{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:BMYD42IRTJ46YM66TBNJAM2ABV","short_pith_number":"pith:BMYD42IR","schema_version":"1.0","canonical_sha256":"0b303e69119a79ec33de985a9033400d63ddc410b0c9d85867e7a20bad994e94","source":{"kind":"arxiv","id":"0706.3669","version":1},"attestation_state":"computed","paper":{"title":"The wave equation on asymptotically de Sitter-like spaces","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Andras Vasy","submitted_at":"2007-06-25T16:32:15Z","abstract_excerpt":"In this paper we obtain the asymptotic behavior of solutions of the Klein-Gordon equation on Lorentzian manifolds $(X^\\circ,g)$ which are de Sitter-like at infinity. Such manifolds are Lorentzian analogues of the so-called Riemannian conformally compact (or asymptotically hyperbolic) spaces. Under global assumptions on the (null)bicharacteristic flow, namely that the boundary of the compactification X is a union of two disjoint manifolds, Y+ and Y-, and each bicharacteristic converges to one of these two manifolds as the parameter along the bicharacteristic goes to plus infinity, and to the ot"},"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":"0706.3669","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2007-06-25T16:32:15Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"9cd521394eaceab3c5f3890172a2b7678fe7e42792ce95d4ddb42d43c15d3a02","abstract_canon_sha256":"eb7bfd600650aada7e22f1804802c09bba56681ba6a8020f79888b12c80bef00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:02:26.274677Z","signature_b64":"V0ysCjSADF9v/nHWX8iIz85vENa1C3vvlsnr98jzjqYRU+J9dtqIUrOZ2biQ8OGk6hPK7Wjdihlx+dcosKl6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b303e69119a79ec33de985a9033400d63ddc410b0c9d85867e7a20bad994e94","last_reissued_at":"2026-07-04T15:02:26.274337Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:02:26.274337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The wave equation on asymptotically de Sitter-like spaces","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Andras Vasy","submitted_at":"2007-06-25T16:32:15Z","abstract_excerpt":"In this paper we obtain the asymptotic behavior of solutions of the Klein-Gordon equation on Lorentzian manifolds $(X^\\circ,g)$ which are de Sitter-like at infinity. Such manifolds are Lorentzian analogues of the so-called Riemannian conformally compact (or asymptotically hyperbolic) spaces. Under global assumptions on the (null)bicharacteristic flow, namely that the boundary of the compactification X is a union of two disjoint manifolds, Y+ and Y-, and each bicharacteristic converges to one of these two manifolds as the parameter along the bicharacteristic goes to plus infinity, and to the ot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.3669","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/0706.3669/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":"0706.3669","created_at":"2026-07-04T15:02:26.274391+00:00"},{"alias_kind":"arxiv_version","alias_value":"0706.3669v1","created_at":"2026-07-04T15:02:26.274391+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.3669","created_at":"2026-07-04T15:02:26.274391+00:00"},{"alias_kind":"pith_short_12","alias_value":"BMYD42IRTJ46","created_at":"2026-07-04T15:02:26.274391+00:00"},{"alias_kind":"pith_short_16","alias_value":"BMYD42IRTJ46YM66","created_at":"2026-07-04T15:02:26.274391+00:00"},{"alias_kind":"pith_short_8","alias_value":"BMYD42IR","created_at":"2026-07-04T15:02:26.274391+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/BMYD42IRTJ46YM66TBNJAM2ABV","json":"https://pith.science/pith/BMYD42IRTJ46YM66TBNJAM2ABV.json","graph_json":"https://pith.science/api/pith-number/BMYD42IRTJ46YM66TBNJAM2ABV/graph.json","events_json":"https://pith.science/api/pith-number/BMYD42IRTJ46YM66TBNJAM2ABV/events.json","paper":"https://pith.science/paper/BMYD42IR"},"agent_actions":{"view_html":"https://pith.science/pith/BMYD42IRTJ46YM66TBNJAM2ABV","download_json":"https://pith.science/pith/BMYD42IRTJ46YM66TBNJAM2ABV.json","view_paper":"https://pith.science/paper/BMYD42IR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0706.3669&json=true","fetch_graph":"https://pith.science/api/pith-number/BMYD42IRTJ46YM66TBNJAM2ABV/graph.json","fetch_events":"https://pith.science/api/pith-number/BMYD42IRTJ46YM66TBNJAM2ABV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BMYD42IRTJ46YM66TBNJAM2ABV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BMYD42IRTJ46YM66TBNJAM2ABV/action/storage_attestation","attest_author":"https://pith.science/pith/BMYD42IRTJ46YM66TBNJAM2ABV/action/author_attestation","sign_citation":"https://pith.science/pith/BMYD42IRTJ46YM66TBNJAM2ABV/action/citation_signature","submit_replication":"https://pith.science/pith/BMYD42IRTJ46YM66TBNJAM2ABV/action/replication_record"}},"created_at":"2026-07-04T15:02:26.274391+00:00","updated_at":"2026-07-04T15:02:26.274391+00:00"}