{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:BDFCDKWDNTLD4CYS6EBI3SKHR7","short_pith_number":"pith:BDFCDKWD","canonical_record":{"source":{"id":"gr-qc/0401010","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2004-01-04T04:21:41Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"47b520437a2729b2bbcf2a19841c690d945fde54fe327a172b3a4faa1f7fc000","abstract_canon_sha256":"ef899695e519a4ecafb34e84e9f66fec4d189a266fc5c6227daf54a855eedaf4"},"schema_version":"1.0"},"canonical_sha256":"08ca21aac36cd63e0b12f1028dc9478ff555ea5b5ba3788c4b4821f78a387126","source":{"kind":"arxiv","id":"gr-qc/0401010","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0401010","created_at":"2026-07-04T15:28:42Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0401010v3","created_at":"2026-07-04T15:28:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0401010","created_at":"2026-07-04T15:28:42Z"},{"alias_kind":"pith_short_12","alias_value":"BDFCDKWDNTLD","created_at":"2026-07-04T15:28:42Z"},{"alias_kind":"pith_short_16","alias_value":"BDFCDKWDNTLD4CYS","created_at":"2026-07-04T15:28:42Z"},{"alias_kind":"pith_short_8","alias_value":"BDFCDKWD","created_at":"2026-07-04T15:28:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:BDFCDKWDNTLD4CYS6EBI3SKHR7","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/0401010","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2004-01-04T04:21:41Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"47b520437a2729b2bbcf2a19841c690d945fde54fe327a172b3a4faa1f7fc000","abstract_canon_sha256":"ef899695e519a4ecafb34e84e9f66fec4d189a266fc5c6227daf54a855eedaf4"},"schema_version":"1.0"},"canonical_sha256":"08ca21aac36cd63e0b12f1028dc9478ff555ea5b5ba3788c4b4821f78a387126","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:28:42.681334Z","signature_b64":"mikU093lvsxG3BfO6yGc2E1dAHnSXcsFJJWxkS9v7z1fcrtHcka8N2ZVJ+zK10Ljent+Yxh9DN+lf948krXoAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08ca21aac36cd63e0b12f1028dc9478ff555ea5b5ba3788c4b4821f78a387126","last_reissued_at":"2026-07-04T15:28:42.680769Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:28:42.680769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/0401010","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:28:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FG6EYnVLhj7f/kbIVErA4jnVQXXypxURcHOwOL893VQv1qI0IH8Nie85QrNKoC/YqY3Q4rePgx24zRrixGtUDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T21:37:47.153601Z"},"content_sha256":"d6527aed5fc84d59cbbd06c636617a0825f63a67b0c8da213404e3ac338c2db4","schema_version":"1.0","event_id":"sha256:d6527aed5fc84d59cbbd06c636617a0825f63a67b0c8da213404e3ac338c2db4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:BDFCDKWDNTLD4CYS6EBI3SKHR7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Alignment and algebraically special tensors in Lorentzian geometry","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"A. Coley, A. Pravdova, R. Milson, V. Pravda","submitted_at":"2004-01-04T04:21:41Z","abstract_excerpt":"We develop a dimension-independent theory of alignment in Lorentzian geometry, and apply it to the tensor classification problem for the Weyl and Ricci tensors. First, we show that the alignment condition is equivalent to the PND equation. In 4D, this recovers the usual Petrov types. For higher dimensions, we prove that, in general, a Weyl tensor does not possess aligned directions. We then go on to describe a number of additional algebraic types for the various alignment configurations. For the case of second-order symmetric (Ricci) tensors, we perform the classification by considering the ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0401010","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/gr-qc/0401010/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:28:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cmJLcbdEACtp1JNw16Kjklq4BukaEBxHqlDHf5UKyMz6SdQXJOmtJA0roItTrVVK5WbrptjeK6YhwcE2WaWDDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T21:37:47.154204Z"},"content_sha256":"9b6920704bd56e103d28dc712f6d5a7ed6b0b30192d3f17d4dc7a4fb3e682098","schema_version":"1.0","event_id":"sha256:9b6920704bd56e103d28dc712f6d5a7ed6b0b30192d3f17d4dc7a4fb3e682098"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BDFCDKWDNTLD4CYS6EBI3SKHR7/bundle.json","state_url":"https://pith.science/pith/BDFCDKWDNTLD4CYS6EBI3SKHR7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BDFCDKWDNTLD4CYS6EBI3SKHR7/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":"2026-08-04T21:37:47Z","links":{"resolver":"https://pith.science/pith/BDFCDKWDNTLD4CYS6EBI3SKHR7","bundle":"https://pith.science/pith/BDFCDKWDNTLD4CYS6EBI3SKHR7/bundle.json","state":"https://pith.science/pith/BDFCDKWDNTLD4CYS6EBI3SKHR7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BDFCDKWDNTLD4CYS6EBI3SKHR7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:BDFCDKWDNTLD4CYS6EBI3SKHR7","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":"ef899695e519a4ecafb34e84e9f66fec4d189a266fc5c6227daf54a855eedaf4","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"gr-qc","submitted_at":"2004-01-04T04:21:41Z","title_canon_sha256":"47b520437a2729b2bbcf2a19841c690d945fde54fe327a172b3a4faa1f7fc000"},"schema_version":"1.0","source":{"id":"gr-qc/0401010","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0401010","created_at":"2026-07-04T15:28:42Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0401010v3","created_at":"2026-07-04T15:28:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0401010","created_at":"2026-07-04T15:28:42Z"},{"alias_kind":"pith_short_12","alias_value":"BDFCDKWDNTLD","created_at":"2026-07-04T15:28:42Z"},{"alias_kind":"pith_short_16","alias_value":"BDFCDKWDNTLD4CYS","created_at":"2026-07-04T15:28:42Z"},{"alias_kind":"pith_short_8","alias_value":"BDFCDKWD","created_at":"2026-07-04T15:28:42Z"}],"graph_snapshots":[{"event_id":"sha256:9b6920704bd56e103d28dc712f6d5a7ed6b0b30192d3f17d4dc7a4fb3e682098","target":"graph","created_at":"2026-07-04T15:28:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/gr-qc/0401010/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a dimension-independent theory of alignment in Lorentzian geometry, and apply it to the tensor classification problem for the Weyl and Ricci tensors. First, we show that the alignment condition is equivalent to the PND equation. In 4D, this recovers the usual Petrov types. For higher dimensions, we prove that, in general, a Weyl tensor does not possess aligned directions. We then go on to describe a number of additional algebraic types for the various alignment configurations. For the case of second-order symmetric (Ricci) tensors, we perform the classification by considering the ge","authors_text":"A. Coley, A. Pravdova, R. Milson, V. Pravda","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2004-01-04T04:21:41Z","title":"Alignment and algebraically special tensors in Lorentzian geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0401010","kind":"arxiv","version":3},"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:d6527aed5fc84d59cbbd06c636617a0825f63a67b0c8da213404e3ac338c2db4","target":"record","created_at":"2026-07-04T15:28:42Z","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":"ef899695e519a4ecafb34e84e9f66fec4d189a266fc5c6227daf54a855eedaf4","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"gr-qc","submitted_at":"2004-01-04T04:21:41Z","title_canon_sha256":"47b520437a2729b2bbcf2a19841c690d945fde54fe327a172b3a4faa1f7fc000"},"schema_version":"1.0","source":{"id":"gr-qc/0401010","kind":"arxiv","version":3}},"canonical_sha256":"08ca21aac36cd63e0b12f1028dc9478ff555ea5b5ba3788c4b4821f78a387126","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08ca21aac36cd63e0b12f1028dc9478ff555ea5b5ba3788c4b4821f78a387126","first_computed_at":"2026-07-04T15:28:42.680769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:28:42.680769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mikU093lvsxG3BfO6yGc2E1dAHnSXcsFJJWxkS9v7z1fcrtHcka8N2ZVJ+zK10Ljent+Yxh9DN+lf948krXoAA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:28:42.681334Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0401010","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6527aed5fc84d59cbbd06c636617a0825f63a67b0c8da213404e3ac338c2db4","sha256:9b6920704bd56e103d28dc712f6d5a7ed6b0b30192d3f17d4dc7a4fb3e682098"],"state_sha256":"ae9396de524ce7df6a2750a8bcf7be091124c305dbc1c09a1e34b6113096f783"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ld/5zrXAIeR0fOb+DJfgTGw4jsgnWsoEyfR22372N7QTSLZOCrLv2rx2oJfUzsooz6gf0EPKoFeM6rojynPGBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T21:37:47.160495Z","bundle_sha256":"2f3541603a2070bd13859f0ab9804d9a5781e0e36c35266f683fd2cd452ba8ec"}}