{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HCWZQA6CZ6M2DO2DUGODE3R5TT","short_pith_number":"pith:HCWZQA6C","canonical_record":{"source":{"id":"1402.6252","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-02-25T17:42:06Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"cccd97402d3a83f0064a91abd544957e7c1ef783c4d225c36634b57183ce1c1c","abstract_canon_sha256":"ca962afc9ebb99b770dc58d4cf3126e77530c707b175a96a21ff9e3869eae481"},"schema_version":"1.0"},"canonical_sha256":"38ad9803c2cf99a1bb43a19c326e3d9ce866ec8cd5a825d9f186a8f73636c290","source":{"kind":"arxiv","id":"1402.6252","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6252","created_at":"2026-05-18T02:49:28Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6252v2","created_at":"2026-05-18T02:49:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6252","created_at":"2026-05-18T02:49:28Z"},{"alias_kind":"pith_short_12","alias_value":"HCWZQA6CZ6M2","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HCWZQA6CZ6M2DO2D","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HCWZQA6C","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HCWZQA6CZ6M2DO2DUGODE3R5TT","target":"record","payload":{"canonical_record":{"source":{"id":"1402.6252","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-02-25T17:42:06Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"cccd97402d3a83f0064a91abd544957e7c1ef783c4d225c36634b57183ce1c1c","abstract_canon_sha256":"ca962afc9ebb99b770dc58d4cf3126e77530c707b175a96a21ff9e3869eae481"},"schema_version":"1.0"},"canonical_sha256":"38ad9803c2cf99a1bb43a19c326e3d9ce866ec8cd5a825d9f186a8f73636c290","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:28.579393Z","signature_b64":"yC57NnK5t2/a5+UAiRPYGbXIbOXchEq81eSRDZCT1RNDf+BDOD8SCGz06we3qlAGln/jRt//RInNfL7wwR2NDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38ad9803c2cf99a1bb43a19c326e3d9ce866ec8cd5a825d9f186a8f73636c290","last_reissued_at":"2026-05-18T02:49:28.578764Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:28.578764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.6252","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":"2026-05-18T02:49:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9K6TrCePPl8xzYnnGRjfu8W03r+I1yZKEiNhip1O+yBZl+xAxJs+UNrs5Hjb9XlFnT4KY1iEJVC5iUDtSiJSAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:38:59.672589Z"},"content_sha256":"31cd9c96ad74c329d609bce84602bb1bc7926bf7d95dc6b5faebc75fe26c7688","schema_version":"1.0","event_id":"sha256:31cd9c96ad74c329d609bce84602bb1bc7926bf7d95dc6b5faebc75fe26c7688"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HCWZQA6CZ6M2DO2DUGODE3R5TT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Second order symmetry operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"gr-qc","authors_text":"Lars Andersson, Pieter Blue, Thomas B\\\"ackdahl","submitted_at":"2014-02-25T17:42:06Z","abstract_excerpt":"Using systematic calculations in spinor language, we obtain simple descriptions of the second order symmetry operators for the conformal wave equation, the Dirac-Weyl equation and the Maxwell equation on a curved four dimensional Lorentzian manifold. The conditions for existence of symmetry operators for the different equations are seen to be related. Computer algebra tools have been developed and used to systematically reduce the equations to a form which allows geometrical interpretation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6252","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":"2026-05-18T02:49:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vwuG0ud5zjZLk8eARy8sqXWWr0NFP1tEXMrzcKzS3iSp6+yM8mDmq7FgONlojSWkbXXIyyQHZT4w7OUrSnc8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:38:59.672936Z"},"content_sha256":"6bebf39c4b570b642771410fd457cab345cb48e1b29019b28c7179ec5f457e9d","schema_version":"1.0","event_id":"sha256:6bebf39c4b570b642771410fd457cab345cb48e1b29019b28c7179ec5f457e9d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HCWZQA6CZ6M2DO2DUGODE3R5TT/bundle.json","state_url":"https://pith.science/pith/HCWZQA6CZ6M2DO2DUGODE3R5TT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HCWZQA6CZ6M2DO2DUGODE3R5TT/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":"2026-05-28T09:38:59Z","links":{"resolver":"https://pith.science/pith/HCWZQA6CZ6M2DO2DUGODE3R5TT","bundle":"https://pith.science/pith/HCWZQA6CZ6M2DO2DUGODE3R5TT/bundle.json","state":"https://pith.science/pith/HCWZQA6CZ6M2DO2DUGODE3R5TT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HCWZQA6CZ6M2DO2DUGODE3R5TT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HCWZQA6CZ6M2DO2DUGODE3R5TT","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":"ca962afc9ebb99b770dc58d4cf3126e77530c707b175a96a21ff9e3869eae481","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-02-25T17:42:06Z","title_canon_sha256":"cccd97402d3a83f0064a91abd544957e7c1ef783c4d225c36634b57183ce1c1c"},"schema_version":"1.0","source":{"id":"1402.6252","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6252","created_at":"2026-05-18T02:49:28Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6252v2","created_at":"2026-05-18T02:49:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6252","created_at":"2026-05-18T02:49:28Z"},{"alias_kind":"pith_short_12","alias_value":"HCWZQA6CZ6M2","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HCWZQA6CZ6M2DO2D","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HCWZQA6C","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:6bebf39c4b570b642771410fd457cab345cb48e1b29019b28c7179ec5f457e9d","target":"graph","created_at":"2026-05-18T02:49:28Z","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":"Using systematic calculations in spinor language, we obtain simple descriptions of the second order symmetry operators for the conformal wave equation, the Dirac-Weyl equation and the Maxwell equation on a curved four dimensional Lorentzian manifold. The conditions for existence of symmetry operators for the different equations are seen to be related. Computer algebra tools have been developed and used to systematically reduce the equations to a form which allows geometrical interpretation.","authors_text":"Lars Andersson, Pieter Blue, Thomas B\\\"ackdahl","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-02-25T17:42:06Z","title":"Second order symmetry operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6252","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":"sha256:31cd9c96ad74c329d609bce84602bb1bc7926bf7d95dc6b5faebc75fe26c7688","target":"record","created_at":"2026-05-18T02:49:28Z","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":"ca962afc9ebb99b770dc58d4cf3126e77530c707b175a96a21ff9e3869eae481","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2014-02-25T17:42:06Z","title_canon_sha256":"cccd97402d3a83f0064a91abd544957e7c1ef783c4d225c36634b57183ce1c1c"},"schema_version":"1.0","source":{"id":"1402.6252","kind":"arxiv","version":2}},"canonical_sha256":"38ad9803c2cf99a1bb43a19c326e3d9ce866ec8cd5a825d9f186a8f73636c290","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38ad9803c2cf99a1bb43a19c326e3d9ce866ec8cd5a825d9f186a8f73636c290","first_computed_at":"2026-05-18T02:49:28.578764Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:28.578764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yC57NnK5t2/a5+UAiRPYGbXIbOXchEq81eSRDZCT1RNDf+BDOD8SCGz06we3qlAGln/jRt//RInNfL7wwR2NDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:28.579393Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.6252","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31cd9c96ad74c329d609bce84602bb1bc7926bf7d95dc6b5faebc75fe26c7688","sha256:6bebf39c4b570b642771410fd457cab345cb48e1b29019b28c7179ec5f457e9d"],"state_sha256":"caa66ce8aeb65ac9757cc3030cca6ad6403982fcf1204a20798cea8e4ccb2267"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"btxIUJ4i7XFr9pjtLMrUHs5jsr55UScQeKToWglwmW/pJeN6AnQNzmsvJ8+GzOOTSqXQL/iPrKoBptlm87mBBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T09:38:59.674986Z","bundle_sha256":"5f19e73eb2d3f14e34f89335f862aedca3b9dee8d85a8740c274e0cd19a3447c"}}