{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:L77ERKKGTLTO7QNFULXG2HWOLE","short_pith_number":"pith:L77ERKKG","schema_version":"1.0","canonical_sha256":"5ffe48a9469ae6efc1a5a2ee6d1ece590a94f77ce068d05a4ba0c3632221d0eb","source":{"kind":"arxiv","id":"gr-qc/0511111","version":4},"attestation_state":"computed","paper":{"title":"Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions","license":"","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Emanuele Berti, Marc Casals, Vitor Cardoso","submitted_at":"2005-11-20T20:38:29Z","abstract_excerpt":"Spin-weighted spheroidal harmonics are useful in a variety of physical situations, including light scattering, nuclear modeling, signal processing, electromagnetic wave propagation, black hole perturbation theory in four and higher dimensions, quantum field theory in curved space-time and studies of D-branes. We first review analytic and numerical calculations of their eigenvalues and eigenfunctions in four dimensions, filling gaps in the existing literature when necessary. Then we compute the angular dependence of the spin-weighted spheroidal harmonics corresponding to slowly-damped quasinorm"},"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":"gr-qc/0511111","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2005-11-20T20:38:29Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"93646941d193b48e670958b8cae346172d30607dc9c9ee4a9dd8baea85c723fc","abstract_canon_sha256":"87edcbfb9ca92439846491eed3f05891e911de6866ec82c381a99d495c2af22b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:27.334366Z","signature_b64":"wM6tjGQBk5E3crjE6b5DU2odoaSAw/5i7N0PBulTQpFZ9UbQnD5jLMvzqD7/EObnF6LQAzW4lGmjTdQR9sItDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ffe48a9469ae6efc1a5a2ee6d1ece590a94f77ce068d05a4ba0c3632221d0eb","last_reissued_at":"2026-05-18T02:37:27.333859Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:27.333859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions","license":"","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Emanuele Berti, Marc Casals, Vitor Cardoso","submitted_at":"2005-11-20T20:38:29Z","abstract_excerpt":"Spin-weighted spheroidal harmonics are useful in a variety of physical situations, including light scattering, nuclear modeling, signal processing, electromagnetic wave propagation, black hole perturbation theory in four and higher dimensions, quantum field theory in curved space-time and studies of D-branes. We first review analytic and numerical calculations of their eigenvalues and eigenfunctions in four dimensions, filling gaps in the existing literature when necessary. Then we compute the angular dependence of the spin-weighted spheroidal harmonics corresponding to slowly-damped quasinorm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0511111","kind":"arxiv","version":4},"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":"gr-qc/0511111","created_at":"2026-05-18T02:37:27.333931+00:00"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0511111v4","created_at":"2026-05-18T02:37:27.333931+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0511111","created_at":"2026-05-18T02:37:27.333931+00:00"},{"alias_kind":"pith_short_12","alias_value":"L77ERKKGTLTO","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"L77ERKKGTLTO7QNF","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"L77ERKKG","created_at":"2026-05-18T12:25:53.335082+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":10,"internal_anchor_count":4,"sample":[{"citing_arxiv_id":"2605.15271","citing_title":"Polarization Analysis of Ringdown Signals","ref_index":45,"is_internal_anchor":true},{"citing_arxiv_id":"2510.05354","citing_title":"Quasinormal modes of Kerr-Newman black holes: revisiting the Dudley-Finley approximation","ref_index":46,"is_internal_anchor":true},{"citing_arxiv_id":"2512.15877","citing_title":"Modeling the frequency-domain ringdown amplitude of comparable-mass mergers with greybody factors","ref_index":52,"is_internal_anchor":true},{"citing_arxiv_id":"1501.06570","citing_title":"Superradiance -- the 2020 Edition","ref_index":244,"is_internal_anchor":true},{"citing_arxiv_id":"2604.02164","citing_title":"Axial gravitational perturbations and echo-like signals of a hairy black hole from gravitational decoupling","ref_index":16,"is_internal_anchor":false},{"citing_arxiv_id":"2505.23895","citing_title":"Black hole spectroscopy: from theory to experiment","ref_index":34,"is_internal_anchor":false},{"citing_arxiv_id":"0905.2975","citing_title":"Quasinormal modes of black holes and black branes","ref_index":154,"is_internal_anchor":false},{"citing_arxiv_id":"2604.11895","citing_title":"Novel ringdown tests of general relativity with black hole greybody factors","ref_index":117,"is_internal_anchor":false},{"citing_arxiv_id":"2604.14638","citing_title":"Probing bulk geometry via pole skipping: from static to rotating spacetimes","ref_index":116,"is_internal_anchor":false},{"citing_arxiv_id":"2604.15431","citing_title":"Highly eccentric non-spinning binary black hole mergers: quadrupolar post-merger waveforms","ref_index":193,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/L77ERKKGTLTO7QNFULXG2HWOLE","json":"https://pith.science/pith/L77ERKKGTLTO7QNFULXG2HWOLE.json","graph_json":"https://pith.science/api/pith-number/L77ERKKGTLTO7QNFULXG2HWOLE/graph.json","events_json":"https://pith.science/api/pith-number/L77ERKKGTLTO7QNFULXG2HWOLE/events.json","paper":"https://pith.science/paper/L77ERKKG"},"agent_actions":{"view_html":"https://pith.science/pith/L77ERKKGTLTO7QNFULXG2HWOLE","download_json":"https://pith.science/pith/L77ERKKGTLTO7QNFULXG2HWOLE.json","view_paper":"https://pith.science/paper/L77ERKKG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=gr-qc/0511111&json=true","fetch_graph":"https://pith.science/api/pith-number/L77ERKKGTLTO7QNFULXG2HWOLE/graph.json","fetch_events":"https://pith.science/api/pith-number/L77ERKKGTLTO7QNFULXG2HWOLE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L77ERKKGTLTO7QNFULXG2HWOLE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L77ERKKGTLTO7QNFULXG2HWOLE/action/storage_attestation","attest_author":"https://pith.science/pith/L77ERKKGTLTO7QNFULXG2HWOLE/action/author_attestation","sign_citation":"https://pith.science/pith/L77ERKKGTLTO7QNFULXG2HWOLE/action/citation_signature","submit_replication":"https://pith.science/pith/L77ERKKGTLTO7QNFULXG2HWOLE/action/replication_record"}},"created_at":"2026-05-18T02:37:27.333931+00:00","updated_at":"2026-05-18T02:37:27.333931+00:00"}