{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7IRUETQYVHTD2OJO5IFTJO4RJA","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":"6322c0746c14de16443bad4d5981f38925093c985faaa0eb69923e22c73db873","cross_cats_sorted":["math.DG","math.MP","quant-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2014-05-03T12:05:16Z","title_canon_sha256":"a7c4fca07ff362ac1df8edd70f76847b969146d346eecb6945a97fa93bea9d7b"},"schema_version":"1.0","source":{"id":"1405.0574","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0574","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0574v2","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0574","created_at":"2026-05-18T02:42:39Z"},{"alias_kind":"pith_short_12","alias_value":"7IRUETQYVHTD","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7IRUETQYVHTD2OJO","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7IRUETQY","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:1e3e212e1ef19ae915acfd19b523206e9ae49be3b14d2c9a7fe20541766b1b0a","target":"graph","created_at":"2026-05-18T02:42:39Z","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 describe an averaging procedure on a Dirac manifold, with respect to a class of compatible actions of a compact Lie group. Some averaging theorems on the existence of invariant realizations of Poisson structures around (singular) symplectic leaves are derived. We show that the construction of coupling Dirac structures (invariant with respect to locally Hamiltonian group actions) on a Poisson foliation is related with a special class of exact gauge transformations.","authors_text":"Jos\\'e A. Vallejo, Yurii Vorobiev","cross_cats":["math.DG","math.MP","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2014-05-03T12:05:16Z","title":"Invariant Poisson Realizations and the Averaging of Dirac Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0574","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:e33c172713583764ba85c05f2bd05aa4ed12b1a178849eea0bfe15d52adecbe2","target":"record","created_at":"2026-05-18T02:42:39Z","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":"6322c0746c14de16443bad4d5981f38925093c985faaa0eb69923e22c73db873","cross_cats_sorted":["math.DG","math.MP","quant-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2014-05-03T12:05:16Z","title_canon_sha256":"a7c4fca07ff362ac1df8edd70f76847b969146d346eecb6945a97fa93bea9d7b"},"schema_version":"1.0","source":{"id":"1405.0574","kind":"arxiv","version":2}},"canonical_sha256":"fa23424e18a9e63d392eea0b34bb9148028a320ef9db26eee4de6329cd40046f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa23424e18a9e63d392eea0b34bb9148028a320ef9db26eee4de6329cd40046f","first_computed_at":"2026-05-18T02:42:39.279962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:39.279962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vgH2Akcwb5mGGAeZcRclQ+TgFJuz4vDa/6jjy+mRjNkovmBhlDsSynWzP1y/y1PQTp9lDMIyJkRt8yZH1F/0Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:39.280511Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.0574","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e33c172713583764ba85c05f2bd05aa4ed12b1a178849eea0bfe15d52adecbe2","sha256:1e3e212e1ef19ae915acfd19b523206e9ae49be3b14d2c9a7fe20541766b1b0a"],"state_sha256":"65f5baaa1a6c3ee4d1006bfbd2f7ddcf6db055a482670280276fe8fd5bb98a6a"}