{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:YPCRVKNUXXGLYMTLMFZKEW7MDH","short_pith_number":"pith:YPCRVKNU","canonical_record":{"source":{"id":"1005.2377","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-05-13T17:10:18Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"63982ccc290a4722aedc6c26182d5cd48fa345050cb675ef44088da0f0456984","abstract_canon_sha256":"4228ec89484ee336e51023f3b403dde345aada2003346fbacc3668d3f521dc88"},"schema_version":"1.0"},"canonical_sha256":"c3c51aa9b4bdccbc326b6172a25bec19c484f210303b6ca091e293036c255c03","source":{"kind":"arxiv","id":"1005.2377","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2377","created_at":"2026-05-18T02:33:26Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2377v1","created_at":"2026-05-18T02:33:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2377","created_at":"2026-05-18T02:33:26Z"},{"alias_kind":"pith_short_12","alias_value":"YPCRVKNUXXGL","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YPCRVKNUXXGLYMTL","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YPCRVKNU","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:YPCRVKNUXXGLYMTLMFZKEW7MDH","target":"record","payload":{"canonical_record":{"source":{"id":"1005.2377","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-05-13T17:10:18Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"63982ccc290a4722aedc6c26182d5cd48fa345050cb675ef44088da0f0456984","abstract_canon_sha256":"4228ec89484ee336e51023f3b403dde345aada2003346fbacc3668d3f521dc88"},"schema_version":"1.0"},"canonical_sha256":"c3c51aa9b4bdccbc326b6172a25bec19c484f210303b6ca091e293036c255c03","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:26.425842Z","signature_b64":"KCwNGg5eWO/jLQqZ2Stfuoi7ehb+sTjhgWi708VPbITpGtMxSOyiazNfKE8hAZHwt5UlYotInjuSGzjwGnkxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3c51aa9b4bdccbc326b6172a25bec19c484f210303b6ca091e293036c255c03","last_reissued_at":"2026-05-18T02:33:26.425351Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:26.425351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.2377","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":"2026-05-18T02:33:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HTd7og7GpHyjTPM2g45hJgfpwf52/T/tkvAbZTsLba7fiJaoLOCij0pFnVX0N709CfmfGmRLjJDE3DY8ty6JBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:04:13.551547Z"},"content_sha256":"4568a736a9e863f6646c9eff24485dd630c0c9403c4aea739e26f5d6de96dbac","schema_version":"1.0","event_id":"sha256:4568a736a9e863f6646c9eff24485dd630c0c9403c4aea739e26f5d6de96dbac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:YPCRVKNUXXGLYMTLMFZKEW7MDH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Type III and N Einstein spacetimes in higher dimensions: general properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Alena Pravdova, Marcello Ortaggio, Vojtech Pravda","submitted_at":"2010-05-13T17:10:18Z","abstract_excerpt":"The Sachs equations governing the evolution of the optical matrix of geodetic WANDs (Weyl aligned null directions) are explicitly solved in n-dimensions in several cases which are of interest in potential applications. This is then used to study Einstein spacetimes of type III and N in the higher dimensional Newman-Penrose formalism, considering both Kundt and expanding (possibly twisting) solutions. In particular, the general dependence of the metric and of the Weyl tensor on an affine parameter r is obtained in a closed form. This allows us to characterize the peeling behaviour of the Weyl \""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2377","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":"2026-05-18T02:33:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hdcsRveRwZGKr5raI0u9BJDreZ2uggNAoYQ5E+yxarnzIEta7yd3TOBE9t5udzlM1U1vfXVjgGDVN9viaPcqAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:04:13.552271Z"},"content_sha256":"75052c567a3827361d8be716a57eb3f17dbd28968952887a95f0e47addfec47b","schema_version":"1.0","event_id":"sha256:75052c567a3827361d8be716a57eb3f17dbd28968952887a95f0e47addfec47b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YPCRVKNUXXGLYMTLMFZKEW7MDH/bundle.json","state_url":"https://pith.science/pith/YPCRVKNUXXGLYMTLMFZKEW7MDH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YPCRVKNUXXGLYMTLMFZKEW7MDH/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":"2026-05-27T07:04:13Z","links":{"resolver":"https://pith.science/pith/YPCRVKNUXXGLYMTLMFZKEW7MDH","bundle":"https://pith.science/pith/YPCRVKNUXXGLYMTLMFZKEW7MDH/bundle.json","state":"https://pith.science/pith/YPCRVKNUXXGLYMTLMFZKEW7MDH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YPCRVKNUXXGLYMTLMFZKEW7MDH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:YPCRVKNUXXGLYMTLMFZKEW7MDH","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":"4228ec89484ee336e51023f3b403dde345aada2003346fbacc3668d3f521dc88","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-05-13T17:10:18Z","title_canon_sha256":"63982ccc290a4722aedc6c26182d5cd48fa345050cb675ef44088da0f0456984"},"schema_version":"1.0","source":{"id":"1005.2377","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2377","created_at":"2026-05-18T02:33:26Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2377v1","created_at":"2026-05-18T02:33:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2377","created_at":"2026-05-18T02:33:26Z"},{"alias_kind":"pith_short_12","alias_value":"YPCRVKNUXXGL","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YPCRVKNUXXGLYMTL","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YPCRVKNU","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:75052c567a3827361d8be716a57eb3f17dbd28968952887a95f0e47addfec47b","target":"graph","created_at":"2026-05-18T02:33:26Z","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":"The Sachs equations governing the evolution of the optical matrix of geodetic WANDs (Weyl aligned null directions) are explicitly solved in n-dimensions in several cases which are of interest in potential applications. This is then used to study Einstein spacetimes of type III and N in the higher dimensional Newman-Penrose formalism, considering both Kundt and expanding (possibly twisting) solutions. In particular, the general dependence of the metric and of the Weyl tensor on an affine parameter r is obtained in a closed form. This allows us to characterize the peeling behaviour of the Weyl \"","authors_text":"Alena Pravdova, Marcello Ortaggio, Vojtech Pravda","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-05-13T17:10:18Z","title":"Type III and N Einstein spacetimes in higher dimensions: general properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2377","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":"sha256:4568a736a9e863f6646c9eff24485dd630c0c9403c4aea739e26f5d6de96dbac","target":"record","created_at":"2026-05-18T02:33:26Z","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":"4228ec89484ee336e51023f3b403dde345aada2003346fbacc3668d3f521dc88","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-05-13T17:10:18Z","title_canon_sha256":"63982ccc290a4722aedc6c26182d5cd48fa345050cb675ef44088da0f0456984"},"schema_version":"1.0","source":{"id":"1005.2377","kind":"arxiv","version":1}},"canonical_sha256":"c3c51aa9b4bdccbc326b6172a25bec19c484f210303b6ca091e293036c255c03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3c51aa9b4bdccbc326b6172a25bec19c484f210303b6ca091e293036c255c03","first_computed_at":"2026-05-18T02:33:26.425351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:33:26.425351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KCwNGg5eWO/jLQqZ2Stfuoi7ehb+sTjhgWi708VPbITpGtMxSOyiazNfKE8hAZHwt5UlYotInjuSGzjwGnkxDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:33:26.425842Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.2377","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4568a736a9e863f6646c9eff24485dd630c0c9403c4aea739e26f5d6de96dbac","sha256:75052c567a3827361d8be716a57eb3f17dbd28968952887a95f0e47addfec47b"],"state_sha256":"8df75e9a4849c9d6df9c2ed4d6aaa8cb9993603a7b9f30b7e66a74872131a113"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"77WTsb7vO+PJWoM5H/++0gWxLDFwa7lMdNrPATu6wtfkfgQFrd1XD32rAq+FRwCARQwwjFYGenrDVLfNLipLBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T07:04:13.556271Z","bundle_sha256":"f77a47c0701156563e805540675f5c049215ae05455912bd19919eb1c18b5b54"}}