{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:FQ7MNNTOSMNT2VDNGPP2OVBJMH","short_pith_number":"pith:FQ7MNNTO","canonical_record":{"source":{"id":"1106.3897","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-06-20T13:36:37Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"75364943b0b5b71591c06435547ddc68100d2e34713b16b7807eac6e070ab605","abstract_canon_sha256":"e0e66e489df9ce9db243feef91d989d69f1250f4d844162b2af08f959f14b56f"},"schema_version":"1.0"},"canonical_sha256":"2c3ec6b66e931b3d546d33dfa7542961d9b6ec7540fa064d55bc1602e0595726","source":{"kind":"arxiv","id":"1106.3897","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3897","created_at":"2026-05-18T02:01:34Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3897v2","created_at":"2026-05-18T02:01:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3897","created_at":"2026-05-18T02:01:34Z"},{"alias_kind":"pith_short_12","alias_value":"FQ7MNNTOSMNT","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FQ7MNNTOSMNT2VDN","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FQ7MNNTO","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:FQ7MNNTOSMNT2VDNGPP2OVBJMH","target":"record","payload":{"canonical_record":{"source":{"id":"1106.3897","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-06-20T13:36:37Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"75364943b0b5b71591c06435547ddc68100d2e34713b16b7807eac6e070ab605","abstract_canon_sha256":"e0e66e489df9ce9db243feef91d989d69f1250f4d844162b2af08f959f14b56f"},"schema_version":"1.0"},"canonical_sha256":"2c3ec6b66e931b3d546d33dfa7542961d9b6ec7540fa064d55bc1602e0595726","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:34.835104Z","signature_b64":"SGlN7vMebgkc8RdLqWWGlpFON0+kzJSWsOD832zLP4bLs/dlh8M6yEyWdgPbRThWlEnj9bgBuOx+G3Aw82TODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c3ec6b66e931b3d546d33dfa7542961d9b6ec7540fa064d55bc1602e0595726","last_reissued_at":"2026-05-18T02:01:34.834431Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:34.834431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.3897","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:01:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IQ0Y5h9om3ucfgw3b6AVXWw6eR66DQ7jzCSh5EyCIyQJKkprvVjyCo7rqk145u30OusI819NSY5QLBJZYd/1AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:20:22.872193Z"},"content_sha256":"84474ab8bcc352e6f4e4a3a4c57b0807627a2c3498d1fcecc1dc7c768b6c4918","schema_version":"1.0","event_id":"sha256:84474ab8bcc352e6f4e4a3a4c57b0807627a2c3498d1fcecc1dc7c768b6c4918"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:FQ7MNNTOSMNT2VDNGPP2OVBJMH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Locally Homogeneous Spaces, Induced Killing Vector Fields and Applications to Bianchi Prototypes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"G. O. Papadopoulos, Th. Grammenos","submitted_at":"2011-06-20T13:36:37Z","abstract_excerpt":"An answer to the question: Can, in general, the adoption of a given symmetry induce a further symmetry, which might be hidden at a first level? has been attempted in the context of differential geometry of locally homogeneous spaces. Based on E. Cartan's theory of moving frames, a methodology for finding all symmetries for any n dimensional locally homogeneous space is provided. The analysis is applied to 3 dimensional spaces, whereby the embedding of them into a 4 dimensional Lorentzian manifold is examined and special solutions to Einstein's field equations are recovered. The analysis is mai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3897","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:01:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wqbTufx9hBHQjX3LY4UcrLZ7bNTTlFNc78Hk3ueNdde7yJombQgzPoihI/pQCg5DZV0LGgWW5VcozuhsJ5IIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:20:22.872583Z"},"content_sha256":"1a0f55d6c7f8c9125433da8730e43fd7e9f938f9cf088f9f4646e7c5e685d048","schema_version":"1.0","event_id":"sha256:1a0f55d6c7f8c9125433da8730e43fd7e9f938f9cf088f9f4646e7c5e685d048"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FQ7MNNTOSMNT2VDNGPP2OVBJMH/bundle.json","state_url":"https://pith.science/pith/FQ7MNNTOSMNT2VDNGPP2OVBJMH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FQ7MNNTOSMNT2VDNGPP2OVBJMH/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":"2026-06-07T04:20:22Z","links":{"resolver":"https://pith.science/pith/FQ7MNNTOSMNT2VDNGPP2OVBJMH","bundle":"https://pith.science/pith/FQ7MNNTOSMNT2VDNGPP2OVBJMH/bundle.json","state":"https://pith.science/pith/FQ7MNNTOSMNT2VDNGPP2OVBJMH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FQ7MNNTOSMNT2VDNGPP2OVBJMH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FQ7MNNTOSMNT2VDNGPP2OVBJMH","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":"e0e66e489df9ce9db243feef91d989d69f1250f4d844162b2af08f959f14b56f","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-06-20T13:36:37Z","title_canon_sha256":"75364943b0b5b71591c06435547ddc68100d2e34713b16b7807eac6e070ab605"},"schema_version":"1.0","source":{"id":"1106.3897","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3897","created_at":"2026-05-18T02:01:34Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3897v2","created_at":"2026-05-18T02:01:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3897","created_at":"2026-05-18T02:01:34Z"},{"alias_kind":"pith_short_12","alias_value":"FQ7MNNTOSMNT","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FQ7MNNTOSMNT2VDN","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FQ7MNNTO","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:1a0f55d6c7f8c9125433da8730e43fd7e9f938f9cf088f9f4646e7c5e685d048","target":"graph","created_at":"2026-05-18T02:01:34Z","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":"An answer to the question: Can, in general, the adoption of a given symmetry induce a further symmetry, which might be hidden at a first level? has been attempted in the context of differential geometry of locally homogeneous spaces. Based on E. Cartan's theory of moving frames, a methodology for finding all symmetries for any n dimensional locally homogeneous space is provided. The analysis is applied to 3 dimensional spaces, whereby the embedding of them into a 4 dimensional Lorentzian manifold is examined and special solutions to Einstein's field equations are recovered. The analysis is mai","authors_text":"G. O. Papadopoulos, Th. Grammenos","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-06-20T13:36:37Z","title":"Locally Homogeneous Spaces, Induced Killing Vector Fields and Applications to Bianchi Prototypes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3897","kind":"arxiv","version":2},"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":"sha256:84474ab8bcc352e6f4e4a3a4c57b0807627a2c3498d1fcecc1dc7c768b6c4918","target":"record","created_at":"2026-05-18T02:01:34Z","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":"e0e66e489df9ce9db243feef91d989d69f1250f4d844162b2af08f959f14b56f","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-06-20T13:36:37Z","title_canon_sha256":"75364943b0b5b71591c06435547ddc68100d2e34713b16b7807eac6e070ab605"},"schema_version":"1.0","source":{"id":"1106.3897","kind":"arxiv","version":2}},"canonical_sha256":"2c3ec6b66e931b3d546d33dfa7542961d9b6ec7540fa064d55bc1602e0595726","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c3ec6b66e931b3d546d33dfa7542961d9b6ec7540fa064d55bc1602e0595726","first_computed_at":"2026-05-18T02:01:34.834431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:01:34.834431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SGlN7vMebgkc8RdLqWWGlpFON0+kzJSWsOD832zLP4bLs/dlh8M6yEyWdgPbRThWlEnj9bgBuOx+G3Aw82TODA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:01:34.835104Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.3897","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84474ab8bcc352e6f4e4a3a4c57b0807627a2c3498d1fcecc1dc7c768b6c4918","sha256:1a0f55d6c7f8c9125433da8730e43fd7e9f938f9cf088f9f4646e7c5e685d048"],"state_sha256":"536935672ea14f50bc8ed36f31336cc666469577c552dfc38962f331f336e01e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+sp++d36QlI81y9HVwLSX3n4eKKmAItnqxTywtuKAfI/93ud+W21FkK10zJSviD9D4anaO4E5KCw4qYGRGe2CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T04:20:22.875389Z","bundle_sha256":"3a1a7061a7765cc3c21a6174f23670906f36d74d74560ac832a51a6cb55e0b15"}}