{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:U232UFOSZKHH72TK2RXJW426GV","short_pith_number":"pith:U232UFOS","schema_version":"1.0","canonical_sha256":"a6b7aa15d2ca8e7fea6ad46e9b735e35544fdbff32a80906ea2fc924a43eb85d","source":{"kind":"arxiv","id":"2203.04380","version":3},"attestation_state":"computed","paper":{"title":"On finite time Type I singularities of the K\\\"ahler-Ricci flow on compact K\\\"ahler surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alix Deruelle, Charles Cifarelli, Ronan J. Conlon","submitted_at":"2022-03-08T20:15:15Z","abstract_excerpt":"We show that the underlying complex manifold of a complete non-compact two-\\linebreak dimensional shrinking gradient K\\\"ahler-Ricci soliton $(M,\\,g,\\,X)$ with soliton metric $g$ with bounded scalar curvature $\\operatorname{R}_{g}$ whose soliton vector field $X$ has an integral curve along which $\\operatorname{R}_{g}\\not\\to0$ is biholomorphic to either $\\mathbb{C}\\times\\mathbb{P}^{1}$ or to the blowup of this manifold at one point. Assuming the existence of such a soliton on this latter manifold, we show that it is toric and unique. We also identify the corresponding soliton vector field. Given"},"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":"2203.04380","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-03-08T20:15:15Z","cross_cats_sorted":[],"title_canon_sha256":"4a7e25609ee33f4eb9a15181e5b6e86eeceaae1f8a840dc974ea29267fad7ef3","abstract_canon_sha256":"f5b855670401d8004951dccde6d2be95e0c6f0731255d476a8933f2b6bd4b4fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:25:14.134922Z","signature_b64":"zXc2jlNMji8CO5D4lKnNO5a6ear8wZCK0NKB6vKEV7MzbNHAoIKbrON+o77auqbMFGG/oG0FqNaFuBt2OT7XBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6b7aa15d2ca8e7fea6ad46e9b735e35544fdbff32a80906ea2fc924a43eb85d","last_reissued_at":"2026-07-05T05:25:14.134302Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:25:14.134302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On finite time Type I singularities of the K\\\"ahler-Ricci flow on compact K\\\"ahler surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alix Deruelle, Charles Cifarelli, Ronan J. Conlon","submitted_at":"2022-03-08T20:15:15Z","abstract_excerpt":"We show that the underlying complex manifold of a complete non-compact two-\\linebreak dimensional shrinking gradient K\\\"ahler-Ricci soliton $(M,\\,g,\\,X)$ with soliton metric $g$ with bounded scalar curvature $\\operatorname{R}_{g}$ whose soliton vector field $X$ has an integral curve along which $\\operatorname{R}_{g}\\not\\to0$ is biholomorphic to either $\\mathbb{C}\\times\\mathbb{P}^{1}$ or to the blowup of this manifold at one point. Assuming the existence of such a soliton on this latter manifold, we show that it is toric and unique. We also identify the corresponding soliton vector field. Given"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.04380","kind":"arxiv","version":3},"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/2203.04380/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":"2203.04380","created_at":"2026-07-05T05:25:14.134376+00:00"},{"alias_kind":"arxiv_version","alias_value":"2203.04380v3","created_at":"2026-07-05T05:25:14.134376+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.04380","created_at":"2026-07-05T05:25:14.134376+00:00"},{"alias_kind":"pith_short_12","alias_value":"U232UFOSZKHH","created_at":"2026-07-05T05:25:14.134376+00:00"},{"alias_kind":"pith_short_16","alias_value":"U232UFOSZKHH72TK","created_at":"2026-07-05T05:25:14.134376+00:00"},{"alias_kind":"pith_short_8","alias_value":"U232UFOS","created_at":"2026-07-05T05:25:14.134376+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2502.16148","citing_title":"Transverse Rigidity of Shrinking Sasaki-Ricci Solitons","ref_index":18,"is_internal_anchor":false},{"citing_arxiv_id":"2605.04476","citing_title":"Topology of gradient Ricci shrinkers via weighted $L^2$ cohomology","ref_index":16,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U232UFOSZKHH72TK2RXJW426GV","json":"https://pith.science/pith/U232UFOSZKHH72TK2RXJW426GV.json","graph_json":"https://pith.science/api/pith-number/U232UFOSZKHH72TK2RXJW426GV/graph.json","events_json":"https://pith.science/api/pith-number/U232UFOSZKHH72TK2RXJW426GV/events.json","paper":"https://pith.science/paper/U232UFOS"},"agent_actions":{"view_html":"https://pith.science/pith/U232UFOSZKHH72TK2RXJW426GV","download_json":"https://pith.science/pith/U232UFOSZKHH72TK2RXJW426GV.json","view_paper":"https://pith.science/paper/U232UFOS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2203.04380&json=true","fetch_graph":"https://pith.science/api/pith-number/U232UFOSZKHH72TK2RXJW426GV/graph.json","fetch_events":"https://pith.science/api/pith-number/U232UFOSZKHH72TK2RXJW426GV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U232UFOSZKHH72TK2RXJW426GV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U232UFOSZKHH72TK2RXJW426GV/action/storage_attestation","attest_author":"https://pith.science/pith/U232UFOSZKHH72TK2RXJW426GV/action/author_attestation","sign_citation":"https://pith.science/pith/U232UFOSZKHH72TK2RXJW426GV/action/citation_signature","submit_replication":"https://pith.science/pith/U232UFOSZKHH72TK2RXJW426GV/action/replication_record"}},"created_at":"2026-07-05T05:25:14.134376+00:00","updated_at":"2026-07-05T05:25:14.134376+00:00"}