{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MZT2FTKLAZNVILB3UXA7ZN4RD4","short_pith_number":"pith:MZT2FTKL","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"},"canonical_sha256":"6667a2cd4b065b542c3ba5c1fcb7911f2e23cf82f706121a92e035b499b5f16d","source":{"kind":"arxiv","id":"1802.09044","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.09044","created_at":"2026-05-18T00:11:06Z"},{"alias_kind":"arxiv_version","alias_value":"1802.09044v1","created_at":"2026-05-18T00:11:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.09044","created_at":"2026-05-18T00:11:06Z"},{"alias_kind":"pith_short_12","alias_value":"MZT2FTKLAZNV","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MZT2FTKLAZNVILB3","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MZT2FTKL","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MZT2FTKLAZNVILB3UXA7ZN4RD4","target":"record","payload":{"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"},"canonical_sha256":"6667a2cd4b065b542c3ba5c1fcb7911f2e23cf82f706121a92e035b499b5f16d","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"},"source_kind":"arxiv","source_id":"1802.09044","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ghhNhTuImxhaRfHbf8Lu+tBKc/aQfhP/qHZymVRK7c466GBM6zGdKzeGssT38a+PuNKJrLw724dFyIiMD7+oAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:47:16.819584Z"},"content_sha256":"291fea1b234d87d2163d5acfdc0856090425d8ce94671a229a2e6f55e329d315","schema_version":"1.0","event_id":"sha256:291fea1b234d87d2163d5acfdc0856090425d8ce94671a229a2e6f55e329d315"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MZT2FTKLAZNVILB3UXA7ZN4RD4","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3vKqkPiqpvTPl4NusxHE62EKhAkukG9PjR+7WpFsBgQ7zFsloHoCNB5S6HHaG/g+fgcu3KF7BpLpKx5QZKlLBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:47:16.820419Z"},"content_sha256":"16afd02d3196d9160cf013faf704be1a7e14fdcdaa48702531dd0d915e4256d0","schema_version":"1.0","event_id":"sha256:16afd02d3196d9160cf013faf704be1a7e14fdcdaa48702531dd0d915e4256d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MZT2FTKLAZNVILB3UXA7ZN4RD4/bundle.json","state_url":"https://pith.science/pith/MZT2FTKLAZNVILB3UXA7ZN4RD4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MZT2FTKLAZNVILB3UXA7ZN4RD4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T17:47:16Z","links":{"resolver":"https://pith.science/pith/MZT2FTKLAZNVILB3UXA7ZN4RD4","bundle":"https://pith.science/pith/MZT2FTKLAZNVILB3UXA7ZN4RD4/bundle.json","state":"https://pith.science/pith/MZT2FTKLAZNVILB3UXA7ZN4RD4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MZT2FTKLAZNVILB3UXA7ZN4RD4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MZT2FTKLAZNVILB3UXA7ZN4RD4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"817d9fe2f9dda65fa525cbf389369f5e0245f28e223b4e0b1c560b8691fa2de0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-02-25T17:08:16Z","title_canon_sha256":"d123d3fee711c053341aa49494681c5a8f308f69c33344ac2f4eb8fdcbc072ed"},"schema_version":"1.0","source":{"id":"1802.09044","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.09044","created_at":"2026-05-18T00:11:06Z"},{"alias_kind":"arxiv_version","alias_value":"1802.09044v1","created_at":"2026-05-18T00:11:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.09044","created_at":"2026-05-18T00:11:06Z"},{"alias_kind":"pith_short_12","alias_value":"MZT2FTKLAZNV","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MZT2FTKLAZNVILB3","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MZT2FTKL","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:16afd02d3196d9160cf013faf704be1a7e14fdcdaa48702531dd0d915e4256d0","target":"graph","created_at":"2026-05-18T00:11:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Petros A. Terzis, T. Christodoulakis, T.Pailas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-02-25T17:08:16Z","title":"The solution space to the Einstein's vacuum field equations for the case of five-dimensional Bianchi Type I (Type 4A1)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09044","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:291fea1b234d87d2163d5acfdc0856090425d8ce94671a229a2e6f55e329d315","target":"record","created_at":"2026-05-18T00:11:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"817d9fe2f9dda65fa525cbf389369f5e0245f28e223b4e0b1c560b8691fa2de0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-02-25T17:08:16Z","title_canon_sha256":"d123d3fee711c053341aa49494681c5a8f308f69c33344ac2f4eb8fdcbc072ed"},"schema_version":"1.0","source":{"id":"1802.09044","kind":"arxiv","version":1}},"canonical_sha256":"6667a2cd4b065b542c3ba5c1fcb7911f2e23cf82f706121a92e035b499b5f16d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6667a2cd4b065b542c3ba5c1fcb7911f2e23cf82f706121a92e035b499b5f16d","first_computed_at":"2026-05-18T00:11:06.053420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:06.053420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/5+9uTSt0gnI4Pad8Q7m+bBx7WE91WZ/ZD0uVnw7uzOpcPYyBUOK+0aLM2l0TtFUw63ZplLRNTU9/R3I8u/qBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:06.054174Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.09044","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:291fea1b234d87d2163d5acfdc0856090425d8ce94671a229a2e6f55e329d315","sha256:16afd02d3196d9160cf013faf704be1a7e14fdcdaa48702531dd0d915e4256d0"],"state_sha256":"afdce521af5738a3c1e82d05a3082400ea6e02c564cec47d2a64cdcc816fbfa1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BawVkkPjj+R+23d72sAM+bCVrsB18YhM9KPKGQQY1VMeZAmTJzXsResgy4ksDk+aQLlW4+qFwc5RtTCi/M7lAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T17:47:16.824335Z","bundle_sha256":"fe2e6f814cbb623da8224af3a9297f0f989a5f00bcaa1a6f419d4d3e18053bb7"}}