{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:FYABKL4B3X23745G3KPUW7WJBK","short_pith_number":"pith:FYABKL4B","schema_version":"1.0","canonical_sha256":"2e00152f81ddf5bff3a6da9f4b7ec90a937dbe0af70d3f041d273398cb092c97","source":{"kind":"arxiv","id":"1702.00987","version":2},"attestation_state":"computed","paper":{"title":"Embedding FLRW Geometries in Pseudo-Euclidean and Anti-de Sitter Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"M. M. Akbar","submitted_at":"2017-02-03T12:27:24Z","abstract_excerpt":"Contrary to the general consensus in the literature that Friedmann--Lema\\^{i}tre--Robertson--Walker (FLRW) geometries are of embedding class one (i.e.,\\ embeddable in one higher dimensional pseudo-Euclidean spaces), we show that the most general $k=0$ and $k=-1$ FLRW geometries are of embedding class two, and their corresponding pseudo-Euclidean spaces have strictly one and two negative eigenvalues, respectively. These are particular results that follow from the new perspective on FLRW embedding that we develop in this paper, namely that these embeddings are equivalent to unit-speed parametriz"},"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":"1702.00987","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-02-03T12:27:24Z","cross_cats_sorted":[],"title_canon_sha256":"2271ea936c99c0f3839ed39fcf034217a892ff2599919a995d0ab474c7c0c203","abstract_canon_sha256":"347d558ccec931a818281969bf471d82d3639f4c58c380637c2ec65297a91756"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:03.795630Z","signature_b64":"J8tCU+TGWpKfpPLDdusrRLAzUqVGEzEZph7N4kiCjhvH7/++9v5un6R+svPQAkn6U7YM287dYaf48GRcIrvgBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e00152f81ddf5bff3a6da9f4b7ec90a937dbe0af70d3f041d273398cb092c97","last_reissued_at":"2026-05-18T00:47:03.794784Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:03.794784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Embedding FLRW Geometries in Pseudo-Euclidean and Anti-de Sitter Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"M. M. Akbar","submitted_at":"2017-02-03T12:27:24Z","abstract_excerpt":"Contrary to the general consensus in the literature that Friedmann--Lema\\^{i}tre--Robertson--Walker (FLRW) geometries are of embedding class one (i.e.,\\ embeddable in one higher dimensional pseudo-Euclidean spaces), we show that the most general $k=0$ and $k=-1$ FLRW geometries are of embedding class two, and their corresponding pseudo-Euclidean spaces have strictly one and two negative eigenvalues, respectively. These are particular results that follow from the new perspective on FLRW embedding that we develop in this paper, namely that these embeddings are equivalent to unit-speed parametriz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00987","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":"1702.00987","created_at":"2026-05-18T00:47:03.794928+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.00987v2","created_at":"2026-05-18T00:47:03.794928+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00987","created_at":"2026-05-18T00:47:03.794928+00:00"},{"alias_kind":"pith_short_12","alias_value":"FYABKL4B3X23","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"FYABKL4B3X23745G","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"FYABKL4B","created_at":"2026-05-18T12:31:15.632608+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/FYABKL4B3X23745G3KPUW7WJBK","json":"https://pith.science/pith/FYABKL4B3X23745G3KPUW7WJBK.json","graph_json":"https://pith.science/api/pith-number/FYABKL4B3X23745G3KPUW7WJBK/graph.json","events_json":"https://pith.science/api/pith-number/FYABKL4B3X23745G3KPUW7WJBK/events.json","paper":"https://pith.science/paper/FYABKL4B"},"agent_actions":{"view_html":"https://pith.science/pith/FYABKL4B3X23745G3KPUW7WJBK","download_json":"https://pith.science/pith/FYABKL4B3X23745G3KPUW7WJBK.json","view_paper":"https://pith.science/paper/FYABKL4B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.00987&json=true","fetch_graph":"https://pith.science/api/pith-number/FYABKL4B3X23745G3KPUW7WJBK/graph.json","fetch_events":"https://pith.science/api/pith-number/FYABKL4B3X23745G3KPUW7WJBK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FYABKL4B3X23745G3KPUW7WJBK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FYABKL4B3X23745G3KPUW7WJBK/action/storage_attestation","attest_author":"https://pith.science/pith/FYABKL4B3X23745G3KPUW7WJBK/action/author_attestation","sign_citation":"https://pith.science/pith/FYABKL4B3X23745G3KPUW7WJBK/action/citation_signature","submit_replication":"https://pith.science/pith/FYABKL4B3X23745G3KPUW7WJBK/action/replication_record"}},"created_at":"2026-05-18T00:47:03.794928+00:00","updated_at":"2026-05-18T00:47:03.794928+00:00"}