{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:FDHQ5IS2IFBFP7FC4DKBN5XBET","short_pith_number":"pith:FDHQ5IS2","schema_version":"1.0","canonical_sha256":"28cf0ea25a414257fca2e0d416f6e124eacc23ad2344395393054b4504bcd45a","source":{"kind":"arxiv","id":"2112.14133","version":2},"attestation_state":"computed","paper":{"title":"Quasinormal Modes of Black Holes with Multiple Photon Spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Guangzhou Guo, Haitang Yang, Houwen Wu, Peng Wang","submitted_at":"2021-12-28T13:22:20Z","abstract_excerpt":"For a static and spherically symmetric black hole, a photon sphere is composed of circular null geodesics of fixed radius, and plays an important role in observing the black hole. Recently, in an Einstein-Maxwell-scalar model with a non-minimal coupling between the scalar and electromagnetic fields, a class of hairy black holes has been found to possess two unstable and one stable circular null geodesics on the equatorial plane, corresponding to three photon spheres outside the event horizon. In this paper, we study quasinormal modes of the scalar field, which are associated with these circula"},"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":"2112.14133","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2021-12-28T13:22:20Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"530826e40b5351ca6e2dbb22dd89a3c78d5f62843644ba1693b269d8ba7c2eac","abstract_canon_sha256":"9c6b362dd347ba754feba2a36fd518747a203ac8e54ca1286851dbfcf41a542d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:35:41.284901Z","signature_b64":"QP0ce1Ti3HSBPW0/l11CFgYIcml4imV08b2lgBqEQxB9L7/FCkumlGK5NN8X3DnnHu9xwrETK70jMxcD4QpiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28cf0ea25a414257fca2e0d416f6e124eacc23ad2344395393054b4504bcd45a","last_reissued_at":"2026-07-05T04:35:41.284419Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:35:41.284419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasinormal Modes of Black Holes with Multiple Photon Spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Guangzhou Guo, Haitang Yang, Houwen Wu, Peng Wang","submitted_at":"2021-12-28T13:22:20Z","abstract_excerpt":"For a static and spherically symmetric black hole, a photon sphere is composed of circular null geodesics of fixed radius, and plays an important role in observing the black hole. Recently, in an Einstein-Maxwell-scalar model with a non-minimal coupling between the scalar and electromagnetic fields, a class of hairy black holes has been found to possess two unstable and one stable circular null geodesics on the equatorial plane, corresponding to three photon spheres outside the event horizon. In this paper, we study quasinormal modes of the scalar field, which are associated with these circula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.14133","kind":"arxiv","version":2},"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/2112.14133/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":"2112.14133","created_at":"2026-07-05T04:35:41.284477+00:00"},{"alias_kind":"arxiv_version","alias_value":"2112.14133v2","created_at":"2026-07-05T04:35:41.284477+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.14133","created_at":"2026-07-05T04:35:41.284477+00:00"},{"alias_kind":"pith_short_12","alias_value":"FDHQ5IS2IFBF","created_at":"2026-07-05T04:35:41.284477+00:00"},{"alias_kind":"pith_short_16","alias_value":"FDHQ5IS2IFBFP7FC","created_at":"2026-07-05T04:35:41.284477+00:00"},{"alias_kind":"pith_short_8","alias_value":"FDHQ5IS2","created_at":"2026-07-05T04:35:41.284477+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2603.08778","citing_title":"Strong-deflection expansion of the deflection angle near a degenerate photon sphere","ref_index":62,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FDHQ5IS2IFBFP7FC4DKBN5XBET","json":"https://pith.science/pith/FDHQ5IS2IFBFP7FC4DKBN5XBET.json","graph_json":"https://pith.science/api/pith-number/FDHQ5IS2IFBFP7FC4DKBN5XBET/graph.json","events_json":"https://pith.science/api/pith-number/FDHQ5IS2IFBFP7FC4DKBN5XBET/events.json","paper":"https://pith.science/paper/FDHQ5IS2"},"agent_actions":{"view_html":"https://pith.science/pith/FDHQ5IS2IFBFP7FC4DKBN5XBET","download_json":"https://pith.science/pith/FDHQ5IS2IFBFP7FC4DKBN5XBET.json","view_paper":"https://pith.science/paper/FDHQ5IS2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2112.14133&json=true","fetch_graph":"https://pith.science/api/pith-number/FDHQ5IS2IFBFP7FC4DKBN5XBET/graph.json","fetch_events":"https://pith.science/api/pith-number/FDHQ5IS2IFBFP7FC4DKBN5XBET/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FDHQ5IS2IFBFP7FC4DKBN5XBET/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FDHQ5IS2IFBFP7FC4DKBN5XBET/action/storage_attestation","attest_author":"https://pith.science/pith/FDHQ5IS2IFBFP7FC4DKBN5XBET/action/author_attestation","sign_citation":"https://pith.science/pith/FDHQ5IS2IFBFP7FC4DKBN5XBET/action/citation_signature","submit_replication":"https://pith.science/pith/FDHQ5IS2IFBFP7FC4DKBN5XBET/action/replication_record"}},"created_at":"2026-07-05T04:35:41.284477+00:00","updated_at":"2026-07-05T04:35:41.284477+00:00"}