{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:ZHFT4LOWZGS4GJIPGXGUUDG7WO","short_pith_number":"pith:ZHFT4LOW","schema_version":"1.0","canonical_sha256":"c9cb3e2dd6c9a5c3250f35cd4a0cdfb398472e8aea454080a58fe20fc41cd8bf","source":{"kind":"arxiv","id":"1207.6350","version":3},"attestation_state":"computed","paper":{"title":"The McVittie solution with a negative cosmological constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-th"],"primary_cat":"gr-qc","authors_text":"Kayll Lake, Majd Abdelqader, Philippe Landry","submitted_at":"2012-07-26T17:51:44Z","abstract_excerpt":"Whereas current cosmological observations suggest that the universe is dominated by a positive cosmological constant ($\\Lambda > 0$), the AdS/CFT correspondence tells us that the case $\\Lambda<0$ is still worthy of consideration. In this paper we study the McVittie solution with $\\Lambda<0$. Following a related study, the solution is understood here by way of a systematic construction of conformal diagrams based on detailed numerical integrations of the null geodesic equations. As in the pure Robertson - Walker case, we find that $\\Lambda<0$ ensures collapse to a Big Crunch, a feature which co"},"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":"1207.6350","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-07-26T17:51:44Z","cross_cats_sorted":["astro-ph.CO","hep-th"],"title_canon_sha256":"c4d5d17f2a4cfdc7925ce0fb937e65968c9d2c392916a2063a0b1df8a7062dfc","abstract_canon_sha256":"be91b54b6b162da0fdc409b92663dcad20d5b4fb73c736c5c9be7ab8cd36e294"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:30.823388Z","signature_b64":"1fu12f5MxkkW8YhplNoS3XC9S6oDBSqoj+w5UsR+xlAZ//8qgQ0tZstp91TchiPlZ5j3vxiLkDtartgaxeKGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9cb3e2dd6c9a5c3250f35cd4a0cdfb398472e8aea454080a58fe20fc41cd8bf","last_reissued_at":"2026-05-18T03:22:30.822664Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:30.822664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The McVittie solution with a negative cosmological constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-th"],"primary_cat":"gr-qc","authors_text":"Kayll Lake, Majd Abdelqader, Philippe Landry","submitted_at":"2012-07-26T17:51:44Z","abstract_excerpt":"Whereas current cosmological observations suggest that the universe is dominated by a positive cosmological constant ($\\Lambda > 0$), the AdS/CFT correspondence tells us that the case $\\Lambda<0$ is still worthy of consideration. In this paper we study the McVittie solution with $\\Lambda<0$. Following a related study, the solution is understood here by way of a systematic construction of conformal diagrams based on detailed numerical integrations of the null geodesic equations. As in the pure Robertson - Walker case, we find that $\\Lambda<0$ ensures collapse to a Big Crunch, a feature which co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6350","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":""},"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":"1207.6350","created_at":"2026-05-18T03:22:30.822773+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.6350v3","created_at":"2026-05-18T03:22:30.822773+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6350","created_at":"2026-05-18T03:22:30.822773+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZHFT4LOWZGS4","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZHFT4LOWZGS4GJIP","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZHFT4LOW","created_at":"2026-05-18T12:27:30.460161+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.04961","citing_title":"Charged cosmological black holes: a thorough study of a family of solutions","ref_index":38,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZHFT4LOWZGS4GJIPGXGUUDG7WO","json":"https://pith.science/pith/ZHFT4LOWZGS4GJIPGXGUUDG7WO.json","graph_json":"https://pith.science/api/pith-number/ZHFT4LOWZGS4GJIPGXGUUDG7WO/graph.json","events_json":"https://pith.science/api/pith-number/ZHFT4LOWZGS4GJIPGXGUUDG7WO/events.json","paper":"https://pith.science/paper/ZHFT4LOW"},"agent_actions":{"view_html":"https://pith.science/pith/ZHFT4LOWZGS4GJIPGXGUUDG7WO","download_json":"https://pith.science/pith/ZHFT4LOWZGS4GJIPGXGUUDG7WO.json","view_paper":"https://pith.science/paper/ZHFT4LOW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.6350&json=true","fetch_graph":"https://pith.science/api/pith-number/ZHFT4LOWZGS4GJIPGXGUUDG7WO/graph.json","fetch_events":"https://pith.science/api/pith-number/ZHFT4LOWZGS4GJIPGXGUUDG7WO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZHFT4LOWZGS4GJIPGXGUUDG7WO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZHFT4LOWZGS4GJIPGXGUUDG7WO/action/storage_attestation","attest_author":"https://pith.science/pith/ZHFT4LOWZGS4GJIPGXGUUDG7WO/action/author_attestation","sign_citation":"https://pith.science/pith/ZHFT4LOWZGS4GJIPGXGUUDG7WO/action/citation_signature","submit_replication":"https://pith.science/pith/ZHFT4LOWZGS4GJIPGXGUUDG7WO/action/replication_record"}},"created_at":"2026-05-18T03:22:30.822773+00:00","updated_at":"2026-05-18T03:22:30.822773+00:00"}