{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:P25MQYLKP6SHTF4WWDA5X4WVE2","short_pith_number":"pith:P25MQYLK","schema_version":"1.0","canonical_sha256":"7ebac8616a7fa4799796b0c1dbf2d526a634da41dc21e417f4fbd2716faa9a4d","source":{"kind":"arxiv","id":"1303.5521","version":1},"attestation_state":"computed","paper":{"title":"Non self-similar blow-up solutions to the heat equation with nonlinear boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Junichi Harada","submitted_at":"2013-03-22T05:33:24Z","abstract_excerpt":"This paper is concerned with finite blow-up solutions of the heat equation with nonlinear boundary conditions. It is known that a rate of blow-up solutions is the same as the self-similar rate for a Sobolev subcritical case. A goal of this paper is to construct a blow-up solution whose blow-up rate is different from the self-similar rate for a Sobolev supercritical case."},"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":"1303.5521","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-22T05:33:24Z","cross_cats_sorted":[],"title_canon_sha256":"406223c73e625a1fbaefae28066b79eb9e31428933daee1c072ece02609cb365","abstract_canon_sha256":"34b93172d406a1f045ce29124547a1b6abdc466a20fd52f9b8c1b895fafa789c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:03.983921Z","signature_b64":"QLN7lqF/ltKmFzoMi8Kz0qeBYrkrWKQpveheNx0/sz2Oukrg9V4ERG0iOSFZFJ/E4w+q/dI7ujAgkJi2FkluAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ebac8616a7fa4799796b0c1dbf2d526a634da41dc21e417f4fbd2716faa9a4d","last_reissued_at":"2026-05-18T03:30:03.983439Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:03.983439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non self-similar blow-up solutions to the heat equation with nonlinear boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Junichi Harada","submitted_at":"2013-03-22T05:33:24Z","abstract_excerpt":"This paper is concerned with finite blow-up solutions of the heat equation with nonlinear boundary conditions. It is known that a rate of blow-up solutions is the same as the self-similar rate for a Sobolev subcritical case. A goal of this paper is to construct a blow-up solution whose blow-up rate is different from the self-similar rate for a Sobolev supercritical case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5521","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":"1303.5521","created_at":"2026-05-18T03:30:03.983516+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.5521v1","created_at":"2026-05-18T03:30:03.983516+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5521","created_at":"2026-05-18T03:30:03.983516+00:00"},{"alias_kind":"pith_short_12","alias_value":"P25MQYLKP6SH","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"P25MQYLKP6SHTF4W","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"P25MQYLK","created_at":"2026-05-18T12:27:54.935989+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/P25MQYLKP6SHTF4WWDA5X4WVE2","json":"https://pith.science/pith/P25MQYLKP6SHTF4WWDA5X4WVE2.json","graph_json":"https://pith.science/api/pith-number/P25MQYLKP6SHTF4WWDA5X4WVE2/graph.json","events_json":"https://pith.science/api/pith-number/P25MQYLKP6SHTF4WWDA5X4WVE2/events.json","paper":"https://pith.science/paper/P25MQYLK"},"agent_actions":{"view_html":"https://pith.science/pith/P25MQYLKP6SHTF4WWDA5X4WVE2","download_json":"https://pith.science/pith/P25MQYLKP6SHTF4WWDA5X4WVE2.json","view_paper":"https://pith.science/paper/P25MQYLK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.5521&json=true","fetch_graph":"https://pith.science/api/pith-number/P25MQYLKP6SHTF4WWDA5X4WVE2/graph.json","fetch_events":"https://pith.science/api/pith-number/P25MQYLKP6SHTF4WWDA5X4WVE2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P25MQYLKP6SHTF4WWDA5X4WVE2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P25MQYLKP6SHTF4WWDA5X4WVE2/action/storage_attestation","attest_author":"https://pith.science/pith/P25MQYLKP6SHTF4WWDA5X4WVE2/action/author_attestation","sign_citation":"https://pith.science/pith/P25MQYLKP6SHTF4WWDA5X4WVE2/action/citation_signature","submit_replication":"https://pith.science/pith/P25MQYLKP6SHTF4WWDA5X4WVE2/action/replication_record"}},"created_at":"2026-05-18T03:30:03.983516+00:00","updated_at":"2026-05-18T03:30:03.983516+00:00"}