPI26T2Q/graph.json","events_json":"https://pith.science/api/pith-number/YA3E3NJJ6JSITACLTEDPI26T2Q/events.json","paper":"https://pith.science/paper/YA3E3NJJ"},"agent_actions":{"view_html":"https://pith.science/pith/YA3E3NJJ6JSITACLTEDPI26T2Q","download_json":"https://pith.science/pith/YA3E3NJJ6JSITACLTEDPI26T2Q.json","view_paper":"https://pith.science/paper/YA3E3NJJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.6482&json=true","fetch_graph":"https://pith.science/api/pith-number/YA3E3NJJ6JSITACLTEDPI26T2Q/graph.json","fetch_events":"https://pith.science/api/pith-number/YA3E3NJJ6JSITACLTEDPI26T2Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YA3E3NJJ6JSITACLTEDPI26T2Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YA3E3NJJ6JSITACLTEDPI26T2Q/action/storage_attestation","attest_author":"https://pith.science/pith/YA3E3NJJ6JSITACLTEDPI26T2Q/action/author_attestation","sign_citation":"https://pith.science/pith/YA3E3NJJ6JSITACLTEDPI26T2Q/action/citation_signature","submit_replication":"https://pith.science/pith/YA3E3NJJ6JSITACLTEDPI26T2Q/action/replication_record"}},"created_at":"2026-05-18T03:17:36.384927+00:00","updated_at":"2026-05-18T03:17:36.384927+00:00"}