{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:ENOCX34DHX7H2VSTKI3MNQDXRY","short_pith_number":"pith:ENOCX34D","schema_version":"1.0","canonical_sha256":"235c2bef833dfe7d56535236c6c0778e1e3cd6ab28afef0a1c9fecead9f51e72","source":{"kind":"arxiv","id":"2210.15935","version":3},"attestation_state":"computed","paper":{"title":"Conserved currents for Kerr and orthogonality of quasinormal modes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Laura Sberna, Peter Zimmerman, Stefan Hollands, Stephen R. Green, Vahid Toomani","submitted_at":"2022-10-28T06:47:50Z","abstract_excerpt":"We introduce a bilinear form for Weyl scalar perturbations of Kerr. The form is symmetric and conserved, and we show that, when combined with a suitable renormalization prescription involving complex r integration contours, quasinormal modes are orthogonal in the bilinear form for different (l, m, n). These properties are apparently not evident consequences of standard properties for the radial and angular solutions to the decoupled Teukolsky relations and rely on the Petrov type D character of Kerr and its t-$\\phi$ reflection isometry. We show that quasinormal mode excitation coefficients are"},"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":"2210.15935","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2022-10-28T06:47:50Z","cross_cats_sorted":[],"title_canon_sha256":"2f25dcc6b5d6732133585017f7a9a0553e519b4eefa9ddf285a80325df57561e","abstract_canon_sha256":"01fea4b0cf8f23175ac4016d40b46c2b870eafcb4353a84921fa808fdacd9d34"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:46:14.512218Z","signature_b64":"2gV10l26nMFl1RLdhqBQ3OejEZJVm2nKJUerRGHIJjzCJ8Ylj/tppzg98FShgzO2ocJgUXW8Z2ZPJBWybTawBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"235c2bef833dfe7d56535236c6c0778e1e3cd6ab28afef0a1c9fecead9f51e72","last_reissued_at":"2026-07-05T07:46:14.511745Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:46:14.511745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conserved currents for Kerr and orthogonality of quasinormal modes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Laura Sberna, Peter Zimmerman, Stefan Hollands, Stephen R. Green, Vahid Toomani","submitted_at":"2022-10-28T06:47:50Z","abstract_excerpt":"We introduce a bilinear form for Weyl scalar perturbations of Kerr. The form is symmetric and conserved, and we show that, when combined with a suitable renormalization prescription involving complex r integration contours, quasinormal modes are orthogonal in the bilinear form for different (l, m, n). These properties are apparently not evident consequences of standard properties for the radial and angular solutions to the decoupled Teukolsky relations and rely on the Petrov type D character of Kerr and its t-$\\phi$ reflection isometry. We show that quasinormal mode excitation coefficients are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.15935","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/2210.15935/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":"2210.15935","created_at":"2026-07-05T07:46:14.511801+00:00"},{"alias_kind":"arxiv_version","alias_value":"2210.15935v3","created_at":"2026-07-05T07:46:14.511801+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.15935","created_at":"2026-07-05T07:46:14.511801+00:00"},{"alias_kind":"pith_short_12","alias_value":"ENOCX34DHX7H","created_at":"2026-07-05T07:46:14.511801+00:00"},{"alias_kind":"pith_short_16","alias_value":"ENOCX34DHX7H2VST","created_at":"2026-07-05T07:46:14.511801+00:00"},{"alias_kind":"pith_short_8","alias_value":"ENOCX34D","created_at":"2026-07-05T07:46:14.511801+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.17883","citing_title":"Long-Lived Ringing of Near-Extremal Kerr Black Holes Resonantly Driven by Extreme-Mass-Ratio Inspirals","ref_index":22,"is_internal_anchor":false},{"citing_arxiv_id":"2505.23895","citing_title":"Black hole spectroscopy: from theory to experiment","ref_index":284,"is_internal_anchor":false},{"citing_arxiv_id":"2605.03018","citing_title":"Gravitational electric-magnetic duality at the light ring and quasinormal mode isospectrality in effective field theories","ref_index":67,"is_internal_anchor":false},{"citing_arxiv_id":"2604.21239","citing_title":"Relativistic frequency shifts in gravitational waves from axion clouds","ref_index":57,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ENOCX34DHX7H2VSTKI3MNQDXRY","json":"https://pith.science/pith/ENOCX34DHX7H2VSTKI3MNQDXRY.json","graph_json":"https://pith.science/api/pith-number/ENOCX34DHX7H2VSTKI3MNQDXRY/graph.json","events_json":"https://pith.science/api/pith-number/ENOCX34DHX7H2VSTKI3MNQDXRY/events.json","paper":"https://pith.science/paper/ENOCX34D"},"agent_actions":{"view_html":"https://pith.science/pith/ENOCX34DHX7H2VSTKI3MNQDXRY","download_json":"https://pith.science/pith/ENOCX34DHX7H2VSTKI3MNQDXRY.json","view_paper":"https://pith.science/paper/ENOCX34D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2210.15935&json=true","fetch_graph":"https://pith.science/api/pith-number/ENOCX34DHX7H2VSTKI3MNQDXRY/graph.json","fetch_events":"https://pith.science/api/pith-number/ENOCX34DHX7H2VSTKI3MNQDXRY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ENOCX34DHX7H2VSTKI3MNQDXRY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ENOCX34DHX7H2VSTKI3MNQDXRY/action/storage_attestation","attest_author":"https://pith.science/pith/ENOCX34DHX7H2VSTKI3MNQDXRY/action/author_attestation","sign_citation":"https://pith.science/pith/ENOCX34DHX7H2VSTKI3MNQDXRY/action/citation_signature","submit_replication":"https://pith.science/pith/ENOCX34DHX7H2VSTKI3MNQDXRY/action/replication_record"}},"created_at":"2026-07-05T07:46:14.511801+00:00","updated_at":"2026-07-05T07:46:14.511801+00:00"}