{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:53Y3U6KISL6QGIWKU6QNFZJDYL","short_pith_number":"pith:53Y3U6KI","schema_version":"1.0","canonical_sha256":"eef1ba794892fd0322caa7a0d2e523c2f2ccc42697f964c9fff0481363d1333b","source":{"kind":"arxiv","id":"1711.07597","version":2},"attestation_state":"computed","paper":{"title":"Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"gr-qc","authors_text":"Jeremie Szeftel, Sergiu Klainerman","submitted_at":"2017-11-21T01:23:42Z","abstract_excerpt":"We prove the nonlinear stability of the Schwarzschild spacetime under axially symmetric polarized perturbations, i.e. solutions of the Einstein vacuum equations for asymptotically flat $1+3$ dimensional Lorentzian metrics which admit a hypersurface orthogonal spacelike Killing vectorfield with closed orbits. While building on the remarkable advances made in last 15 years on establishing quantitative linear stability, the paper introduces a series of new ideas among which we emphasize the general covariant modulation (GCM) procedure which allows us to construct, dynamically, the center of mass "},"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":"1711.07597","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-11-21T01:23:42Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"e6642242e1ce44490286c9fa4eedb7d5fcac800964b889cc1f215a310a2d592f","abstract_canon_sha256":"087061eaae17e99bf5ca3d439ff8ec70eb921ab46018d841bc6deadeba5a41eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:48.790237Z","signature_b64":"zwo+9954tIbpnuQVuHK5DsZtVIMc0ufycbnwafzeIwiXEKtVsBaOjmZfQI5ofSk37CvlUTQ2DNPtgQDcDs3eAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eef1ba794892fd0322caa7a0d2e523c2f2ccc42697f964c9fff0481363d1333b","last_reissued_at":"2026-05-17T23:57:48.789744Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:48.789744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"gr-qc","authors_text":"Jeremie Szeftel, Sergiu Klainerman","submitted_at":"2017-11-21T01:23:42Z","abstract_excerpt":"We prove the nonlinear stability of the Schwarzschild spacetime under axially symmetric polarized perturbations, i.e. solutions of the Einstein vacuum equations for asymptotically flat $1+3$ dimensional Lorentzian metrics which admit a hypersurface orthogonal spacelike Killing vectorfield with closed orbits. While building on the remarkable advances made in last 15 years on establishing quantitative linear stability, the paper introduces a series of new ideas among which we emphasize the general covariant modulation (GCM) procedure which allows us to construct, dynamically, the center of mass "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07597","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":""},"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":"1711.07597","created_at":"2026-05-17T23:57:48.789825+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.07597v2","created_at":"2026-05-17T23:57:48.789825+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07597","created_at":"2026-05-17T23:57:48.789825+00:00"},{"alias_kind":"pith_short_12","alias_value":"53Y3U6KISL6Q","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"53Y3U6KISL6QGIWK","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"53Y3U6KI","created_at":"2026-05-18T12:31:00.734936+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2410.04758","citing_title":"Asymptotically Anti-de Sitter Spherically Symmetric Hairy Black Holes","ref_index":34,"is_internal_anchor":true},{"citing_arxiv_id":"1904.05363","citing_title":"Testing the nature of dark compact objects: a status report","ref_index":4,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/53Y3U6KISL6QGIWKU6QNFZJDYL","json":"https://pith.science/pith/53Y3U6KISL6QGIWKU6QNFZJDYL.json","graph_json":"https://pith.science/api/pith-number/53Y3U6KISL6QGIWKU6QNFZJDYL/graph.json","events_json":"https://pith.science/api/pith-number/53Y3U6KISL6QGIWKU6QNFZJDYL/events.json","paper":"https://pith.science/paper/53Y3U6KI"},"agent_actions":{"view_html":"https://pith.science/pith/53Y3U6KISL6QGIWKU6QNFZJDYL","download_json":"https://pith.science/pith/53Y3U6KISL6QGIWKU6QNFZJDYL.json","view_paper":"https://pith.science/paper/53Y3U6KI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.07597&json=true","fetch_graph":"https://pith.science/api/pith-number/53Y3U6KISL6QGIWKU6QNFZJDYL/graph.json","fetch_events":"https://pith.science/api/pith-number/53Y3U6KISL6QGIWKU6QNFZJDYL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/53Y3U6KISL6QGIWKU6QNFZJDYL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/53Y3U6KISL6QGIWKU6QNFZJDYL/action/storage_attestation","attest_author":"https://pith.science/pith/53Y3U6KISL6QGIWKU6QNFZJDYL/action/author_attestation","sign_citation":"https://pith.science/pith/53Y3U6KISL6QGIWKU6QNFZJDYL/action/citation_signature","submit_replication":"https://pith.science/pith/53Y3U6KISL6QGIWKU6QNFZJDYL/action/replication_record"}},"created_at":"2026-05-17T23:57:48.789825+00:00","updated_at":"2026-05-17T23:57:48.789825+00:00"}