{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:BITE25VSGB7KGRLK4IQ2CCTIJV","short_pith_number":"pith:BITE25VS","schema_version":"1.0","canonical_sha256":"0a264d76b2307ea3456ae221a10a684d7709a9acbc592692dd47fde03417a8db","source":{"kind":"arxiv","id":"2212.05267","version":1},"attestation_state":"computed","paper":{"title":"Rigidity of four-dimensional K\\\"ahler-Ricci solitons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ernani Ribeiro Jr, Hung Tran, Xiaodong Cao","submitted_at":"2022-12-10T11:06:23Z","abstract_excerpt":"In this article, we investigate four-dimensional gradient shrinking Ricci solitons close to a K\\\"ahler model. The first theorem could be considered as a rigidity result for the K\\\"ahler-Ricci soliton structure on $\\mathbb{S}^2\\times \\mathbb{R}^2$ (in the sense of Remark 1). Moreover, we show that if the quotient of norm of the self-dual Weyl tensor and scalar curvature is close to that on a K\\\"ahler metric in a specific sense, then the gradient Ricci soliton must be either half-conformally flat or locally K\\\"ahler."},"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":"2212.05267","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-12-10T11:06:23Z","cross_cats_sorted":[],"title_canon_sha256":"b4783ef9533080615e8d2aa7d4348b3f6018a089d51f15e3915596e14e6c8bae","abstract_canon_sha256":"f13012565d29406363c3602e490cab14f6c0ec7972d433e07d3ab1a0d8b2b74c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:24:02.098838Z","signature_b64":"l24i9Ug5kGvqA0i2+DLvDYi7TjoWq4toGIipqlGDOkhKcxEzqJD/64zyouvwvjAOQYctBCMit96xdim3/t/tDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a264d76b2307ea3456ae221a10a684d7709a9acbc592692dd47fde03417a8db","last_reissued_at":"2026-07-05T05:24:02.098391Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:24:02.098391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigidity of four-dimensional K\\\"ahler-Ricci solitons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ernani Ribeiro Jr, Hung Tran, Xiaodong Cao","submitted_at":"2022-12-10T11:06:23Z","abstract_excerpt":"In this article, we investigate four-dimensional gradient shrinking Ricci solitons close to a K\\\"ahler model. The first theorem could be considered as a rigidity result for the K\\\"ahler-Ricci soliton structure on $\\mathbb{S}^2\\times \\mathbb{R}^2$ (in the sense of Remark 1). Moreover, we show that if the quotient of norm of the self-dual Weyl tensor and scalar curvature is close to that on a K\\\"ahler metric in a specific sense, then the gradient Ricci soliton must be either half-conformally flat or locally K\\\"ahler."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.05267","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.05267/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":"2212.05267","created_at":"2026-07-05T05:24:02.098446+00:00"},{"alias_kind":"arxiv_version","alias_value":"2212.05267v1","created_at":"2026-07-05T05:24:02.098446+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.05267","created_at":"2026-07-05T05:24:02.098446+00:00"},{"alias_kind":"pith_short_12","alias_value":"BITE25VSGB7K","created_at":"2026-07-05T05:24:02.098446+00:00"},{"alias_kind":"pith_short_16","alias_value":"BITE25VSGB7KGRLK","created_at":"2026-07-05T05:24:02.098446+00:00"},{"alias_kind":"pith_short_8","alias_value":"BITE25VS","created_at":"2026-07-05T05:24:02.098446+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/BITE25VSGB7KGRLK4IQ2CCTIJV","json":"https://pith.science/pith/BITE25VSGB7KGRLK4IQ2CCTIJV.json","graph_json":"https://pith.science/api/pith-number/BITE25VSGB7KGRLK4IQ2CCTIJV/graph.json","events_json":"https://pith.science/api/pith-number/BITE25VSGB7KGRLK4IQ2CCTIJV/events.json","paper":"https://pith.science/paper/BITE25VS"},"agent_actions":{"view_html":"https://pith.science/pith/BITE25VSGB7KGRLK4IQ2CCTIJV","download_json":"https://pith.science/pith/BITE25VSGB7KGRLK4IQ2CCTIJV.json","view_paper":"https://pith.science/paper/BITE25VS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2212.05267&json=true","fetch_graph":"https://pith.science/api/pith-number/BITE25VSGB7KGRLK4IQ2CCTIJV/graph.json","fetch_events":"https://pith.science/api/pith-number/BITE25VSGB7KGRLK4IQ2CCTIJV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BITE25VSGB7KGRLK4IQ2CCTIJV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BITE25VSGB7KGRLK4IQ2CCTIJV/action/storage_attestation","attest_author":"https://pith.science/pith/BITE25VSGB7KGRLK4IQ2CCTIJV/action/author_attestation","sign_citation":"https://pith.science/pith/BITE25VSGB7KGRLK4IQ2CCTIJV/action/citation_signature","submit_replication":"https://pith.science/pith/BITE25VSGB7KGRLK4IQ2CCTIJV/action/replication_record"}},"created_at":"2026-07-05T05:24:02.098446+00:00","updated_at":"2026-07-05T05:24:02.098446+00:00"}