{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:FX36PVUP3LYDKHQHL4HTYOLFJ5","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":"2c8f6fa3533cd907383dce87baf6f9003a0107c052884c074f94fd2cd110cc9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-03-13T00:19:04Z","title_canon_sha256":"cd84f9244669c8b5948f8ff7cda1682c743242b0838fb00034f3e2663b7613b1"},"schema_version":"1.0","source":{"id":"2303.06786","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.06786","created_at":"2026-07-05T06:30:04Z"},{"alias_kind":"arxiv_version","alias_value":"2303.06786v2","created_at":"2026-07-05T06:30:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.06786","created_at":"2026-07-05T06:30:04Z"},{"alias_kind":"pith_short_12","alias_value":"FX36PVUP3LYD","created_at":"2026-07-05T06:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"FX36PVUP3LYDKHQH","created_at":"2026-07-05T06:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"FX36PVUP","created_at":"2026-07-05T06:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:49ed6e09bf9d7850e259b0784d53095797b7aeed486c6a9e8cf9d4cadbba25ef","target":"graph","created_at":"2026-07-05T06:30:04Z","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/2303.06786/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In a recent paper, it was shown that in diffeomorphism-invariant theories, Noether charges associated with a given codimension-2 surface become integrable if one introduces an extended phase space. In this paper we extend the notion of extended phase space to all gauge theories with arbitrary combinations of internal and spacetime local symmetries. We formulate this in terms of a corresponding Atiyah Lie algebroid, a geometric object derived from a principal bundle which features internal symmetries and diffeomorphisms on an equal footing. In this language, gauge transformations are understood","authors_text":"Marc S. Klinger, Pin-Chun Pai, Robert G. Leigh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-03-13T00:19:04Z","title":"Extended Phase Space in General Gauge Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.06786","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":"sha256:73e8cf7349deb48bd9bd975080919abb6ec53d2adc0e0835fcdf47aed947ae93","target":"record","created_at":"2026-07-05T06:30:04Z","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":"2c8f6fa3533cd907383dce87baf6f9003a0107c052884c074f94fd2cd110cc9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-03-13T00:19:04Z","title_canon_sha256":"cd84f9244669c8b5948f8ff7cda1682c743242b0838fb00034f3e2663b7613b1"},"schema_version":"1.0","source":{"id":"2303.06786","kind":"arxiv","version":2}},"canonical_sha256":"2df7e7d68fdaf0351e075f0f3c39654f516e79ac2128aaaa3a430acdb8de2f7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2df7e7d68fdaf0351e075f0f3c39654f516e79ac2128aaaa3a430acdb8de2f7a","first_computed_at":"2026-07-05T06:30:04.480192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:30:04.480192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lu0kzMZo5SaqGiqSMIYD8oX05MS1sx4hcIkNpBfbMxuH5eqEY97B+h/T7+aOkKmseqWbONgWpkVSmS/sdRS8BA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:30:04.480548Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.06786","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73e8cf7349deb48bd9bd975080919abb6ec53d2adc0e0835fcdf47aed947ae93","sha256:49ed6e09bf9d7850e259b0784d53095797b7aeed486c6a9e8cf9d4cadbba25ef"],"state_sha256":"f9b35ff859ed206c1fea65036780c7236c2fc0f677da044f7c6126ab2c168b78"}