{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:BEWUHUZFJ7J54DJINC4SZ2OFWC","short_pith_number":"pith:BEWUHUZF","canonical_record":{"source":{"id":"quant-ph/9811025","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1998-11-12T13:22:23Z","cross_cats_sorted":["chao-dyn","math-ph","math.MP","nlin.CD"],"title_canon_sha256":"714eb10700a2b887f423cfefbde5aee26b27a7e0bd3fe3539d48917de4e5064b","abstract_canon_sha256":"48188fcf06f477f8355ead0f3836bf13111ba5285142ca639fdedc55b7e9e421"},"schema_version":"1.0"},"canonical_sha256":"092d43d3254fd3de0d2868b92ce9c5b0b6050fa433985d4b7fab6389182c510d","source":{"kind":"arxiv","id":"quant-ph/9811025","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9811025","created_at":"2026-07-04T16:11:02Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9811025v1","created_at":"2026-07-04T16:11:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9811025","created_at":"2026-07-04T16:11:02Z"},{"alias_kind":"pith_short_12","alias_value":"BEWUHUZFJ7J5","created_at":"2026-07-04T16:11:02Z"},{"alias_kind":"pith_short_16","alias_value":"BEWUHUZFJ7J54DJI","created_at":"2026-07-04T16:11:02Z"},{"alias_kind":"pith_short_8","alias_value":"BEWUHUZF","created_at":"2026-07-04T16:11:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:BEWUHUZFJ7J54DJINC4SZ2OFWC","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/9811025","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1998-11-12T13:22:23Z","cross_cats_sorted":["chao-dyn","math-ph","math.MP","nlin.CD"],"title_canon_sha256":"714eb10700a2b887f423cfefbde5aee26b27a7e0bd3fe3539d48917de4e5064b","abstract_canon_sha256":"48188fcf06f477f8355ead0f3836bf13111ba5285142ca639fdedc55b7e9e421"},"schema_version":"1.0"},"canonical_sha256":"092d43d3254fd3de0d2868b92ce9c5b0b6050fa433985d4b7fab6389182c510d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:11:02.140035Z","signature_b64":"03yc4cO1GEgh5lgCALrZwAYw9Si3DLeMWW8KyRG9/s8FkAx3a1Itea1ZjYvTKvLRrurIWUAH+FU2sLRW8/GeDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"092d43d3254fd3de0d2868b92ce9c5b0b6050fa433985d4b7fab6389182c510d","last_reissued_at":"2026-07-04T16:11:02.139632Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:11:02.139632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/9811025","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:11:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0JHj3XCJ35QMoMxT1rA+bL7Il3+WYbXseujFdhyIDKsQLXEPXwXQM1RU4GO2ZHoAxs8AWdGSGjuholC7layfCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T04:01:50.950330Z"},"content_sha256":"d1d5361dc07f6b00cc7b91b0df4b55282b872c11918c0266abe3277690fea3a4","schema_version":"1.0","event_id":"sha256:d1d5361dc07f6b00cc7b91b0df4b55282b872c11918c0266abe3277690fea3a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:BEWUHUZFJ7J54DJINC4SZ2OFWC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A semiclassical approach to the Dirac equation","license":"","headline":"","cross_cats":["chao-dyn","math-ph","math.MP","nlin.CD"],"primary_cat":"quant-ph","authors_text":"Jens Bolte, Stefan Keppeler","submitted_at":"1998-11-12T13:22:23Z","abstract_excerpt":"We derive a semiclassical time evolution kernel and a trace formula for the Dirac equation. The classical trajectories that enter the expressions are determined by the dynamics of relativistic point particles. We carefully investigate the transport of the spin degrees of freedom along the trajectories which can be understood geometrically as parallel transport in a vector bundle with SU(2) holonomy. Furthermore, we give an interpretation in terms of a classical spin vector that is transported along the trajectories and whose dynamics, dictated by the equation of Thomas precession, gives rise t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9811025","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/quant-ph/9811025/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T16:11:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cx62dgZPeeX3Y6gGvubV7+1txLx6sdzV0LwTCnzzhP8YFSCjjngDuhwKbhBc75ZLRF98/V8XvFYv8txw85F6Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T04:01:50.950702Z"},"content_sha256":"05b6a6d0a86d5cade3518826977182f01845bef44b11ddddb2c52f930f288fd4","schema_version":"1.0","event_id":"sha256:05b6a6d0a86d5cade3518826977182f01845bef44b11ddddb2c52f930f288fd4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BEWUHUZFJ7J54DJINC4SZ2OFWC/bundle.json","state_url":"https://pith.science/pith/BEWUHUZFJ7J54DJINC4SZ2OFWC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BEWUHUZFJ7J54DJINC4SZ2OFWC/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":"2026-07-05T04:01:50Z","links":{"resolver":"https://pith.science/pith/BEWUHUZFJ7J54DJINC4SZ2OFWC","bundle":"https://pith.science/pith/BEWUHUZFJ7J54DJINC4SZ2OFWC/bundle.json","state":"https://pith.science/pith/BEWUHUZFJ7J54DJINC4SZ2OFWC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BEWUHUZFJ7J54DJINC4SZ2OFWC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:BEWUHUZFJ7J54DJINC4SZ2OFWC","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":"48188fcf06f477f8355ead0f3836bf13111ba5285142ca639fdedc55b7e9e421","cross_cats_sorted":["chao-dyn","math-ph","math.MP","nlin.CD"],"license":"","primary_cat":"quant-ph","submitted_at":"1998-11-12T13:22:23Z","title_canon_sha256":"714eb10700a2b887f423cfefbde5aee26b27a7e0bd3fe3539d48917de4e5064b"},"schema_version":"1.0","source":{"id":"quant-ph/9811025","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9811025","created_at":"2026-07-04T16:11:02Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9811025v1","created_at":"2026-07-04T16:11:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9811025","created_at":"2026-07-04T16:11:02Z"},{"alias_kind":"pith_short_12","alias_value":"BEWUHUZFJ7J5","created_at":"2026-07-04T16:11:02Z"},{"alias_kind":"pith_short_16","alias_value":"BEWUHUZFJ7J54DJI","created_at":"2026-07-04T16:11:02Z"},{"alias_kind":"pith_short_8","alias_value":"BEWUHUZF","created_at":"2026-07-04T16:11:02Z"}],"graph_snapshots":[{"event_id":"sha256:05b6a6d0a86d5cade3518826977182f01845bef44b11ddddb2c52f930f288fd4","target":"graph","created_at":"2026-07-04T16:11:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/quant-ph/9811025/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive a semiclassical time evolution kernel and a trace formula for the Dirac equation. The classical trajectories that enter the expressions are determined by the dynamics of relativistic point particles. We carefully investigate the transport of the spin degrees of freedom along the trajectories which can be understood geometrically as parallel transport in a vector bundle with SU(2) holonomy. Furthermore, we give an interpretation in terms of a classical spin vector that is transported along the trajectories and whose dynamics, dictated by the equation of Thomas precession, gives rise t","authors_text":"Jens Bolte, Stefan Keppeler","cross_cats":["chao-dyn","math-ph","math.MP","nlin.CD"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"1998-11-12T13:22:23Z","title":"A semiclassical approach to the Dirac equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9811025","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:d1d5361dc07f6b00cc7b91b0df4b55282b872c11918c0266abe3277690fea3a4","target":"record","created_at":"2026-07-04T16:11:02Z","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":"48188fcf06f477f8355ead0f3836bf13111ba5285142ca639fdedc55b7e9e421","cross_cats_sorted":["chao-dyn","math-ph","math.MP","nlin.CD"],"license":"","primary_cat":"quant-ph","submitted_at":"1998-11-12T13:22:23Z","title_canon_sha256":"714eb10700a2b887f423cfefbde5aee26b27a7e0bd3fe3539d48917de4e5064b"},"schema_version":"1.0","source":{"id":"quant-ph/9811025","kind":"arxiv","version":1}},"canonical_sha256":"092d43d3254fd3de0d2868b92ce9c5b0b6050fa433985d4b7fab6389182c510d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"092d43d3254fd3de0d2868b92ce9c5b0b6050fa433985d4b7fab6389182c510d","first_computed_at":"2026-07-04T16:11:02.139632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:11:02.139632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"03yc4cO1GEgh5lgCALrZwAYw9Si3DLeMWW8KyRG9/s8FkAx3a1Itea1ZjYvTKvLRrurIWUAH+FU2sLRW8/GeDg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:11:02.140035Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/9811025","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1d5361dc07f6b00cc7b91b0df4b55282b872c11918c0266abe3277690fea3a4","sha256:05b6a6d0a86d5cade3518826977182f01845bef44b11ddddb2c52f930f288fd4"],"state_sha256":"bbffdb8ba08532008d2466b4cec4ea2356db864abf16a548d0b7c71f66de9f1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d+thHPkDIuOprjDVAVqxmIO2lDiZjtSfWMi7Yqy/Ys2S8NHCeIqKChs9a0OJ4FB/rINCWO9wVhscnidwqnNGDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T04:01:50.952747Z","bundle_sha256":"464dc6ad6ec636f82eaf7a3d2f326bb5be6b2c4d4ff99cf78c5aed2a5c0a88e4"}}