{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1999:EQVD63VQ5KMNTHUONNWN2NEC32","short_pith_number":"pith:EQVD63VQ","schema_version":"1.0","canonical_sha256":"242a3f6eb0ea98d99e8e6b6cdd3482de9c46cd60ad156a0191f1173fba41dd35","source":{"kind":"arxiv","id":"hep-th/9908200","version":1},"attestation_state":"computed","paper":{"title":"On the equivalence of Daviau's space Clifford algebraic, Hestenes' and Parra's formulations of (real) Dirac theory","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Bertfried Fauser","submitted_at":"1999-08-30T15:42:44Z","abstract_excerpt":"Recently Daviau showed the equivalence of ordinary matrix based Dirac theory -formulated within a spinor bundle S_x \\simeq C^4_x-, to a Clifford algebraic formulation within space Clifford algebra CL(R^3,delta) \\simeq M_2(C) \\simeq P \\simeq Pauli algebra (matrices) \\simeq H \\oplu H \\simeq biquaternions. We will show, that Daviau's map theta : C^4 \\mapsto M_2(C) is an isomorphism. Furthermore it is shown that Hestenes' and Parra's formulations are equivalent to Daviau's space Clifford algebra formulation, which however uses outer automorphisms. The connection between such different formulations"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"hep-th/9908200","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1999-08-30T15:42:44Z","cross_cats_sorted":[],"title_canon_sha256":"45a0e0e21233e91abccfdbf8b2d5e3a54724cadcc7c92105a6ed1347d4081c8e","abstract_canon_sha256":"897d5f5cde22e598852224bbbfab3c5127d38ac4654189c66b53f3f3a3362918"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:15.359557Z","signature_b64":"+NUnuAN6Pf7n6yiOFUBvbo5/Jh4ocFwOOszQ6ecg//81+ZzPF/IzsVi5sU0FNvGIRGxeX1Rs9helZoV8J95rAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"242a3f6eb0ea98d99e8e6b6cdd3482de9c46cd60ad156a0191f1173fba41dd35","last_reissued_at":"2026-05-18T04:24:15.358833Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:15.358833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the equivalence of Daviau's space Clifford algebraic, Hestenes' and Parra's formulations of (real) Dirac theory","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Bertfried Fauser","submitted_at":"1999-08-30T15:42:44Z","abstract_excerpt":"Recently Daviau showed the equivalence of ordinary matrix based Dirac theory -formulated within a spinor bundle S_x \\simeq C^4_x-, to a Clifford algebraic formulation within space Clifford algebra CL(R^3,delta) \\simeq M_2(C) \\simeq P \\simeq Pauli algebra (matrices) \\simeq H \\oplu H \\simeq biquaternions. We will show, that Daviau's map theta : C^4 \\mapsto M_2(C) is an isomorphism. Furthermore it is shown that Hestenes' and Parra's formulations are equivalent to Daviau's space Clifford algebra formulation, which however uses outer automorphisms. The connection between such different formulations"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9908200","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9908200","created_at":"2026-05-18T04:24:15.358955+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9908200v1","created_at":"2026-05-18T04:24:15.358955+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9908200","created_at":"2026-05-18T04:24:15.358955+00:00"},{"alias_kind":"pith_short_12","alias_value":"EQVD63VQ5KMN","created_at":"2026-05-18T12:25:49.631198+00:00"},{"alias_kind":"pith_short_16","alias_value":"EQVD63VQ5KMNTHUO","created_at":"2026-05-18T12:25:49.631198+00:00"},{"alias_kind":"pith_short_8","alias_value":"EQVD63VQ","created_at":"2026-05-18T12:25:49.631198+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EQVD63VQ5KMNTHUONNWN2NEC32","json":"https://pith.science/pith/EQVD63VQ5KMNTHUONNWN2NEC32.json","graph_json":"https://pith.science/api/pith-number/EQVD63VQ5KMNTHUONNWN2NEC32/graph.json","events_json":"https://pith.science/api/pith-number/EQVD63VQ5KMNTHUONNWN2NEC32/events.json","paper":"https://pith.science/paper/EQVD63VQ"},"agent_actions":{"view_html":"https://pith.science/pith/EQVD63VQ5KMNTHUONNWN2NEC32","download_json":"https://pith.science/pith/EQVD63VQ5KMNTHUONNWN2NEC32.json","view_paper":"https://pith.science/paper/EQVD63VQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/9908200&json=true","fetch_graph":"https://pith.science/api/pith-number/EQVD63VQ5KMNTHUONNWN2NEC32/graph.json","fetch_events":"https://pith.science/api/pith-number/EQVD63VQ5KMNTHUONNWN2NEC32/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EQVD63VQ5KMNTHUONNWN2NEC32/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EQVD63VQ5KMNTHUONNWN2NEC32/action/storage_attestation","attest_author":"https://pith.science/pith/EQVD63VQ5KMNTHUONNWN2NEC32/action/author_attestation","sign_citation":"https://pith.science/pith/EQVD63VQ5KMNTHUONNWN2NEC32/action/citation_signature","submit_replication":"https://pith.science/pith/EQVD63VQ5KMNTHUONNWN2NEC32/action/replication_record"}},"created_at":"2026-05-18T04:24:15.358955+00:00","updated_at":"2026-05-18T04:24:15.358955+00:00"}