{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:AXMN3YLDVWOFMX6P6A6E4JXQKT","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":"b1ba5a9acb83deb20fe6ca5cad06c2b29b54566273e1a1b9a41076af79cfde83","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-02-22T13:40:29Z","title_canon_sha256":"8d46e802e252c062fe0db1c29c890a5746d01841e84dee3ee411908e674969e2"},"schema_version":"1.0","source":{"id":"1102.4501","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4501","created_at":"2026-05-18T04:16:01Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4501v1","created_at":"2026-05-18T04:16:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4501","created_at":"2026-05-18T04:16:01Z"},{"alias_kind":"pith_short_12","alias_value":"AXMN3YLDVWOF","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AXMN3YLDVWOFMX6P","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AXMN3YLD","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:8f0897b7472366ca368792a4b806b653dd7c79b55bfe2e6a2385768fec3a9924","target":"graph","created_at":"2026-05-18T04:16:01Z","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":"In this paper we derive the most general first-order symmetry operator commuting with the Dirac operator in all dimensions and signatures. Such an operator splits into Clifford even and Clifford odd parts which are given in terms of odd Killing-Yano and even closed conformal Killing-Yano inhomogeneous forms respectively. We study commutators of these symmetry operators and give necessary and sufficient conditions under which they remain of the first-order. In this specific setting we can introduce a Killing-Yano bracket, a bilinear operation acting on odd Killing-Yano and even closed conformal","authors_text":"David Kubiznak, Marco Cariglia, Pavel Krtous","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-02-22T13:40:29Z","title":"Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4501","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":"sha256:76f11cde0ec9d4da22ac98995854aeadcbb0838d19ef6ebd703c0e491a582322","target":"record","created_at":"2026-05-18T04:16:01Z","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":"b1ba5a9acb83deb20fe6ca5cad06c2b29b54566273e1a1b9a41076af79cfde83","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-02-22T13:40:29Z","title_canon_sha256":"8d46e802e252c062fe0db1c29c890a5746d01841e84dee3ee411908e674969e2"},"schema_version":"1.0","source":{"id":"1102.4501","kind":"arxiv","version":1}},"canonical_sha256":"05d8dde163ad9c565fcff03c4e26f054f27765d8cc4f39fecc439eb0c97e07c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05d8dde163ad9c565fcff03c4e26f054f27765d8cc4f39fecc439eb0c97e07c2","first_computed_at":"2026-05-18T04:16:01.977941Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:01.977941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LTxR/bfxzQmTKQyNwKULGAtUW6vcYEZhb6jlGJY0LCP9vrzQ0c3pImGwtNqSEtgkezmtmExXo74DUlj0+i5JDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:01.978565Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4501","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76f11cde0ec9d4da22ac98995854aeadcbb0838d19ef6ebd703c0e491a582322","sha256:8f0897b7472366ca368792a4b806b653dd7c79b55bfe2e6a2385768fec3a9924"],"state_sha256":"cf7b41c4ba5bcde001fa3ca8381be483c221e1bae10c83ac9552b5acb1bcd47c"}