{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:MDTUQPCFEBPW67WGHDZXWSBYUD","short_pith_number":"pith:MDTUQPCF","schema_version":"1.0","canonical_sha256":"60e7483c45205f6f7ec638f37b4838a0eafa0c759a139f69adb6aaa180abb045","source":{"kind":"arxiv","id":"2111.04489","version":3},"attestation_state":"computed","paper":{"title":"Sharp decay for Teukolsky equation in Kerr spacetimes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"gr-qc","authors_text":"Lin Zhang, Siyuan Ma","submitted_at":"2021-11-08T13:25:23Z","abstract_excerpt":"In this work, we derive the global sharp decay, as both a lower and an upper bounds, for the spin $\\pm \\mathfrak{s}$ components, which are solutions to the Teukolsky equation, in the black hole exterior and on the event horizon of a slowly rotating Kerr spacetime. These estimates are generalized to any subextreme Kerr background under an integrated local energy decay estimate. Our results apply to the scalar field $(\\mathfrak{s}=0)$, the Maxwell field $(\\mathfrak{s}=1)$ and the linearized gravity $(\\mathfrak{s}=2)$ and confirm the Price's law decay that is conjectured to be sharp. Our analyses"},"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":"2111.04489","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2021-11-08T13:25:23Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"845549c7262f13e9342d905fd0bea50ae3a0f259bf18b35ad655124a8c71c703","abstract_canon_sha256":"942fedc2a8aa704d4335262b275644f994f2dee599e3dd2e7483646d91f2ccd2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:27:38.012737Z","signature_b64":"lVe9ZiabCjr6IEC0WG24HfL9lLpjIA6WKEMxFuXuFEHzTjIsuSt595CXFzecbvXsOdR/IuGN9RONeZvtHwwGBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60e7483c45205f6f7ec638f37b4838a0eafa0c759a139f69adb6aaa180abb045","last_reissued_at":"2026-07-05T06:27:38.012326Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:27:38.012326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp decay for Teukolsky equation in Kerr spacetimes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"gr-qc","authors_text":"Lin Zhang, Siyuan Ma","submitted_at":"2021-11-08T13:25:23Z","abstract_excerpt":"In this work, we derive the global sharp decay, as both a lower and an upper bounds, for the spin $\\pm \\mathfrak{s}$ components, which are solutions to the Teukolsky equation, in the black hole exterior and on the event horizon of a slowly rotating Kerr spacetime. These estimates are generalized to any subextreme Kerr background under an integrated local energy decay estimate. Our results apply to the scalar field $(\\mathfrak{s}=0)$, the Maxwell field $(\\mathfrak{s}=1)$ and the linearized gravity $(\\mathfrak{s}=2)$ and confirm the Price's law decay that is conjectured to be sharp. Our analyses"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.04489","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/2111.04489/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":"2111.04489","created_at":"2026-07-05T06:27:38.012383+00:00"},{"alias_kind":"arxiv_version","alias_value":"2111.04489v3","created_at":"2026-07-05T06:27:38.012383+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.04489","created_at":"2026-07-05T06:27:38.012383+00:00"},{"alias_kind":"pith_short_12","alias_value":"MDTUQPCFEBPW","created_at":"2026-07-05T06:27:38.012383+00:00"},{"alias_kind":"pith_short_16","alias_value":"MDTUQPCFEBPW67WG","created_at":"2026-07-05T06:27:38.012383+00:00"},{"alias_kind":"pith_short_8","alias_value":"MDTUQPCF","created_at":"2026-07-05T06:27:38.012383+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.06828","citing_title":"Elliptic curvature estimates for linearised gravitational perturbations of Kerr in the full sub-extremal range $|a|<M$","ref_index":16,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MDTUQPCFEBPW67WGHDZXWSBYUD","json":"https://pith.science/pith/MDTUQPCFEBPW67WGHDZXWSBYUD.json","graph_json":"https://pith.science/api/pith-number/MDTUQPCFEBPW67WGHDZXWSBYUD/graph.json","events_json":"https://pith.science/api/pith-number/MDTUQPCFEBPW67WGHDZXWSBYUD/events.json","paper":"https://pith.science/paper/MDTUQPCF"},"agent_actions":{"view_html":"https://pith.science/pith/MDTUQPCFEBPW67WGHDZXWSBYUD","download_json":"https://pith.science/pith/MDTUQPCFEBPW67WGHDZXWSBYUD.json","view_paper":"https://pith.science/paper/MDTUQPCF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2111.04489&json=true","fetch_graph":"https://pith.science/api/pith-number/MDTUQPCFEBPW67WGHDZXWSBYUD/graph.json","fetch_events":"https://pith.science/api/pith-number/MDTUQPCFEBPW67WGHDZXWSBYUD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MDTUQPCFEBPW67WGHDZXWSBYUD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MDTUQPCFEBPW67WGHDZXWSBYUD/action/storage_attestation","attest_author":"https://pith.science/pith/MDTUQPCFEBPW67WGHDZXWSBYUD/action/author_attestation","sign_citation":"https://pith.science/pith/MDTUQPCFEBPW67WGHDZXWSBYUD/action/citation_signature","submit_replication":"https://pith.science/pith/MDTUQPCFEBPW67WGHDZXWSBYUD/action/replication_record"}},"created_at":"2026-07-05T06:27:38.012383+00:00","updated_at":"2026-07-05T06:27:38.012383+00:00"}