{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:VRZTEDV62OG4I34YEEOAABHQPS","short_pith_number":"pith:VRZTEDV6","schema_version":"1.0","canonical_sha256":"ac73320ebed38dc46f98211c0004f07cb4eb3d09402598b4cc9a018cc0a4a600","source":{"kind":"arxiv","id":"1810.11788","version":3},"attestation_state":"computed","paper":{"title":"Future stability of the FLRW spacetime for a large class of perfect fluids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"gr-qc","authors_text":"Changhua Wei, Chao Liu","submitted_at":"2018-10-28T09:48:07Z","abstract_excerpt":"We establish the future non-linear stability of Friedmann-Lema\\^{\\i}tre-Robertson-Walker (FLRW) solutions to the Einstein-Euler equations of the universe filled with a large class of perfect fluids (the equations of state are allowed to be certain nonlinear or linear types both). Several previous results as specific examples can be covered in the results of this article. We emphasize that the future stability of FLRW metric for polytropic fluids with positive cosmological constant has been a difficult problem and can not be directly generalized from the previous known results. Our result in th"},"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":"1810.11788","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-10-28T09:48:07Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"fc3995bf0d7a21146efb1546406042674730e6220f67189767d05fa96603c738","abstract_canon_sha256":"15900245df1f843079274ac72c2912082febda9f8fc3c23dfcc1079c07f5d91a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:11:19.100180Z","signature_b64":"WNSEjdSAUq0sza8yHHMROTntoCE5S5O/SDemCE4WkhxlfM1K6NlvpvB2BS9n/r3MeFJiTGjTLJjyo9guwgfwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac73320ebed38dc46f98211c0004f07cb4eb3d09402598b4cc9a018cc0a4a600","last_reissued_at":"2026-07-05T02:11:19.099768Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:11:19.099768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Future stability of the FLRW spacetime for a large class of perfect fluids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"gr-qc","authors_text":"Changhua Wei, Chao Liu","submitted_at":"2018-10-28T09:48:07Z","abstract_excerpt":"We establish the future non-linear stability of Friedmann-Lema\\^{\\i}tre-Robertson-Walker (FLRW) solutions to the Einstein-Euler equations of the universe filled with a large class of perfect fluids (the equations of state are allowed to be certain nonlinear or linear types both). Several previous results as specific examples can be covered in the results of this article. We emphasize that the future stability of FLRW metric for polytropic fluids with positive cosmological constant has been a difficult problem and can not be directly generalized from the previous known results. Our result in th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11788","kind":"arxiv","version":3},"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/1810.11788/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":"1810.11788","created_at":"2026-07-05T02:11:19.099822+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.11788v3","created_at":"2026-07-05T02:11:19.099822+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.11788","created_at":"2026-07-05T02:11:19.099822+00:00"},{"alias_kind":"pith_short_12","alias_value":"VRZTEDV62OG4","created_at":"2026-07-05T02:11:19.099822+00:00"},{"alias_kind":"pith_short_16","alias_value":"VRZTEDV62OG4I34Y","created_at":"2026-07-05T02:11:19.099822+00:00"},{"alias_kind":"pith_short_8","alias_value":"VRZTEDV6","created_at":"2026-07-05T02:11:19.099822+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/VRZTEDV62OG4I34YEEOAABHQPS","json":"https://pith.science/pith/VRZTEDV62OG4I34YEEOAABHQPS.json","graph_json":"https://pith.science/api/pith-number/VRZTEDV62OG4I34YEEOAABHQPS/graph.json","events_json":"https://pith.science/api/pith-number/VRZTEDV62OG4I34YEEOAABHQPS/events.json","paper":"https://pith.science/paper/VRZTEDV6"},"agent_actions":{"view_html":"https://pith.science/pith/VRZTEDV62OG4I34YEEOAABHQPS","download_json":"https://pith.science/pith/VRZTEDV62OG4I34YEEOAABHQPS.json","view_paper":"https://pith.science/paper/VRZTEDV6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.11788&json=true","fetch_graph":"https://pith.science/api/pith-number/VRZTEDV62OG4I34YEEOAABHQPS/graph.json","fetch_events":"https://pith.science/api/pith-number/VRZTEDV62OG4I34YEEOAABHQPS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VRZTEDV62OG4I34YEEOAABHQPS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VRZTEDV62OG4I34YEEOAABHQPS/action/storage_attestation","attest_author":"https://pith.science/pith/VRZTEDV62OG4I34YEEOAABHQPS/action/author_attestation","sign_citation":"https://pith.science/pith/VRZTEDV62OG4I34YEEOAABHQPS/action/citation_signature","submit_replication":"https://pith.science/pith/VRZTEDV62OG4I34YEEOAABHQPS/action/replication_record"}},"created_at":"2026-07-05T02:11:19.099822+00:00","updated_at":"2026-07-05T02:11:19.099822+00:00"}