{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5UX4VHELHAEXQPNEPIHL2YQ25H","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":"021a6ef812723f6facc47df13c51d3fba41d155689363eca30d51e347e4e419a","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-09-11T10:06:18Z","title_canon_sha256":"d933f121548b18fc7c32d6939c25d71032b5264a4ced92bd3b3fde2f25d44fa2"},"schema_version":"1.0","source":{"id":"1209.2276","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2276","created_at":"2026-05-18T03:45:52Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2276v1","created_at":"2026-05-18T03:45:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2276","created_at":"2026-05-18T03:45:52Z"},{"alias_kind":"pith_short_12","alias_value":"5UX4VHELHAEX","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5UX4VHELHAEXQPNE","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5UX4VHEL","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:5318c08559d7656b543a279a779d6becce03c4ab811663391b608a8fce0fb2b7","target":"graph","created_at":"2026-05-18T03:45:52Z","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":"We show that the Dirac factorization method can be successfully employed to treat problems involving operators raised to a fractional power. The technique we adopt is based on an extension of the Pauli matrices and the properties of the roots of unity. We also comment about the possibility of using the method to linearize evolution equations containing the $n$-th root of differential operators and make a comparison with other techniques involving suitable transforms.","authors_text":"D. Babusci, G. Dattoli, M. Quattromini, P. E. Ricci","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-09-11T10:06:18Z","title":"Dirac factorization and fractional calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2276","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":"sha256:9cb2cfbc63971e02c85357245f7786399937c6005bf58e5da3430b90eca5aa91","target":"record","created_at":"2026-05-18T03:45:52Z","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":"021a6ef812723f6facc47df13c51d3fba41d155689363eca30d51e347e4e419a","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-09-11T10:06:18Z","title_canon_sha256":"d933f121548b18fc7c32d6939c25d71032b5264a4ced92bd3b3fde2f25d44fa2"},"schema_version":"1.0","source":{"id":"1209.2276","kind":"arxiv","version":1}},"canonical_sha256":"ed2fca9c8b3809783da47a0ebd621ae9d0589dbca74f564ef516247060cb4f3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed2fca9c8b3809783da47a0ebd621ae9d0589dbca74f564ef516247060cb4f3c","first_computed_at":"2026-05-18T03:45:52.353765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:52.353765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BPW20jTF+KeN//LUqBsh81R6l6RvlYCVafAi40gvu3ySvv4ikDvr/a311HeldbGkPOk8gsV8Y4sCqu1NR+fuCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:52.354398Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.2276","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cb2cfbc63971e02c85357245f7786399937c6005bf58e5da3430b90eca5aa91","sha256:5318c08559d7656b543a279a779d6becce03c4ab811663391b608a8fce0fb2b7"],"state_sha256":"b6fc1c9333de581475702eb6a1776c799a3209ebba8c1bf0650a0c749a5de242"}