{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MKO3IG4TYMVN4IJKBB3GDUMGPO","short_pith_number":"pith:MKO3IG4T","canonical_record":{"source":{"id":"1705.08370","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2017-05-23T15:36:31Z","cross_cats_sorted":["hep-th","nucl-th"],"title_canon_sha256":"6379694545485e334e6128c24ec2c44639b741f5cfd6b4b91db7df8d264de503","abstract_canon_sha256":"e2075d907064c0b0afbfd4f242ef038c4ded530ae123db7060a0729fe9292a07"},"schema_version":"1.0"},"canonical_sha256":"629db41b93c32ade212a087661d1867b822574c9d2010612531a3cd65723b181","source":{"kind":"arxiv","id":"1705.08370","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08370","created_at":"2026-05-18T00:25:45Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08370v2","created_at":"2026-05-18T00:25:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08370","created_at":"2026-05-18T00:25:45Z"},{"alias_kind":"pith_short_12","alias_value":"MKO3IG4TYMVN","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MKO3IG4TYMVN4IJK","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MKO3IG4T","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MKO3IG4TYMVN4IJKBB3GDUMGPO","target":"record","payload":{"canonical_record":{"source":{"id":"1705.08370","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2017-05-23T15:36:31Z","cross_cats_sorted":["hep-th","nucl-th"],"title_canon_sha256":"6379694545485e334e6128c24ec2c44639b741f5cfd6b4b91db7df8d264de503","abstract_canon_sha256":"e2075d907064c0b0afbfd4f242ef038c4ded530ae123db7060a0729fe9292a07"},"schema_version":"1.0"},"canonical_sha256":"629db41b93c32ade212a087661d1867b822574c9d2010612531a3cd65723b181","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:45.610180Z","signature_b64":"itdz48jk9BY3t+x3GLMIe4bhJjPrOmtiWfMpcTyxmAWTbGQxyrBhpK7Gh20VfVUde4QwehIeJgXkPhNiKDS8CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"629db41b93c32ade212a087661d1867b822574c9d2010612531a3cd65723b181","last_reissued_at":"2026-05-18T00:25:45.609570Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:45.609570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.08370","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:25:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cp2MmIjDyE9znHyFIusN15PKqcVerX2VGQjEf0kAi/tETVBcMmkviGJP/5n0p9CpxUVmSkLMChCO00DdaYV5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:03:59.305838Z"},"content_sha256":"267ced527a59daf426075869381d7586b3e217285ad63e541f8a56185f5501c8","schema_version":"1.0","event_id":"sha256:267ced527a59daf426075869381d7586b3e217285ad63e541f8a56185f5501c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MKO3IG4TYMVN4IJKBB3GDUMGPO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New explicit expressions for Dirac bilinears","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","nucl-th"],"primary_cat":"hep-ph","authors_text":"C\\'edric Lorc\\'e (Ecole polytechnique, CPHT)","submitted_at":"2017-05-23T15:36:31Z","abstract_excerpt":"We derive new explicit expressions for the Dirac bilinears based on a generic representation of the massive Dirac spinors with canonical polarization. These bilinears depend on a direction $n$ in Minkowski space which specifies the form of dynamics. We argue that such a dependence is unavoidable in a relativistic theory with spin, since it originates from Wigner rotation effects. Contrary to most of the expressions found in the literature, our ones are valid for all momenta and canonical polarizations of the spinors. As a by-product, we also obtain a generic explicit expression for the covaria"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08370","kind":"arxiv","version":2},"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":"2026-05-18T00:25:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tlcf1BP+Yyl/sQt2xfGyWZ+4Kg9TJsla3q+sCcRC6W5GrMRprMhpytJHCot4cn8OJ0KEiQszpdh4apHUvoaNBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:03:59.306524Z"},"content_sha256":"e6f4535eb30013f88815098b71790d3ce7578d433d2dfa310c724bddd98cd739","schema_version":"1.0","event_id":"sha256:e6f4535eb30013f88815098b71790d3ce7578d433d2dfa310c724bddd98cd739"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MKO3IG4TYMVN4IJKBB3GDUMGPO/bundle.json","state_url":"https://pith.science/pith/MKO3IG4TYMVN4IJKBB3GDUMGPO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MKO3IG4TYMVN4IJKBB3GDUMGPO/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":"2026-05-26T15:03:59Z","links":{"resolver":"https://pith.science/pith/MKO3IG4TYMVN4IJKBB3GDUMGPO","bundle":"https://pith.science/pith/MKO3IG4TYMVN4IJKBB3GDUMGPO/bundle.json","state":"https://pith.science/pith/MKO3IG4TYMVN4IJKBB3GDUMGPO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MKO3IG4TYMVN4IJKBB3GDUMGPO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MKO3IG4TYMVN4IJKBB3GDUMGPO","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":"e2075d907064c0b0afbfd4f242ef038c4ded530ae123db7060a0729fe9292a07","cross_cats_sorted":["hep-th","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2017-05-23T15:36:31Z","title_canon_sha256":"6379694545485e334e6128c24ec2c44639b741f5cfd6b4b91db7df8d264de503"},"schema_version":"1.0","source":{"id":"1705.08370","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08370","created_at":"2026-05-18T00:25:45Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08370v2","created_at":"2026-05-18T00:25:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08370","created_at":"2026-05-18T00:25:45Z"},{"alias_kind":"pith_short_12","alias_value":"MKO3IG4TYMVN","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MKO3IG4TYMVN4IJK","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MKO3IG4T","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:e6f4535eb30013f88815098b71790d3ce7578d433d2dfa310c724bddd98cd739","target":"graph","created_at":"2026-05-18T00:25:45Z","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 derive new explicit expressions for the Dirac bilinears based on a generic representation of the massive Dirac spinors with canonical polarization. These bilinears depend on a direction $n$ in Minkowski space which specifies the form of dynamics. We argue that such a dependence is unavoidable in a relativistic theory with spin, since it originates from Wigner rotation effects. Contrary to most of the expressions found in the literature, our ones are valid for all momenta and canonical polarizations of the spinors. As a by-product, we also obtain a generic explicit expression for the covaria","authors_text":"C\\'edric Lorc\\'e (Ecole polytechnique, CPHT)","cross_cats":["hep-th","nucl-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2017-05-23T15:36:31Z","title":"New explicit expressions for Dirac bilinears"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08370","kind":"arxiv","version":2},"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":"sha256:267ced527a59daf426075869381d7586b3e217285ad63e541f8a56185f5501c8","target":"record","created_at":"2026-05-18T00:25:45Z","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":"e2075d907064c0b0afbfd4f242ef038c4ded530ae123db7060a0729fe9292a07","cross_cats_sorted":["hep-th","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2017-05-23T15:36:31Z","title_canon_sha256":"6379694545485e334e6128c24ec2c44639b741f5cfd6b4b91db7df8d264de503"},"schema_version":"1.0","source":{"id":"1705.08370","kind":"arxiv","version":2}},"canonical_sha256":"629db41b93c32ade212a087661d1867b822574c9d2010612531a3cd65723b181","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"629db41b93c32ade212a087661d1867b822574c9d2010612531a3cd65723b181","first_computed_at":"2026-05-18T00:25:45.609570Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:45.609570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"itdz48jk9BY3t+x3GLMIe4bhJjPrOmtiWfMpcTyxmAWTbGQxyrBhpK7Gh20VfVUde4QwehIeJgXkPhNiKDS8CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:45.610180Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.08370","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:267ced527a59daf426075869381d7586b3e217285ad63e541f8a56185f5501c8","sha256:e6f4535eb30013f88815098b71790d3ce7578d433d2dfa310c724bddd98cd739"],"state_sha256":"ff58e0c573bd88dab94901b2f6a9b89c4860a48e37a5ed9edb3f4aa0c8f90a91"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cxaHgKdkIYCQN8DQaTfWOmrnYNuYosmQ63W4iGC5D6/u8W1BwSwDKshUTt18eKOIHfjQ5Ju8gQlHLk+Pdgu5AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T15:03:59.310299Z","bundle_sha256":"2e0147c99e80ad6d39f56b21149b5476105c011f9f1d0c3f32ce8c42d3700157"}}