{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HZYEEPMJ5AYMVNN2PRIISQAWI2","short_pith_number":"pith:HZYEEPMJ","schema_version":"1.0","canonical_sha256":"3e70423d89e830cab5ba7c5089401646a75f54bd347f18faf8c3d5eb56fb6da3","source":{"kind":"arxiv","id":"1804.09614","version":3},"attestation_state":"computed","paper":{"title":"The Petrov type D equation on genus $>0$ sections of isolated horizons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Adam Szereszewski, Denis Dobkowski-Ry{\\l}ko, Jerzy lewandowski, Wojciech Kami\\'nski","submitted_at":"2018-04-25T15:10:25Z","abstract_excerpt":"The Petrov type D equation imposed on the 2-metric tensor and the rotation scalar of a cross-section of an isolated horizon can be used to uniquely distinguish the Kerr - (anti) de Sitter spacetime in the case the topology of the cross-section is that of a sphere. In the current paper we study that equation on closed 2-dimensional surfaces that have genus $>0$. We derive all the solutions assuming the embeddability in 4-dimensional spacetime that satisfies the vacuum Einstein equations with (possibly 0) cosmological constant. We prove all of them have constant Gauss curvature and zero rotation"},"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":"1804.09614","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-04-25T15:10:25Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"7ff7b00f740a2519a187c3b13752cb5201d85413916de431f863bc5344844a15","abstract_canon_sha256":"c72a14f6b625ae99eeb54c6166032dfa1653ffb1ff9de88a5827183d46fb1463"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:14.925828Z","signature_b64":"IBniNI8MrdecnKg6T/j2pfX/5uaU9LKSK2aEpGX9NVxz3gT/GEiYzOv/EWSgRWFknOjqpO95lTIrWwxdjfs4DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e70423d89e830cab5ba7c5089401646a75f54bd347f18faf8c3d5eb56fb6da3","last_reissued_at":"2026-05-18T00:08:14.925442Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:14.925442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Petrov type D equation on genus $>0$ sections of isolated horizons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Adam Szereszewski, Denis Dobkowski-Ry{\\l}ko, Jerzy lewandowski, Wojciech Kami\\'nski","submitted_at":"2018-04-25T15:10:25Z","abstract_excerpt":"The Petrov type D equation imposed on the 2-metric tensor and the rotation scalar of a cross-section of an isolated horizon can be used to uniquely distinguish the Kerr - (anti) de Sitter spacetime in the case the topology of the cross-section is that of a sphere. In the current paper we study that equation on closed 2-dimensional surfaces that have genus $>0$. We derive all the solutions assuming the embeddability in 4-dimensional spacetime that satisfies the vacuum Einstein equations with (possibly 0) cosmological constant. We prove all of them have constant Gauss curvature and zero rotation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09614","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":""},"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":"1804.09614","created_at":"2026-05-18T00:08:14.925508+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.09614v3","created_at":"2026-05-18T00:08:14.925508+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09614","created_at":"2026-05-18T00:08:14.925508+00:00"},{"alias_kind":"pith_short_12","alias_value":"HZYEEPMJ5AYM","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HZYEEPMJ5AYMVNN2","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HZYEEPMJ","created_at":"2026-05-18T12:32:28.185984+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/HZYEEPMJ5AYMVNN2PRIISQAWI2","json":"https://pith.science/pith/HZYEEPMJ5AYMVNN2PRIISQAWI2.json","graph_json":"https://pith.science/api/pith-number/HZYEEPMJ5AYMVNN2PRIISQAWI2/graph.json","events_json":"https://pith.science/api/pith-number/HZYEEPMJ5AYMVNN2PRIISQAWI2/events.json","paper":"https://pith.science/paper/HZYEEPMJ"},"agent_actions":{"view_html":"https://pith.science/pith/HZYEEPMJ5AYMVNN2PRIISQAWI2","download_json":"https://pith.science/pith/HZYEEPMJ5AYMVNN2PRIISQAWI2.json","view_paper":"https://pith.science/paper/HZYEEPMJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.09614&json=true","fetch_graph":"https://pith.science/api/pith-number/HZYEEPMJ5AYMVNN2PRIISQAWI2/graph.json","fetch_events":"https://pith.science/api/pith-number/HZYEEPMJ5AYMVNN2PRIISQAWI2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HZYEEPMJ5AYMVNN2PRIISQAWI2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HZYEEPMJ5AYMVNN2PRIISQAWI2/action/storage_attestation","attest_author":"https://pith.science/pith/HZYEEPMJ5AYMVNN2PRIISQAWI2/action/author_attestation","sign_citation":"https://pith.science/pith/HZYEEPMJ5AYMVNN2PRIISQAWI2/action/citation_signature","submit_replication":"https://pith.science/pith/HZYEEPMJ5AYMVNN2PRIISQAWI2/action/replication_record"}},"created_at":"2026-05-18T00:08:14.925508+00:00","updated_at":"2026-05-18T00:08:14.925508+00:00"}