{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:NPBJV5QYBOQXWR2FBNF2RVIVQQ","short_pith_number":"pith:NPBJV5QY","canonical_record":{"source":{"id":"2302.10966","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2023-02-21T19:50:09Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"84d3aa60016e5d35fc8374223ed2b209eda8d3b4216af4ac5a996de21b9a3399","abstract_canon_sha256":"588152115492f60778460cf4f734f48494ed097ddf15deec36d3e54428ee1ef4"},"schema_version":"1.0"},"canonical_sha256":"6bc29af6180ba17b47450b4ba8d5158421acb40d364994ba80a57bfc1f1e4b2f","source":{"kind":"arxiv","id":"2302.10966","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.10966","created_at":"2026-07-05T11:55:34Z"},{"alias_kind":"arxiv_version","alias_value":"2302.10966v2","created_at":"2026-07-05T11:55:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.10966","created_at":"2026-07-05T11:55:34Z"},{"alias_kind":"pith_short_12","alias_value":"NPBJV5QYBOQX","created_at":"2026-07-05T11:55:34Z"},{"alias_kind":"pith_short_16","alias_value":"NPBJV5QYBOQXWR2F","created_at":"2026-07-05T11:55:34Z"},{"alias_kind":"pith_short_8","alias_value":"NPBJV5QY","created_at":"2026-07-05T11:55:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:NPBJV5QYBOQXWR2FBNF2RVIVQQ","target":"record","payload":{"canonical_record":{"source":{"id":"2302.10966","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2023-02-21T19:50:09Z","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"title_canon_sha256":"84d3aa60016e5d35fc8374223ed2b209eda8d3b4216af4ac5a996de21b9a3399","abstract_canon_sha256":"588152115492f60778460cf4f734f48494ed097ddf15deec36d3e54428ee1ef4"},"schema_version":"1.0"},"canonical_sha256":"6bc29af6180ba17b47450b4ba8d5158421acb40d364994ba80a57bfc1f1e4b2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:55:34.429060Z","signature_b64":"YaceDiSEzQY/OM2jOIOMYpdjefkcQFoWIrWm71Vdv7G9KU6o3slOKpojW6rMJ1DSX1S6PwNqi4yEzYyWLKv/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bc29af6180ba17b47450b4ba8d5158421acb40d364994ba80a57bfc1f1e4b2f","last_reissued_at":"2026-07-05T11:55:34.428640Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:55:34.428640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.10966","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":"2026-07-05T11:55:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"82SRDg0ymtOs4Bk7CtIABOqFnFFC9rn6feD99ojeCE0qGHidUhgSgkBO3j7sB+XRmoNmW59x1WcWfQKsMk8yBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T07:40:29.371390Z"},"content_sha256":"004363dccb3f6233ecd7f3775fa9734d8c534f2632f327ac286ffa3d2d85ab41","schema_version":"1.0","event_id":"sha256:004363dccb3f6233ecd7f3775fa9734d8c534f2632f327ac286ffa3d2d85ab41"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:NPBJV5QYBOQXWR2FBNF2RVIVQQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dirac bracket and time dependent constraints","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"gr-qc","authors_text":"Nuno Barros e S\\'a","submitted_at":"2023-02-21T19:50:09Z","abstract_excerpt":"We provide a simultaneous derivation of the Dirac bracket and of the equations of motion for second-class constrained systems when the constraints are time-dependent. The necessity of time-dependent gauge-fixing conditions is shown in the example of parameterized mechanics and is illustrated geometrically."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.10966","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.10966/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":"2026-07-05T11:55:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JsJnqv4jaZk9uN8ZMnyWsrpeiqrlUlXflHq3C79BjYaXnoJLm/zMmjiRSu/oxVnvKgLWDiiztDDReu0Or9yTBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T07:40:29.371918Z"},"content_sha256":"a4c40542d7e013d96965eebc1fa1b1f10189f5a644b75901546fe0c97cc6ba29","schema_version":"1.0","event_id":"sha256:a4c40542d7e013d96965eebc1fa1b1f10189f5a644b75901546fe0c97cc6ba29"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NPBJV5QYBOQXWR2FBNF2RVIVQQ/bundle.json","state_url":"https://pith.science/pith/NPBJV5QYBOQXWR2FBNF2RVIVQQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NPBJV5QYBOQXWR2FBNF2RVIVQQ/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":"2026-08-19T07:40:29Z","links":{"resolver":"https://pith.science/pith/NPBJV5QYBOQXWR2FBNF2RVIVQQ","bundle":"https://pith.science/pith/NPBJV5QYBOQXWR2FBNF2RVIVQQ/bundle.json","state":"https://pith.science/pith/NPBJV5QYBOQXWR2FBNF2RVIVQQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NPBJV5QYBOQXWR2FBNF2RVIVQQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:NPBJV5QYBOQXWR2FBNF2RVIVQQ","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":"588152115492f60778460cf4f734f48494ed097ddf15deec36d3e54428ee1ef4","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2023-02-21T19:50:09Z","title_canon_sha256":"84d3aa60016e5d35fc8374223ed2b209eda8d3b4216af4ac5a996de21b9a3399"},"schema_version":"1.0","source":{"id":"2302.10966","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.10966","created_at":"2026-07-05T11:55:34Z"},{"alias_kind":"arxiv_version","alias_value":"2302.10966v2","created_at":"2026-07-05T11:55:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.10966","created_at":"2026-07-05T11:55:34Z"},{"alias_kind":"pith_short_12","alias_value":"NPBJV5QYBOQX","created_at":"2026-07-05T11:55:34Z"},{"alias_kind":"pith_short_16","alias_value":"NPBJV5QYBOQXWR2F","created_at":"2026-07-05T11:55:34Z"},{"alias_kind":"pith_short_8","alias_value":"NPBJV5QY","created_at":"2026-07-05T11:55:34Z"}],"graph_snapshots":[{"event_id":"sha256:a4c40542d7e013d96965eebc1fa1b1f10189f5a644b75901546fe0c97cc6ba29","target":"graph","created_at":"2026-07-05T11:55:34Z","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/2302.10966/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide a simultaneous derivation of the Dirac bracket and of the equations of motion for second-class constrained systems when the constraints are time-dependent. The necessity of time-dependent gauge-fixing conditions is shown in the example of parameterized mechanics and is illustrated geometrically.","authors_text":"Nuno Barros e S\\'a","cross_cats":["math-ph","math.MP","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2023-02-21T19:50:09Z","title":"Dirac bracket and time dependent constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.10966","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":"sha256:004363dccb3f6233ecd7f3775fa9734d8c534f2632f327ac286ffa3d2d85ab41","target":"record","created_at":"2026-07-05T11:55:34Z","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":"588152115492f60778460cf4f734f48494ed097ddf15deec36d3e54428ee1ef4","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2023-02-21T19:50:09Z","title_canon_sha256":"84d3aa60016e5d35fc8374223ed2b209eda8d3b4216af4ac5a996de21b9a3399"},"schema_version":"1.0","source":{"id":"2302.10966","kind":"arxiv","version":2}},"canonical_sha256":"6bc29af6180ba17b47450b4ba8d5158421acb40d364994ba80a57bfc1f1e4b2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bc29af6180ba17b47450b4ba8d5158421acb40d364994ba80a57bfc1f1e4b2f","first_computed_at":"2026-07-05T11:55:34.428640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:55:34.428640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YaceDiSEzQY/OM2jOIOMYpdjefkcQFoWIrWm71Vdv7G9KU6o3slOKpojW6rMJ1DSX1S6PwNqi4yEzYyWLKv/CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:55:34.429060Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.10966","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:004363dccb3f6233ecd7f3775fa9734d8c534f2632f327ac286ffa3d2d85ab41","sha256:a4c40542d7e013d96965eebc1fa1b1f10189f5a644b75901546fe0c97cc6ba29"],"state_sha256":"cf1cf12b1876975ef26894a5c962550322b778f29c02077af4c25fcefa02710e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pK7slMJ3mJb4pOtaM+1eHvyv3td+KkfSSaro3lsHtXazFszlGtc3BN3ybPp5ZFxWVD0gHfx3WiSR2GqtXwIzAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T07:40:29.376891Z","bundle_sha256":"370f1700cad15215906862407c8d7d2c0a8dcaf9cb42c7ba1decd5983c31ba50"}}