{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:FGCQFZIG6WV3KI6T2ND5WFQVNK","short_pith_number":"pith:FGCQFZIG","canonical_record":{"source":{"id":"1007.4695","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-07-27T12:37:58Z","cross_cats_sorted":[],"title_canon_sha256":"dcda94992a120788a4b223a1121001bb6e3157e74f0743b58f2334dd2d35c493","abstract_canon_sha256":"f1d108c82fe40398c3e565296a91daf24231cb05eb6bbb989c81c6a5081da42d"},"schema_version":"1.0"},"canonical_sha256":"298502e506f5abb523d3d347db16156a90c6bd154e9bb92f045fe24cbdb7e9c7","source":{"kind":"arxiv","id":"1007.4695","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.4695","created_at":"2026-05-18T04:35:04Z"},{"alias_kind":"arxiv_version","alias_value":"1007.4695v2","created_at":"2026-05-18T04:35:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4695","created_at":"2026-05-18T04:35:04Z"},{"alias_kind":"pith_short_12","alias_value":"FGCQFZIG6WV3","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FGCQFZIG6WV3KI6T","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FGCQFZIG","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:FGCQFZIG6WV3KI6T2ND5WFQVNK","target":"record","payload":{"canonical_record":{"source":{"id":"1007.4695","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-07-27T12:37:58Z","cross_cats_sorted":[],"title_canon_sha256":"dcda94992a120788a4b223a1121001bb6e3157e74f0743b58f2334dd2d35c493","abstract_canon_sha256":"f1d108c82fe40398c3e565296a91daf24231cb05eb6bbb989c81c6a5081da42d"},"schema_version":"1.0"},"canonical_sha256":"298502e506f5abb523d3d347db16156a90c6bd154e9bb92f045fe24cbdb7e9c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:04.728721Z","signature_b64":"OLK8/CrmsF+zA7jNv7cp4YUU2/NMTeMYUj3b15AG49WFsAiqo4v0LxZ0dgKq4Qfb1aKeimVXvPaSZmMNmr01Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"298502e506f5abb523d3d347db16156a90c6bd154e9bb92f045fe24cbdb7e9c7","last_reissued_at":"2026-05-18T04:35:04.728279Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:04.728279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.4695","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":"2026-05-18T04:35:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VVMYJvw43br2oksFk8hlN26atuavEbcnNeLyFlrFVjHdtEu2OuF/wHn5om61WrclqmPMaKkUEW8q53kaZ9X/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T18:40:40.812077Z"},"content_sha256":"7e8b70a98fc9fd1d751e984c7fb4194248d778d148e23f5dad997cf440658e6b","schema_version":"1.0","event_id":"sha256:7e8b70a98fc9fd1d751e984c7fb4194248d778d148e23f5dad997cf440658e6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:FGCQFZIG6WV3KI6T2ND5WFQVNK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Naturally reductive pseudo-Riemannian spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Gabriela P. Ovando","submitted_at":"2010-07-27T12:37:58Z","abstract_excerpt":"A family of naturally reductive pseudo-Riemannian spaces is constructed out of the representations of Lie algebras with ad-invariant metrics. We exhibit peculiar examples, study their geometry and characterize the corresponding naturally reductive homogeneous structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4695","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":"2026-05-18T04:35:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vYDadX2eOSjwc2N34UGlG9uZu9Vty9y9HZatQB2vMvyR9yVRVOktXQqNTJcPMLCFBSzGtUGE+XVIKLLAN+xmBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T18:40:40.812414Z"},"content_sha256":"0db692c935d3e88b01d1aeda7baa8712d339ae5e98248a9a9857ac62796859c0","schema_version":"1.0","event_id":"sha256:0db692c935d3e88b01d1aeda7baa8712d339ae5e98248a9a9857ac62796859c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FGCQFZIG6WV3KI6T2ND5WFQVNK/bundle.json","state_url":"https://pith.science/pith/FGCQFZIG6WV3KI6T2ND5WFQVNK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FGCQFZIG6WV3KI6T2ND5WFQVNK/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":"2026-06-28T18:40:40Z","links":{"resolver":"https://pith.science/pith/FGCQFZIG6WV3KI6T2ND5WFQVNK","bundle":"https://pith.science/pith/FGCQFZIG6WV3KI6T2ND5WFQVNK/bundle.json","state":"https://pith.science/pith/FGCQFZIG6WV3KI6T2ND5WFQVNK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FGCQFZIG6WV3KI6T2ND5WFQVNK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:FGCQFZIG6WV3KI6T2ND5WFQVNK","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":"f1d108c82fe40398c3e565296a91daf24231cb05eb6bbb989c81c6a5081da42d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-07-27T12:37:58Z","title_canon_sha256":"dcda94992a120788a4b223a1121001bb6e3157e74f0743b58f2334dd2d35c493"},"schema_version":"1.0","source":{"id":"1007.4695","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.4695","created_at":"2026-05-18T04:35:04Z"},{"alias_kind":"arxiv_version","alias_value":"1007.4695v2","created_at":"2026-05-18T04:35:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4695","created_at":"2026-05-18T04:35:04Z"},{"alias_kind":"pith_short_12","alias_value":"FGCQFZIG6WV3","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FGCQFZIG6WV3KI6T","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FGCQFZIG","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:0db692c935d3e88b01d1aeda7baa8712d339ae5e98248a9a9857ac62796859c0","target":"graph","created_at":"2026-05-18T04:35:04Z","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":"A family of naturally reductive pseudo-Riemannian spaces is constructed out of the representations of Lie algebras with ad-invariant metrics. We exhibit peculiar examples, study their geometry and characterize the corresponding naturally reductive homogeneous structure.","authors_text":"Gabriela P. Ovando","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-07-27T12:37:58Z","title":"Naturally reductive pseudo-Riemannian spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4695","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":"sha256:7e8b70a98fc9fd1d751e984c7fb4194248d778d148e23f5dad997cf440658e6b","target":"record","created_at":"2026-05-18T04:35:04Z","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":"f1d108c82fe40398c3e565296a91daf24231cb05eb6bbb989c81c6a5081da42d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-07-27T12:37:58Z","title_canon_sha256":"dcda94992a120788a4b223a1121001bb6e3157e74f0743b58f2334dd2d35c493"},"schema_version":"1.0","source":{"id":"1007.4695","kind":"arxiv","version":2}},"canonical_sha256":"298502e506f5abb523d3d347db16156a90c6bd154e9bb92f045fe24cbdb7e9c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"298502e506f5abb523d3d347db16156a90c6bd154e9bb92f045fe24cbdb7e9c7","first_computed_at":"2026-05-18T04:35:04.728279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:04.728279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OLK8/CrmsF+zA7jNv7cp4YUU2/NMTeMYUj3b15AG49WFsAiqo4v0LxZ0dgKq4Qfb1aKeimVXvPaSZmMNmr01Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:04.728721Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.4695","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e8b70a98fc9fd1d751e984c7fb4194248d778d148e23f5dad997cf440658e6b","sha256:0db692c935d3e88b01d1aeda7baa8712d339ae5e98248a9a9857ac62796859c0"],"state_sha256":"3f9f0de2967c65dfe17c235211909a1de354bd89e6660460a58ec9b49e459972"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"55Mx6UZbNGjSjPkGk368oAJGaSfHnYj++C0XYYyYImaHTlzmJpAQx+XSNh3NUcLHCIersVVpNXZPFW2T/Ss2Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T18:40:40.814249Z","bundle_sha256":"ebaf544e58f636dfaa42fa71af1ec01d602cbf9c1a27887c7f1910375998fe0b"}}