{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:6OVRSICBUITSY3QNKQXS3YDNG5","short_pith_number":"pith:6OVRSICB","schema_version":"1.0","canonical_sha256":"f3ab192041a2272c6e0d542f2de06d37617a220c0cf165b246ca5f4e101dab4b","source":{"kind":"arxiv","id":"1306.0859","version":1},"attestation_state":"computed","paper":{"title":"Extinction profile of complete non-compact solutions to the Yamabe flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"John King, Natasa Sesum, Panagiota Daskalopoulos","submitted_at":"2013-06-04T17:38:05Z","abstract_excerpt":"This work addresses the {\\em singularity formation} of complete non-compact solutions to the conformally flat Yamabe flow whose conformal factors have {\\em cylindrical behavior at infinity}. Their singularity profiles happen to be {\\em Yamabe solitons}, which are {\\em self-similar solutions} to the fast diffusion equation satisfied by the conformal factor of the evolving metric. The self-similar profile is determined by the second order asymptotics at infinity of the initial data which is matched with that of the corresponding self-similar solution. Solutions may become extinct at the extincti"},"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":"1306.0859","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-06-04T17:38:05Z","cross_cats_sorted":[],"title_canon_sha256":"426b17d331f2c06afa8f055afcb383f3508eed0519ef9387ffcf8b0ad0f3c28d","abstract_canon_sha256":"6ed5f958ffdf4fc996950b4360285346897187649f072398ce0a1f84830fb8e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:46.166472Z","signature_b64":"w+8xUcBiIJKnUPmQU/tv9qHb9g6AmfXpFgq+r3XoG5URiR9PEeFaRu4rmTLEQzsq4Vq+qhYY8X1+kHUIeMaZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3ab192041a2272c6e0d542f2de06d37617a220c0cf165b246ca5f4e101dab4b","last_reissued_at":"2026-05-18T03:21:46.165579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:46.165579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extinction profile of complete non-compact solutions to the Yamabe flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"John King, Natasa Sesum, Panagiota Daskalopoulos","submitted_at":"2013-06-04T17:38:05Z","abstract_excerpt":"This work addresses the {\\em singularity formation} of complete non-compact solutions to the conformally flat Yamabe flow whose conformal factors have {\\em cylindrical behavior at infinity}. Their singularity profiles happen to be {\\em Yamabe solitons}, which are {\\em self-similar solutions} to the fast diffusion equation satisfied by the conformal factor of the evolving metric. The self-similar profile is determined by the second order asymptotics at infinity of the initial data which is matched with that of the corresponding self-similar solution. Solutions may become extinct at the extincti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0859","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":"1306.0859","created_at":"2026-05-18T03:21:46.165724+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.0859v1","created_at":"2026-05-18T03:21:46.165724+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0859","created_at":"2026-05-18T03:21:46.165724+00:00"},{"alias_kind":"pith_short_12","alias_value":"6OVRSICBUITS","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"6OVRSICBUITSY3QN","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"6OVRSICB","created_at":"2026-05-18T12:27:36.564083+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/6OVRSICBUITSY3QNKQXS3YDNG5","json":"https://pith.science/pith/6OVRSICBUITSY3QNKQXS3YDNG5.json","graph_json":"https://pith.science/api/pith-number/6OVRSICBUITSY3QNKQXS3YDNG5/graph.json","events_json":"https://pith.science/api/pith-number/6OVRSICBUITSY3QNKQXS3YDNG5/events.json","paper":"https://pith.science/paper/6OVRSICB"},"agent_actions":{"view_html":"https://pith.science/pith/6OVRSICBUITSY3QNKQXS3YDNG5","download_json":"https://pith.science/pith/6OVRSICBUITSY3QNKQXS3YDNG5.json","view_paper":"https://pith.science/paper/6OVRSICB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.0859&json=true","fetch_graph":"https://pith.science/api/pith-number/6OVRSICBUITSY3QNKQXS3YDNG5/graph.json","fetch_events":"https://pith.science/api/pith-number/6OVRSICBUITSY3QNKQXS3YDNG5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6OVRSICBUITSY3QNKQXS3YDNG5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6OVRSICBUITSY3QNKQXS3YDNG5/action/storage_attestation","attest_author":"https://pith.science/pith/6OVRSICBUITSY3QNKQXS3YDNG5/action/author_attestation","sign_citation":"https://pith.science/pith/6OVRSICBUITSY3QNKQXS3YDNG5/action/citation_signature","submit_replication":"https://pith.science/pith/6OVRSICBUITSY3QNKQXS3YDNG5/action/replication_record"}},"created_at":"2026-05-18T03:21:46.165724+00:00","updated_at":"2026-05-18T03:21:46.165724+00:00"}