{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:CS23FE4CWHDQSMU7QHEQOGKJFS","short_pith_number":"pith:CS23FE4C","schema_version":"1.0","canonical_sha256":"14b5b29382b1c709329f81c90719492c8416980385228e20517056985438d971","source":{"kind":"arxiv","id":"1806.05023","version":1},"attestation_state":"computed","paper":{"title":"Non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics: Birkhoff-type results in linearized gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"gr-qc","authors_text":"Paul Klinger","submitted_at":"2018-06-13T13:24:32Z","abstract_excerpt":"We prove Birkhoff-type results showing that $L^2$ solutions of the linearized Einstein equations around Riemannian Kottler (\"Schwarzschild-anti de Sitter\") metrics in arbitrary dimension and horizon topology, which are not controlled by \"master functions\" are pure gauge. Together with earlier results this implies that the $TT$-gauge-fixed linearized Einstein operator for these metrics is non-degenerate for open ranges of the mass parameter."},"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":"1806.05023","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-06-13T13:24:32Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"051bb58b8672f32ea74a0030ab09738a475be2afaca1b55b3e61a8f094a5dd4b","abstract_canon_sha256":"081db13f38bec21376a620db55f9bf14cbca92c2f456d0d00b9d3da90544c5b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:20.333246Z","signature_b64":"brs2m0pmCl8p1hz3/yv8CSyhYYFlkxeHF/fof8ss2eWudpiapkqUeaNo89dW+ZZEMey+KHo22TKBZ8CRBHQPBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14b5b29382b1c709329f81c90719492c8416980385228e20517056985438d971","last_reissued_at":"2026-05-18T00:13:20.332714Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:20.332714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics: Birkhoff-type results in linearized gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"gr-qc","authors_text":"Paul Klinger","submitted_at":"2018-06-13T13:24:32Z","abstract_excerpt":"We prove Birkhoff-type results showing that $L^2$ solutions of the linearized Einstein equations around Riemannian Kottler (\"Schwarzschild-anti de Sitter\") metrics in arbitrary dimension and horizon topology, which are not controlled by \"master functions\" are pure gauge. Together with earlier results this implies that the $TT$-gauge-fixed linearized Einstein operator for these metrics is non-degenerate for open ranges of the mass parameter."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05023","kind":"arxiv","version":1},"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":"1806.05023","created_at":"2026-05-18T00:13:20.332782+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.05023v1","created_at":"2026-05-18T00:13:20.332782+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05023","created_at":"2026-05-18T00:13:20.332782+00:00"},{"alias_kind":"pith_short_12","alias_value":"CS23FE4CWHDQ","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"CS23FE4CWHDQSMU7","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"CS23FE4C","created_at":"2026-05-18T12:32:19.392346+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.10877","citing_title":"Holographic is Hamiltonian, relatively","ref_index":20,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CS23FE4CWHDQSMU7QHEQOGKJFS","json":"https://pith.science/pith/CS23FE4CWHDQSMU7QHEQOGKJFS.json","graph_json":"https://pith.science/api/pith-number/CS23FE4CWHDQSMU7QHEQOGKJFS/graph.json","events_json":"https://pith.science/api/pith-number/CS23FE4CWHDQSMU7QHEQOGKJFS/events.json","paper":"https://pith.science/paper/CS23FE4C"},"agent_actions":{"view_html":"https://pith.science/pith/CS23FE4CWHDQSMU7QHEQOGKJFS","download_json":"https://pith.science/pith/CS23FE4CWHDQSMU7QHEQOGKJFS.json","view_paper":"https://pith.science/paper/CS23FE4C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.05023&json=true","fetch_graph":"https://pith.science/api/pith-number/CS23FE4CWHDQSMU7QHEQOGKJFS/graph.json","fetch_events":"https://pith.science/api/pith-number/CS23FE4CWHDQSMU7QHEQOGKJFS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CS23FE4CWHDQSMU7QHEQOGKJFS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CS23FE4CWHDQSMU7QHEQOGKJFS/action/storage_attestation","attest_author":"https://pith.science/pith/CS23FE4CWHDQSMU7QHEQOGKJFS/action/author_attestation","sign_citation":"https://pith.science/pith/CS23FE4CWHDQSMU7QHEQOGKJFS/action/citation_signature","submit_replication":"https://pith.science/pith/CS23FE4CWHDQSMU7QHEQOGKJFS/action/replication_record"}},"created_at":"2026-05-18T00:13:20.332782+00:00","updated_at":"2026-05-18T00:13:20.332782+00:00"}