{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:A7FK6WDR5UIDGCCRPMHOFBXPEP","short_pith_number":"pith:A7FK6WDR","canonical_record":{"source":{"id":"1205.1119","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-05-05T10:14:12Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"834d39a76518e15fa52198d55e2711bd66e3e910d39056c108a01f93e5e5a22d","abstract_canon_sha256":"80ad947e37cbad87bc357e879cc4226cd43cd39d62b2baab254c128be25ed670"},"schema_version":"1.0"},"canonical_sha256":"07caaf5871ed103308517b0ee286ef23ed7e71b4aa2e049e7a7acf602386c40c","source":{"kind":"arxiv","id":"1205.1119","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1119","created_at":"2026-05-18T03:45:31Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1119v1","created_at":"2026-05-18T03:45:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1119","created_at":"2026-05-18T03:45:31Z"},{"alias_kind":"pith_short_12","alias_value":"A7FK6WDR5UID","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"A7FK6WDR5UIDGCCR","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"A7FK6WDR","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:A7FK6WDR5UIDGCCRPMHOFBXPEP","target":"record","payload":{"canonical_record":{"source":{"id":"1205.1119","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-05-05T10:14:12Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"834d39a76518e15fa52198d55e2711bd66e3e910d39056c108a01f93e5e5a22d","abstract_canon_sha256":"80ad947e37cbad87bc357e879cc4226cd43cd39d62b2baab254c128be25ed670"},"schema_version":"1.0"},"canonical_sha256":"07caaf5871ed103308517b0ee286ef23ed7e71b4aa2e049e7a7acf602386c40c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:31.640344Z","signature_b64":"K2qY5m0viy8G8b3tDzAK+rntsDB5iYdnt/p94fCMIzSwQg5tmV03Ac/06o2TUApxA8QXfUNPXS+KkbM2L8mAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07caaf5871ed103308517b0ee286ef23ed7e71b4aa2e049e7a7acf602386c40c","last_reissued_at":"2026-05-18T03:45:31.639594Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:31.639594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.1119","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":"2026-05-18T03:45:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"81F7mldOUo6QWaC1zRUteGgB63sr4V5HzNlZrhWjbKt6SrcSjXR7BfA9km2Xsv2o2fYzx/pdvgvKAy1Ri0m1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:08:31.847963Z"},"content_sha256":"fcdfcd47dfdd8fe7f5cc0c423c015d30f097470d40672387ad17a7ae980bd6ce","schema_version":"1.0","event_id":"sha256:fcdfcd47dfdd8fe7f5cc0c423c015d30f097470d40672387ad17a7ae980bd6ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:A7FK6WDR5UIDGCCRPMHOFBXPEP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a five-dimensional version of the Goldberg-Sachs theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Alena Pravdova, Harvey S. Reall, Marcello Ortaggio, Vojtech Pravda","submitted_at":"2012-05-05T10:14:12Z","abstract_excerpt":"Previous work has found a higher-dimensional generalization of the \"geodesic part\" of the Goldberg-Sachs theorem. We investigate the generalization of the \"shear-free part\" of the theorem. A spacetime is defined to be algebraically special if it admits a multiple Weyl Aligned Null Direction (WAND). The algebraically special property restricts the form of the \"optical matrix\" that defines the expansion, rotation and shear of the multiple WAND. After working out some general constraints that hold in arbitrary dimensions, we determine necessary algebraic conditions on the optical matrix of a mult"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1119","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":"2026-05-18T03:45:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qlQNfOKVr8m176zCIICwnbfjqu+PXFaidg7d5rMOjoEGoHOaGy2CMceZ16cbqvMZn0PwE4+tieaRZ8q9QRw+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:08:31.848592Z"},"content_sha256":"ee1088915ca2bf2a6571758444284247808031e96396c1a89af66d7b5da77dbf","schema_version":"1.0","event_id":"sha256:ee1088915ca2bf2a6571758444284247808031e96396c1a89af66d7b5da77dbf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A7FK6WDR5UIDGCCRPMHOFBXPEP/bundle.json","state_url":"https://pith.science/pith/A7FK6WDR5UIDGCCRPMHOFBXPEP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A7FK6WDR5UIDGCCRPMHOFBXPEP/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":"2026-05-27T01:08:31Z","links":{"resolver":"https://pith.science/pith/A7FK6WDR5UIDGCCRPMHOFBXPEP","bundle":"https://pith.science/pith/A7FK6WDR5UIDGCCRPMHOFBXPEP/bundle.json","state":"https://pith.science/pith/A7FK6WDR5UIDGCCRPMHOFBXPEP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A7FK6WDR5UIDGCCRPMHOFBXPEP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:A7FK6WDR5UIDGCCRPMHOFBXPEP","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":"80ad947e37cbad87bc357e879cc4226cd43cd39d62b2baab254c128be25ed670","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-05-05T10:14:12Z","title_canon_sha256":"834d39a76518e15fa52198d55e2711bd66e3e910d39056c108a01f93e5e5a22d"},"schema_version":"1.0","source":{"id":"1205.1119","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1119","created_at":"2026-05-18T03:45:31Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1119v1","created_at":"2026-05-18T03:45:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1119","created_at":"2026-05-18T03:45:31Z"},{"alias_kind":"pith_short_12","alias_value":"A7FK6WDR5UID","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"A7FK6WDR5UIDGCCR","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"A7FK6WDR","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:ee1088915ca2bf2a6571758444284247808031e96396c1a89af66d7b5da77dbf","target":"graph","created_at":"2026-05-18T03:45:31Z","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":"Previous work has found a higher-dimensional generalization of the \"geodesic part\" of the Goldberg-Sachs theorem. We investigate the generalization of the \"shear-free part\" of the theorem. A spacetime is defined to be algebraically special if it admits a multiple Weyl Aligned Null Direction (WAND). The algebraically special property restricts the form of the \"optical matrix\" that defines the expansion, rotation and shear of the multiple WAND. After working out some general constraints that hold in arbitrary dimensions, we determine necessary algebraic conditions on the optical matrix of a mult","authors_text":"Alena Pravdova, Harvey S. Reall, Marcello Ortaggio, Vojtech Pravda","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-05-05T10:14:12Z","title":"On a five-dimensional version of the Goldberg-Sachs theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1119","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:fcdfcd47dfdd8fe7f5cc0c423c015d30f097470d40672387ad17a7ae980bd6ce","target":"record","created_at":"2026-05-18T03:45:31Z","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":"80ad947e37cbad87bc357e879cc4226cd43cd39d62b2baab254c128be25ed670","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-05-05T10:14:12Z","title_canon_sha256":"834d39a76518e15fa52198d55e2711bd66e3e910d39056c108a01f93e5e5a22d"},"schema_version":"1.0","source":{"id":"1205.1119","kind":"arxiv","version":1}},"canonical_sha256":"07caaf5871ed103308517b0ee286ef23ed7e71b4aa2e049e7a7acf602386c40c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07caaf5871ed103308517b0ee286ef23ed7e71b4aa2e049e7a7acf602386c40c","first_computed_at":"2026-05-18T03:45:31.639594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:31.639594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K2qY5m0viy8G8b3tDzAK+rntsDB5iYdnt/p94fCMIzSwQg5tmV03Ac/06o2TUApxA8QXfUNPXS+KkbM2L8mAAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:31.640344Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1119","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcdfcd47dfdd8fe7f5cc0c423c015d30f097470d40672387ad17a7ae980bd6ce","sha256:ee1088915ca2bf2a6571758444284247808031e96396c1a89af66d7b5da77dbf"],"state_sha256":"0cf3af193c0007b27bae6530400ed113a1324223ff99723e980d23462c86f64e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tt84lbmgmB3lMFmUsH/QVYa9aGWkmGzJUZlXsO60+y6nmodhMRlltAsgxER/iTl7gAv/rIPn7G/HSilelrcqCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T01:08:31.851912Z","bundle_sha256":"ec7a480dc1b5c783e1ca18c73442d84dfc35a905a28110341c705624a99bcc3d"}}