{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:T4G2VX7TGIP3OSJHIRRZE2Y3HI","short_pith_number":"pith:T4G2VX7T","schema_version":"1.0","canonical_sha256":"9f0daadff3321fb749274463926b1b3a37372c37bc67068f8858f180db4e5c4b","source":{"kind":"arxiv","id":"gr-qc/0607046","version":5},"attestation_state":"computed","paper":{"title":"Decay of Solutions of the Teukolsky Equation for Higher Spin in the Schwarzschild Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph","math-ph","math.FA","math.MP"],"primary_cat":"gr-qc","authors_text":"Felix Finster, Joel Smoller","submitted_at":"2006-07-11T16:25:44Z","abstract_excerpt":"We prove that the Schwarzschild black hole is linearly stable under electromagnetic and gravitational perturbations. Our method is to show that for spin $s=1$ or $s=2$, solutions of the Teukolsky equation with smooth, compactly supported initial data outside the event horizon, decay in $L^\\infty_{loc}$."},"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/0607046","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2006-07-11T16:25:44Z","cross_cats_sorted":["astro-ph","math-ph","math.FA","math.MP"],"title_canon_sha256":"891090b3b2cb2b7bdb9606a1800560a2bbcac50c16156ba14e9aa6611f1de102","abstract_canon_sha256":"f6453c90ae46dab478c30c97170a1a7d40803da903d02e0cb6ffd3ed1b67bef8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:36.051616Z","signature_b64":"ApolsEi1csNQ9HjtrPO6vBy3wcBnEAJcOasJzeGvt6xrlhG1EW+29iCSe6+HuD2mIzTWcMyP0P0VT8qEJD+WBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f0daadff3321fb749274463926b1b3a37372c37bc67068f8858f180db4e5c4b","last_reissued_at":"2026-05-18T00:36:36.051021Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:36.051021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decay of Solutions of the Teukolsky Equation for Higher Spin in the Schwarzschild Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph","math-ph","math.FA","math.MP"],"primary_cat":"gr-qc","authors_text":"Felix Finster, Joel Smoller","submitted_at":"2006-07-11T16:25:44Z","abstract_excerpt":"We prove that the Schwarzschild black hole is linearly stable under electromagnetic and gravitational perturbations. Our method is to show that for spin $s=1$ or $s=2$, solutions of the Teukolsky equation with smooth, compactly supported initial data outside the event horizon, decay in $L^\\infty_{loc}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0607046","kind":"arxiv","version":5},"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/0607046","created_at":"2026-05-18T00:36:36.051101+00:00"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0607046v5","created_at":"2026-05-18T00:36:36.051101+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0607046","created_at":"2026-05-18T00:36:36.051101+00:00"},{"alias_kind":"pith_short_12","alias_value":"T4G2VX7TGIP3","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"T4G2VX7TGIP3OSJH","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"T4G2VX7T","created_at":"2026-05-18T12:25:54.717736+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/T4G2VX7TGIP3OSJHIRRZE2Y3HI","json":"https://pith.science/pith/T4G2VX7TGIP3OSJHIRRZE2Y3HI.json","graph_json":"https://pith.science/api/pith-number/T4G2VX7TGIP3OSJHIRRZE2Y3HI/graph.json","events_json":"https://pith.science/api/pith-number/T4G2VX7TGIP3OSJHIRRZE2Y3HI/events.json","paper":"https://pith.science/paper/T4G2VX7T"},"agent_actions":{"view_html":"https://pith.science/pith/T4G2VX7TGIP3OSJHIRRZE2Y3HI","download_json":"https://pith.science/pith/T4G2VX7TGIP3OSJHIRRZE2Y3HI.json","view_paper":"https://pith.science/paper/T4G2VX7T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=gr-qc/0607046&json=true","fetch_graph":"https://pith.science/api/pith-number/T4G2VX7TGIP3OSJHIRRZE2Y3HI/graph.json","fetch_events":"https://pith.science/api/pith-number/T4G2VX7TGIP3OSJHIRRZE2Y3HI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T4G2VX7TGIP3OSJHIRRZE2Y3HI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T4G2VX7TGIP3OSJHIRRZE2Y3HI/action/storage_attestation","attest_author":"https://pith.science/pith/T4G2VX7TGIP3OSJHIRRZE2Y3HI/action/author_attestation","sign_citation":"https://pith.science/pith/T4G2VX7TGIP3OSJHIRRZE2Y3HI/action/citation_signature","submit_replication":"https://pith.science/pith/T4G2VX7TGIP3OSJHIRRZE2Y3HI/action/replication_record"}},"created_at":"2026-05-18T00:36:36.051101+00:00","updated_at":"2026-05-18T00:36:36.051101+00:00"}