{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:MZT2FTKLAZNVILB3UXA7ZN4RD4","short_pith_number":"pith:MZT2FTKL","schema_version":"1.0","canonical_sha256":"6667a2cd4b065b542c3ba5c1fcb7911f2e23cf82f706121a92e035b499b5f16d","source":{"kind":"arxiv","id":"1802.09044","version":1},"attestation_state":"computed","paper":{"title":"The solution space to the Einstein's vacuum field equations for the case of five-dimensional Bianchi Type I (Type 4A1)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Petros A. Terzis, T. Christodoulakis, T.Pailas","submitted_at":"2018-02-25T17:08:16Z","abstract_excerpt":"We consider the 4+1 Einstein's field equations (EFE's) in vacuum, simplified by the assumption that there is a four-dimensional sub-manifold on which an isometry group of dimension four acts simply transitive. In particular we consider the Abelian group Type 4A1; and thus the emerging homogeneous sub-space is flat. Through the use of coordinate transformations that preserve the sub-manifold's manifest homogeneity, a coordinate system is chosen in which the shift vector is zero. The resulting equations remain form invariant under the action of the constant Automorphisms group. This group is use"},"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":"1802.09044","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-02-25T17:08:16Z","cross_cats_sorted":[],"title_canon_sha256":"d123d3fee711c053341aa49494681c5a8f308f69c33344ac2f4eb8fdcbc072ed","abstract_canon_sha256":"817d9fe2f9dda65fa525cbf389369f5e0245f28e223b4e0b1c560b8691fa2de0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:06.054174Z","signature_b64":"/5+9uTSt0gnI4Pad8Q7m+bBx7WE91WZ/ZD0uVnw7uzOpcPYyBUOK+0aLM2l0TtFUw63ZplLRNTU9/R3I8u/qBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6667a2cd4b065b542c3ba5c1fcb7911f2e23cf82f706121a92e035b499b5f16d","last_reissued_at":"2026-05-18T00:11:06.053420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:06.053420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The solution space to the Einstein's vacuum field equations for the case of five-dimensional Bianchi Type I (Type 4A1)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Petros A. Terzis, T. Christodoulakis, T.Pailas","submitted_at":"2018-02-25T17:08:16Z","abstract_excerpt":"We consider the 4+1 Einstein's field equations (EFE's) in vacuum, simplified by the assumption that there is a four-dimensional sub-manifold on which an isometry group of dimension four acts simply transitive. In particular we consider the Abelian group Type 4A1; and thus the emerging homogeneous sub-space is flat. Through the use of coordinate transformations that preserve the sub-manifold's manifest homogeneity, a coordinate system is chosen in which the shift vector is zero. The resulting equations remain form invariant under the action of the constant Automorphisms group. This group is use"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09044","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":""},"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":"1802.09044","created_at":"2026-05-18T00:11:06.053551+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.09044v1","created_at":"2026-05-18T00:11:06.053551+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.09044","created_at":"2026-05-18T00:11:06.053551+00:00"},{"alias_kind":"pith_short_12","alias_value":"MZT2FTKLAZNV","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_16","alias_value":"MZT2FTKLAZNVILB3","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_8","alias_value":"MZT2FTKL","created_at":"2026-05-18T12:32:40.477152+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/MZT2FTKLAZNVILB3UXA7ZN4RD4","json":"https://pith.science/pith/MZT2FTKLAZNVILB3UXA7ZN4RD4.json","graph_json":"https://pith.science/api/pith-number/MZT2FTKLAZNVILB3UXA7ZN4RD4/graph.json","events_json":"https://pith.science/api/pith-number/MZT2FTKLAZNVILB3UXA7ZN4RD4/events.json","paper":"https://pith.science/paper/MZT2FTKL"},"agent_actions":{"view_html":"https://pith.science/pith/MZT2FTKLAZNVILB3UXA7ZN4RD4","download_json":"https://pith.science/pith/MZT2FTKLAZNVILB3UXA7ZN4RD4.json","view_paper":"https://pith.science/paper/MZT2FTKL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.09044&json=true","fetch_graph":"https://pith.science/api/pith-number/MZT2FTKLAZNVILB3UXA7ZN4RD4/graph.json","fetch_events":"https://pith.science/api/pith-number/MZT2FTKLAZNVILB3UXA7ZN4RD4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MZT2FTKLAZNVILB3UXA7ZN4RD4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MZT2FTKLAZNVILB3UXA7ZN4RD4/action/storage_attestation","attest_author":"https://pith.science/pith/MZT2FTKLAZNVILB3UXA7ZN4RD4/action/author_attestation","sign_citation":"https://pith.science/pith/MZT2FTKLAZNVILB3UXA7ZN4RD4/action/citation_signature","submit_replication":"https://pith.science/pith/MZT2FTKLAZNVILB3UXA7ZN4RD4/action/replication_record"}},"created_at":"2026-05-18T00:11:06.053551+00:00","updated_at":"2026-05-18T00:11:06.053551+00:00"}