{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:YEIBB6MKELOOMNINIERPJKG4P6","short_pith_number":"pith:YEIBB6MK","schema_version":"1.0","canonical_sha256":"c11010f98a22dce6350d4122f4a8dc7f96bd949248585364b027976cb5bac4c6","source":{"kind":"arxiv","id":"gr-qc/0512070","version":2},"attestation_state":"computed","paper":{"title":"The late-time behaviour of vortic Bianchi type VIII Universes","license":"","headline":"","cross_cats":["astro-ph","hep-th"],"primary_cat":"gr-qc","authors_text":"Sigbjorn Hervik, Woei Chet Lim","submitted_at":"2005-12-12T17:31:35Z","abstract_excerpt":"We use the dynamical systems approach to investigate the Bianchi type VIII models with a tilted $\\gamma$-law perfect fluid. We introduce expansion-normalised variables and investigate the late-time asymptotic behaviour of the models and determine the late-time asymptotic states. For the Bianchi type VIII models the state space is unbounded and consequently, for all non-inflationary perfect fluids, one of the curvature variables grows without bound. Moreover, we show that for fluids stiffer than dust ($1<\\gamma<2$), the fluid will in general tend towards a state of extreme tilt. For dust ($\\gam"},"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":"gr-qc/0512070","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2005-12-12T17:31:35Z","cross_cats_sorted":["astro-ph","hep-th"],"title_canon_sha256":"f09434850eb13a8080c944ac87667fce2937afbbe3596b0f4586f5dc34249836","abstract_canon_sha256":"b46ffe6b052a2edfdd956ada4a7f538cc32caff9c017c0f293ae798961778b60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:37:00.840355Z","signature_b64":"Pms/A/nK5j3b+tbuzW/7rrMLhFdZ+W/mgaqfe+SZRTcQW9wkMnnXFPL67oLRMsuNWS1fS+KHdiEvSpDugNeKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c11010f98a22dce6350d4122f4a8dc7f96bd949248585364b027976cb5bac4c6","last_reissued_at":"2026-05-18T04:37:00.839660Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:37:00.839660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The late-time behaviour of vortic Bianchi type VIII Universes","license":"","headline":"","cross_cats":["astro-ph","hep-th"],"primary_cat":"gr-qc","authors_text":"Sigbjorn Hervik, Woei Chet Lim","submitted_at":"2005-12-12T17:31:35Z","abstract_excerpt":"We use the dynamical systems approach to investigate the Bianchi type VIII models with a tilted $\\gamma$-law perfect fluid. We introduce expansion-normalised variables and investigate the late-time asymptotic behaviour of the models and determine the late-time asymptotic states. For the Bianchi type VIII models the state space is unbounded and consequently, for all non-inflationary perfect fluids, one of the curvature variables grows without bound. Moreover, we show that for fluids stiffer than dust ($1<\\gamma<2$), the fluid will in general tend towards a state of extreme tilt. For dust ($\\gam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0512070","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":"gr-qc/0512070","created_at":"2026-05-18T04:37:00.839768+00:00"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0512070v2","created_at":"2026-05-18T04:37:00.839768+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0512070","created_at":"2026-05-18T04:37:00.839768+00:00"},{"alias_kind":"pith_short_12","alias_value":"YEIBB6MKELOO","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"YEIBB6MKELOOMNIN","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"YEIBB6MK","created_at":"2026-05-18T12:25:53.939244+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/YEIBB6MKELOOMNINIERPJKG4P6","json":"https://pith.science/pith/YEIBB6MKELOOMNINIERPJKG4P6.json","graph_json":"https://pith.science/api/pith-number/YEIBB6MKELOOMNINIERPJKG4P6/graph.json","events_json":"https://pith.science/api/pith-number/YEIBB6MKELOOMNINIERPJKG4P6/events.json","paper":"https://pith.science/paper/YEIBB6MK"},"agent_actions":{"view_html":"https://pith.science/pith/YEIBB6MKELOOMNINIERPJKG4P6","download_json":"https://pith.science/pith/YEIBB6MKELOOMNINIERPJKG4P6.json","view_paper":"https://pith.science/paper/YEIBB6MK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=gr-qc/0512070&json=true","fetch_graph":"https://pith.science/api/pith-number/YEIBB6MKELOOMNINIERPJKG4P6/graph.json","fetch_events":"https://pith.science/api/pith-number/YEIBB6MKELOOMNINIERPJKG4P6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YEIBB6MKELOOMNINIERPJKG4P6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YEIBB6MKELOOMNINIERPJKG4P6/action/storage_attestation","attest_author":"https://pith.science/pith/YEIBB6MKELOOMNINIERPJKG4P6/action/author_attestation","sign_citation":"https://pith.science/pith/YEIBB6MKELOOMNINIERPJKG4P6/action/citation_signature","submit_replication":"https://pith.science/pith/YEIBB6MKELOOMNINIERPJKG4P6/action/replication_record"}},"created_at":"2026-05-18T04:37:00.839768+00:00","updated_at":"2026-05-18T04:37:00.839768+00:00"}