{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:32K5IGISVHQY22GNLEDQ2GN6EY","short_pith_number":"pith:32K5IGIS","schema_version":"1.0","canonical_sha256":"de95d41912a9e18d68cd59070d19be2600dd847016bc05b359cccb170211dfc2","source":{"kind":"arxiv","id":"2207.12952","version":1},"attestation_state":"computed","paper":{"title":"Mode analysis for the linearized Einstein equations on the Kerr metric : the large $\\mathfrak{a}$ case","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Bernard F. Whiting, Dietrich H\\\"afner, Lars Andersson","submitted_at":"2022-07-26T14:57:41Z","abstract_excerpt":"We give a complete analysis of mode solutions for the linearized Einstein equations and the $1-$form wave operator on the Kerr metric in the large $\\mathfrak{a}$ case. By mode solutions we mean solutions of the form $e^{-it_*\\sigma}\\tilde{h}(r,\\theta,\\varphi)$ where $t_*$ is a suitable time variable. The corresponding Fourier transformed $1-$form wave operator and linearized Einstein operator are shown to be Fredholm between suitable function spaces and $\\tilde{h}$ has to lie in the domain of these operators. These spaces are constructed following the general framework of Vasy. No mode solutio"},"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":"2207.12952","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-07-26T14:57:41Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"5e99a220ec29a2f9ec4159f9ec26e02c861cb778f9efe8daf6594b10d27050ce","abstract_canon_sha256":"41278184fc7a4e82e0f81bd004dc62be8ee827adc9e0e12a1c42ecd95e17e8f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:43:51.899336Z","signature_b64":"Jj4NWGvxXrK/EMgWaKrgWw+I4InEnm/SXxNe6k1jCxlA2XO0+LGPNhHUMnyjMZ7hRitqWhg0Sb3lENBtDQDWDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de95d41912a9e18d68cd59070d19be2600dd847016bc05b359cccb170211dfc2","last_reissued_at":"2026-07-05T04:43:51.898933Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:43:51.898933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mode analysis for the linearized Einstein equations on the Kerr metric : the large $\\mathfrak{a}$ case","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Bernard F. Whiting, Dietrich H\\\"afner, Lars Andersson","submitted_at":"2022-07-26T14:57:41Z","abstract_excerpt":"We give a complete analysis of mode solutions for the linearized Einstein equations and the $1-$form wave operator on the Kerr metric in the large $\\mathfrak{a}$ case. By mode solutions we mean solutions of the form $e^{-it_*\\sigma}\\tilde{h}(r,\\theta,\\varphi)$ where $t_*$ is a suitable time variable. The corresponding Fourier transformed $1-$form wave operator and linearized Einstein operator are shown to be Fredholm between suitable function spaces and $\\tilde{h}$ has to lie in the domain of these operators. These spaces are constructed following the general framework of Vasy. No mode solutio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.12952","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.12952/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":"2207.12952","created_at":"2026-07-05T04:43:51.898983+00:00"},{"alias_kind":"arxiv_version","alias_value":"2207.12952v1","created_at":"2026-07-05T04:43:51.898983+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.12952","created_at":"2026-07-05T04:43:51.898983+00:00"},{"alias_kind":"pith_short_12","alias_value":"32K5IGISVHQY","created_at":"2026-07-05T04:43:51.898983+00:00"},{"alias_kind":"pith_short_16","alias_value":"32K5IGISVHQY22GN","created_at":"2026-07-05T04:43:51.898983+00:00"},{"alias_kind":"pith_short_8","alias_value":"32K5IGIS","created_at":"2026-07-05T04:43:51.898983+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.06828","citing_title":"Elliptic curvature estimates for linearised gravitational perturbations of Kerr in the full sub-extremal range $|a|<M$","ref_index":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/32K5IGISVHQY22GNLEDQ2GN6EY","json":"https://pith.science/pith/32K5IGISVHQY22GNLEDQ2GN6EY.json","graph_json":"https://pith.science/api/pith-number/32K5IGISVHQY22GNLEDQ2GN6EY/graph.json","events_json":"https://pith.science/api/pith-number/32K5IGISVHQY22GNLEDQ2GN6EY/events.json","paper":"https://pith.science/paper/32K5IGIS"},"agent_actions":{"view_html":"https://pith.science/pith/32K5IGISVHQY22GNLEDQ2GN6EY","download_json":"https://pith.science/pith/32K5IGISVHQY22GNLEDQ2GN6EY.json","view_paper":"https://pith.science/paper/32K5IGIS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2207.12952&json=true","fetch_graph":"https://pith.science/api/pith-number/32K5IGISVHQY22GNLEDQ2GN6EY/graph.json","fetch_events":"https://pith.science/api/pith-number/32K5IGISVHQY22GNLEDQ2GN6EY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/32K5IGISVHQY22GNLEDQ2GN6EY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/32K5IGISVHQY22GNLEDQ2GN6EY/action/storage_attestation","attest_author":"https://pith.science/pith/32K5IGISVHQY22GNLEDQ2GN6EY/action/author_attestation","sign_citation":"https://pith.science/pith/32K5IGISVHQY22GNLEDQ2GN6EY/action/citation_signature","submit_replication":"https://pith.science/pith/32K5IGISVHQY22GNLEDQ2GN6EY/action/replication_record"}},"created_at":"2026-07-05T04:43:51.898983+00:00","updated_at":"2026-07-05T04:43:51.898983+00:00"}