{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:6E6V45LNZ5N23PBXVCN3ELVJRN","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":"9e58ac564e51d145929c9d4cc2ac7be374b77427c754f2734f2f70f42c54b52a","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"1999-06-03T22:12:39Z","title_canon_sha256":"42180fa3d2b3a1f28896b31d3b6688b1ec30131530aa67048ea7bd30f41ce66a"},"schema_version":"1.0","source":{"id":"hep-ph/9906243","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/9906243","created_at":"2026-05-18T02:36:27Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/9906243v1","created_at":"2026-05-18T02:36:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/9906243","created_at":"2026-05-18T02:36:27Z"},{"alias_kind":"pith_short_12","alias_value":"6E6V45LNZ5N2","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"6E6V45LNZ5N23PBX","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"6E6V45LN","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:35d3eb9099677ab27beef6569cc423d0b7054961c45df188645e460c11b001b1","target":"graph","created_at":"2026-05-18T02:36:27Z","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 discuss the variational principle within Quantum Mechanics in terms of the noncommutative even Space Time sub-Algebra, the Clifford $\\Ra$-algebra $Cl_{1,3}^+$. A fundamental ingredient, in our multivectorial algebraic formulation, is the adoption of a $\\D $-complex geometry, $\\D \\equiv span_{\\RR} \\{1,\\gamma_{21} \\}$, $\\gamma_{21} \\in Cl_{1,3}^+$. We derive the Lagrangian for the Dirac-Hestenes equation and show that such Lagrangian must be mapped on $\\D \\otimes {\\cal F}$, where $\\cal F$ denotes an $\\Ra$-algebra of functions.","authors_text":"J. Vaz, S. De Leo, WA. Rodrigues (IMECC-UNICAMP), Z. Oziewicz","cross_cats":[],"headline":"","license":"","primary_cat":"hep-ph","submitted_at":"1999-06-03T22:12:39Z","title":"The Dirac-Hestenes Lagrangian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9906243","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":"sha256:2029f7041e6433453ba4823d28854a10879e6d945c6945b8352e291304101a28","target":"record","created_at":"2026-05-18T02:36:27Z","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":"9e58ac564e51d145929c9d4cc2ac7be374b77427c754f2734f2f70f42c54b52a","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"1999-06-03T22:12:39Z","title_canon_sha256":"42180fa3d2b3a1f28896b31d3b6688b1ec30131530aa67048ea7bd30f41ce66a"},"schema_version":"1.0","source":{"id":"hep-ph/9906243","kind":"arxiv","version":1}},"canonical_sha256":"f13d5e756dcf5badbc37a89bb22ea98b5f94497ab9c4619224dff675f92a46df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f13d5e756dcf5badbc37a89bb22ea98b5f94497ab9c4619224dff675f92a46df","first_computed_at":"2026-05-18T02:36:27.859208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:36:27.859208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ekjD7qvmndVNW23cbxVBp3IF8Oy8+c+1ISX0/Bd+ISrBjVauJbtu99YD8ZMhY5NYsKmLyC65h7hEAwPp+0b/DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:36:27.859861Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-ph/9906243","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2029f7041e6433453ba4823d28854a10879e6d945c6945b8352e291304101a28","sha256:35d3eb9099677ab27beef6569cc423d0b7054961c45df188645e460c11b001b1"],"state_sha256":"5897eaff71571e2ca1f9200e584ab46f75d838823e69e1da1ed65f5e5c2da89e"}