{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LJACBRDCUAH4ST4UVMVZAIIVEL","short_pith_number":"pith:LJACBRDC","schema_version":"1.0","canonical_sha256":"5a4020c462a00fc94f94ab2b90211522e3fb68fcb7c376bf1a56e2a3ca9309ee","source":{"kind":"arxiv","id":"1812.02278","version":2},"attestation_state":"computed","paper":{"title":"Boundedness and decay for the Teukolsky equation of spin $\\pm1$ on Reissner-Nordstr\\\"om spacetime: the $\\ell=1$ spherical mode","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.DG","math.MP"],"primary_cat":"gr-qc","authors_text":"Elena Giorgi","submitted_at":"2018-12-06T00:36:51Z","abstract_excerpt":"We prove boundedness and polynomial decay statements for solutions to the spin $\\pm1$ Teukolsky-type equation projected to the $\\ell=1$ spherical harmonic on Reissner-Nordstr\\\"om spacetime. The equation is verified by a gauge-invariant quantity which we identify and which involves the electromagnetic and curvature tensor. This gives a first description in physical space of gauge-invariant quantities transporting the electromagnetic radiation in perturbations of a charged black hole.\n  The proof is based on the use of derived quantities, introduced in previous works on linear stability of Schwa"},"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":"1812.02278","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-12-06T00:36:51Z","cross_cats_sorted":["math-ph","math.AP","math.DG","math.MP"],"title_canon_sha256":"4dbc8f17956fc79a1330ce18d47a58040319f27c34056aa295cf8cfad54b15ec","abstract_canon_sha256":"063e6392fd08d3363baaf62d6915d8689d4a7355cb841ddb7429706711394e93"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:05:22.286443Z","signature_b64":"IS8AWbVuuw1t9L3+L7cdaVGncXuO/sAYLYfisR7jlWCpXJrvTZtGohW4F4XmhGcZ8LENksrhJFduaXrTOMNqDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a4020c462a00fc94f94ab2b90211522e3fb68fcb7c376bf1a56e2a3ca9309ee","last_reissued_at":"2026-07-05T00:05:22.285945Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:05:22.285945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Boundedness and decay for the Teukolsky equation of spin $\\pm1$ on Reissner-Nordstr\\\"om spacetime: the $\\ell=1$ spherical mode","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.DG","math.MP"],"primary_cat":"gr-qc","authors_text":"Elena Giorgi","submitted_at":"2018-12-06T00:36:51Z","abstract_excerpt":"We prove boundedness and polynomial decay statements for solutions to the spin $\\pm1$ Teukolsky-type equation projected to the $\\ell=1$ spherical harmonic on Reissner-Nordstr\\\"om spacetime. The equation is verified by a gauge-invariant quantity which we identify and which involves the electromagnetic and curvature tensor. This gives a first description in physical space of gauge-invariant quantities transporting the electromagnetic radiation in perturbations of a charged black hole.\n  The proof is based on the use of derived quantities, introduced in previous works on linear stability of Schwa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02278","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/1812.02278/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":"1812.02278","created_at":"2026-07-05T00:05:22.286007+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.02278v2","created_at":"2026-07-05T00:05:22.286007+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02278","created_at":"2026-07-05T00:05:22.286007+00:00"},{"alias_kind":"pith_short_12","alias_value":"LJACBRDCUAH4","created_at":"2026-07-05T00:05:22.286007+00:00"},{"alias_kind":"pith_short_16","alias_value":"LJACBRDCUAH4ST4U","created_at":"2026-07-05T00:05:22.286007+00:00"},{"alias_kind":"pith_short_8","alias_value":"LJACBRDC","created_at":"2026-07-05T00:05:22.286007+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/LJACBRDCUAH4ST4UVMVZAIIVEL","json":"https://pith.science/pith/LJACBRDCUAH4ST4UVMVZAIIVEL.json","graph_json":"https://pith.science/api/pith-number/LJACBRDCUAH4ST4UVMVZAIIVEL/graph.json","events_json":"https://pith.science/api/pith-number/LJACBRDCUAH4ST4UVMVZAIIVEL/events.json","paper":"https://pith.science/paper/LJACBRDC"},"agent_actions":{"view_html":"https://pith.science/pith/LJACBRDCUAH4ST4UVMVZAIIVEL","download_json":"https://pith.science/pith/LJACBRDCUAH4ST4UVMVZAIIVEL.json","view_paper":"https://pith.science/paper/LJACBRDC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.02278&json=true","fetch_graph":"https://pith.science/api/pith-number/LJACBRDCUAH4ST4UVMVZAIIVEL/graph.json","fetch_events":"https://pith.science/api/pith-number/LJACBRDCUAH4ST4UVMVZAIIVEL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LJACBRDCUAH4ST4UVMVZAIIVEL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LJACBRDCUAH4ST4UVMVZAIIVEL/action/storage_attestation","attest_author":"https://pith.science/pith/LJACBRDCUAH4ST4UVMVZAIIVEL/action/author_attestation","sign_citation":"https://pith.science/pith/LJACBRDCUAH4ST4UVMVZAIIVEL/action/citation_signature","submit_replication":"https://pith.science/pith/LJACBRDCUAH4ST4UVMVZAIIVEL/action/replication_record"}},"created_at":"2026-07-05T00:05:22.286007+00:00","updated_at":"2026-07-05T00:05:22.286007+00:00"}