{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:DPTCKTDJLBZZ5HU4IDS3NLV3LN","short_pith_number":"pith:DPTCKTDJ","canonical_record":{"source":{"id":"0911.3428","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-11-17T23:51:46Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"f4a57852f9dfcf514a8288c0909a94174312bd3bf19bc5f2ccd28b665bcd1738","abstract_canon_sha256":"8cfcc9786e0c53da03e7090358562db6ce8c911f83b267b8b6fbd2f7c608f109"},"schema_version":"1.0"},"canonical_sha256":"1be6254c6958739e9e9c40e5b6aebb5b432e33b4fd43657c0767f6ebec11ccde","source":{"kind":"arxiv","id":"0911.3428","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.3428","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"arxiv_version","alias_value":"0911.3428v1","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.3428","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"pith_short_12","alias_value":"DPTCKTDJLBZZ","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"DPTCKTDJLBZZ5HU4","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"DPTCKTDJ","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:DPTCKTDJLBZZ5HU4IDS3NLV3LN","target":"record","payload":{"canonical_record":{"source":{"id":"0911.3428","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-11-17T23:51:46Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"f4a57852f9dfcf514a8288c0909a94174312bd3bf19bc5f2ccd28b665bcd1738","abstract_canon_sha256":"8cfcc9786e0c53da03e7090358562db6ce8c911f83b267b8b6fbd2f7c608f109"},"schema_version":"1.0"},"canonical_sha256":"1be6254c6958739e9e9c40e5b6aebb5b432e33b4fd43657c0767f6ebec11ccde","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:14.332818Z","signature_b64":"UZtNjmu37KZzPKUp2TowLuMd/ASCCP/dAkIp5UX3hRyl3yWFdCdle5rjfnw1hZO23wTQGyc5mzrTRJyg7hljAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1be6254c6958739e9e9c40e5b6aebb5b432e33b4fd43657c0767f6ebec11ccde","last_reissued_at":"2026-05-18T04:38:14.332195Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:14.332195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.3428","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":"2026-05-18T04:38:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2i+U1a+PxpoTfAe18VyfCNzr0bkESrCVwAKhX80Dz/gj2b1zYQ5VyCcyUFUcyOSJEDFN8gDNpQVez/TVZy0ZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:24:47.780298Z"},"content_sha256":"66a018889d88f533443e77daf25329cabca299fc4f6e43ffa2695029341ca5d7","schema_version":"1.0","event_id":"sha256:66a018889d88f533443e77daf25329cabca299fc4f6e43ffa2695029341ca5d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:DPTCKTDJLBZZ5HU4IDS3NLV3LN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Relation between Operator Constraint --, Master Constraint --, Reduced Phase Space --, and Path Integral Quantisation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Muxin Han, Thomas Thiemann","submitted_at":"2009-11-17T23:51:46Z","abstract_excerpt":"Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space formulation. In this article we review this rather involved procedure in full generality. Moreover, we demonstrate that the reduced phase space path integral formulation formally agrees with the Dirac's operator constraint quantisation and, more specifically, with the Master constraint quantisation for first class constraints. For first class constraints with non trivial structure functions the eq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.3428","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:38:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k6sEtg5A78z1KroFyq5raw6sG6oXwh41xc/TTqqGM/TtxjuQ5iYipsdXoXMri+0LjoLXSVzSDkc5ZmrKQrK2Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:24:47.781035Z"},"content_sha256":"bdfa56dca8594eb5b8f1cb042b712ba8ffe29d366a74631f55b170e37ca0dd0b","schema_version":"1.0","event_id":"sha256:bdfa56dca8594eb5b8f1cb042b712ba8ffe29d366a74631f55b170e37ca0dd0b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DPTCKTDJLBZZ5HU4IDS3NLV3LN/bundle.json","state_url":"https://pith.science/pith/DPTCKTDJLBZZ5HU4IDS3NLV3LN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DPTCKTDJLBZZ5HU4IDS3NLV3LN/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":"2026-05-25T18:24:47Z","links":{"resolver":"https://pith.science/pith/DPTCKTDJLBZZ5HU4IDS3NLV3LN","bundle":"https://pith.science/pith/DPTCKTDJLBZZ5HU4IDS3NLV3LN/bundle.json","state":"https://pith.science/pith/DPTCKTDJLBZZ5HU4IDS3NLV3LN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DPTCKTDJLBZZ5HU4IDS3NLV3LN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:DPTCKTDJLBZZ5HU4IDS3NLV3LN","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":"8cfcc9786e0c53da03e7090358562db6ce8c911f83b267b8b6fbd2f7c608f109","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-11-17T23:51:46Z","title_canon_sha256":"f4a57852f9dfcf514a8288c0909a94174312bd3bf19bc5f2ccd28b665bcd1738"},"schema_version":"1.0","source":{"id":"0911.3428","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.3428","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"arxiv_version","alias_value":"0911.3428v1","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.3428","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"pith_short_12","alias_value":"DPTCKTDJLBZZ","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"DPTCKTDJLBZZ5HU4","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"DPTCKTDJ","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:bdfa56dca8594eb5b8f1cb042b712ba8ffe29d366a74631f55b170e37ca0dd0b","target":"graph","created_at":"2026-05-18T04:38:14Z","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":"Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space formulation. In this article we review this rather involved procedure in full generality. Moreover, we demonstrate that the reduced phase space path integral formulation formally agrees with the Dirac's operator constraint quantisation and, more specifically, with the Master constraint quantisation for first class constraints. For first class constraints with non trivial structure functions the eq","authors_text":"Muxin Han, Thomas Thiemann","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-11-17T23:51:46Z","title":"On the Relation between Operator Constraint --, Master Constraint --, Reduced Phase Space --, and Path Integral Quantisation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.3428","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":"sha256:66a018889d88f533443e77daf25329cabca299fc4f6e43ffa2695029341ca5d7","target":"record","created_at":"2026-05-18T04:38:14Z","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":"8cfcc9786e0c53da03e7090358562db6ce8c911f83b267b8b6fbd2f7c608f109","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-11-17T23:51:46Z","title_canon_sha256":"f4a57852f9dfcf514a8288c0909a94174312bd3bf19bc5f2ccd28b665bcd1738"},"schema_version":"1.0","source":{"id":"0911.3428","kind":"arxiv","version":1}},"canonical_sha256":"1be6254c6958739e9e9c40e5b6aebb5b432e33b4fd43657c0767f6ebec11ccde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1be6254c6958739e9e9c40e5b6aebb5b432e33b4fd43657c0767f6ebec11ccde","first_computed_at":"2026-05-18T04:38:14.332195Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:14.332195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UZtNjmu37KZzPKUp2TowLuMd/ASCCP/dAkIp5UX3hRyl3yWFdCdle5rjfnw1hZO23wTQGyc5mzrTRJyg7hljAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:14.332818Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.3428","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66a018889d88f533443e77daf25329cabca299fc4f6e43ffa2695029341ca5d7","sha256:bdfa56dca8594eb5b8f1cb042b712ba8ffe29d366a74631f55b170e37ca0dd0b"],"state_sha256":"0d2f9d97d9fe5bdb453e9e210bafaf9784b42f01c497096f68afff816fd3484c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qQtwEOUa0lfRNaXkjMS7ZrQf4TjwOQhBW9MrRpAogRuETfq56rSXR4XAlK37fWJtICm8l20YXgI8gGwa625fDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T18:24:47.784811Z","bundle_sha256":"a4bfea40d74288e04711eeba3c37f68e80feeb90582aa02490e351e87319ba98"}}