{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7B2HX7VQR5LM2T4NORG4B2NES2","short_pith_number":"pith:7B2HX7VQ","canonical_record":{"source":{"id":"1411.7845","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-11-28T12:43:44Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6fece5fb7d688158fcaf4ab46766a460092032b571ed7a278d3e05fb1bb015ed","abstract_canon_sha256":"481ee420a9130d2841e8d28666587eea30fdee4c1b835f6dd1181586ce2c1881"},"schema_version":"1.0"},"canonical_sha256":"f8747bfeb08f56cd4f8d744dc0e9a4969b3a5eca7ec191020a0154419a6c9471","source":{"kind":"arxiv","id":"1411.7845","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.7845","created_at":"2026-05-18T01:25:39Z"},{"alias_kind":"arxiv_version","alias_value":"1411.7845v3","created_at":"2026-05-18T01:25:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7845","created_at":"2026-05-18T01:25:39Z"},{"alias_kind":"pith_short_12","alias_value":"7B2HX7VQR5LM","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7B2HX7VQR5LM2T4N","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7B2HX7VQ","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7B2HX7VQR5LM2T4NORG4B2NES2","target":"record","payload":{"canonical_record":{"source":{"id":"1411.7845","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-11-28T12:43:44Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6fece5fb7d688158fcaf4ab46766a460092032b571ed7a278d3e05fb1bb015ed","abstract_canon_sha256":"481ee420a9130d2841e8d28666587eea30fdee4c1b835f6dd1181586ce2c1881"},"schema_version":"1.0"},"canonical_sha256":"f8747bfeb08f56cd4f8d744dc0e9a4969b3a5eca7ec191020a0154419a6c9471","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:39.623283Z","signature_b64":"FlBZIGtyDk3DC+A2Mg0va0sEhHZjuYOXyt8k3Sl3ncyTwDRQTVN1OVknZex62Z++2o2/jjhg5L4IEjfs46hABg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8747bfeb08f56cd4f8d744dc0e9a4969b3a5eca7ec191020a0154419a6c9471","last_reissued_at":"2026-05-18T01:25:39.622760Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:39.622760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.7845","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:25:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MlGfWYWdmw/ZL2vePzOrIng2/+NMQYZYVIvdwrH75g7fO1PM39a19S/yphhNf7QcIwT//FSgUcgHNfYIM5AVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:24:56.860257Z"},"content_sha256":"8f8dac692fe0e9981f7ff60abe41782b5e045f1b4cae295cfb256a452cbba08a","schema_version":"1.0","event_id":"sha256:8f8dac692fe0e9981f7ff60abe41782b5e045f1b4cae295cfb256a452cbba08a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7B2HX7VQR5LM2T4NORG4B2NES2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Concept of Lie Derivative of Spinor Fields. A Geometric Motivated Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Rafael F. Le\\~ao, Samuel A. Wainer, Waldyr A. Rodrigues Jr","submitted_at":"2014-11-28T12:43:44Z","abstract_excerpt":"In this paper using the Clifford bundle (Cl(M,g)) and spin-Clifford bundle (Cl_{Spin_{1,3}^{e}}(M,g)) formalism, which permit to give a meaningfull representative of a Dirac-Hestenes spinor field (even section of Cl_{Spin_{1,3}^{e}}(M,g)) in the Clifford bundle , we give a geometrical motivated definition for the Lie derivative of spinor fields in a Lorentzian structure (M,g) where M is a manifold such that dimM =4, g is Lorentzian of signature (1,3). Our Lie derivative, called the spinor Lie derivative (and denoted {\\pounds}_{{\\xi}}) is given by nice formulas when applied to Clifford and spin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7845","kind":"arxiv","version":3},"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":"2026-05-18T01:25:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qBZDhIYTD13CJl1b0mLxd5NURZFBKQHMirUSpVcqnOUUpOQLL+kohIm9b4RJLcx+X2lo7GFrXOIlqPd80VZDCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:24:56.860921Z"},"content_sha256":"a034440addbdc58506aeeebdc02727ace1a893a8d9ecd08e4fc122c00fe95e84","schema_version":"1.0","event_id":"sha256:a034440addbdc58506aeeebdc02727ace1a893a8d9ecd08e4fc122c00fe95e84"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7B2HX7VQR5LM2T4NORG4B2NES2/bundle.json","state_url":"https://pith.science/pith/7B2HX7VQR5LM2T4NORG4B2NES2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7B2HX7VQR5LM2T4NORG4B2NES2/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":"2026-06-04T20:24:56Z","links":{"resolver":"https://pith.science/pith/7B2HX7VQR5LM2T4NORG4B2NES2","bundle":"https://pith.science/pith/7B2HX7VQR5LM2T4NORG4B2NES2/bundle.json","state":"https://pith.science/pith/7B2HX7VQR5LM2T4NORG4B2NES2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7B2HX7VQR5LM2T4NORG4B2NES2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7B2HX7VQR5LM2T4NORG4B2NES2","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":"481ee420a9130d2841e8d28666587eea30fdee4c1b835f6dd1181586ce2c1881","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-11-28T12:43:44Z","title_canon_sha256":"6fece5fb7d688158fcaf4ab46766a460092032b571ed7a278d3e05fb1bb015ed"},"schema_version":"1.0","source":{"id":"1411.7845","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.7845","created_at":"2026-05-18T01:25:39Z"},{"alias_kind":"arxiv_version","alias_value":"1411.7845v3","created_at":"2026-05-18T01:25:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7845","created_at":"2026-05-18T01:25:39Z"},{"alias_kind":"pith_short_12","alias_value":"7B2HX7VQR5LM","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7B2HX7VQR5LM2T4N","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7B2HX7VQ","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:a034440addbdc58506aeeebdc02727ace1a893a8d9ecd08e4fc122c00fe95e84","target":"graph","created_at":"2026-05-18T01:25:39Z","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 using the Clifford bundle (Cl(M,g)) and spin-Clifford bundle (Cl_{Spin_{1,3}^{e}}(M,g)) formalism, which permit to give a meaningfull representative of a Dirac-Hestenes spinor field (even section of Cl_{Spin_{1,3}^{e}}(M,g)) in the Clifford bundle , we give a geometrical motivated definition for the Lie derivative of spinor fields in a Lorentzian structure (M,g) where M is a manifold such that dimM =4, g is Lorentzian of signature (1,3). Our Lie derivative, called the spinor Lie derivative (and denoted {\\pounds}_{{\\xi}}) is given by nice formulas when applied to Clifford and spin","authors_text":"Rafael F. Le\\~ao, Samuel A. Wainer, Waldyr A. Rodrigues Jr","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-11-28T12:43:44Z","title":"Concept of Lie Derivative of Spinor Fields. A Geometric Motivated Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7845","kind":"arxiv","version":3},"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":"sha256:8f8dac692fe0e9981f7ff60abe41782b5e045f1b4cae295cfb256a452cbba08a","target":"record","created_at":"2026-05-18T01:25:39Z","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":"481ee420a9130d2841e8d28666587eea30fdee4c1b835f6dd1181586ce2c1881","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-11-28T12:43:44Z","title_canon_sha256":"6fece5fb7d688158fcaf4ab46766a460092032b571ed7a278d3e05fb1bb015ed"},"schema_version":"1.0","source":{"id":"1411.7845","kind":"arxiv","version":3}},"canonical_sha256":"f8747bfeb08f56cd4f8d744dc0e9a4969b3a5eca7ec191020a0154419a6c9471","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8747bfeb08f56cd4f8d744dc0e9a4969b3a5eca7ec191020a0154419a6c9471","first_computed_at":"2026-05-18T01:25:39.622760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:39.622760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FlBZIGtyDk3DC+A2Mg0va0sEhHZjuYOXyt8k3Sl3ncyTwDRQTVN1OVknZex62Z++2o2/jjhg5L4IEjfs46hABg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:39.623283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.7845","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f8dac692fe0e9981f7ff60abe41782b5e045f1b4cae295cfb256a452cbba08a","sha256:a034440addbdc58506aeeebdc02727ace1a893a8d9ecd08e4fc122c00fe95e84"],"state_sha256":"9d3bd813d381be05b36ddcc2020bf6853ad4a589ec5dbfea4b1e78d531168113"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6/OHJ2rArp31BZ5b5DaOj7Ap8XAl9mpV0kjGI3QSpD2OSJeY0M9yQuszoi/3+G8b81SWyFZDYOXZL4YGyxYDAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T20:24:56.864074Z","bundle_sha256":"2be05d4e510bf055f6544654c3d109411dd76f3ddb0f647b1a0f7cc0feb7fd95"}}