{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:72PGEP3ZHSQZBN2EQPNNMIRWBW","short_pith_number":"pith:72PGEP3Z","canonical_record":{"source":{"id":"1311.7398","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-11-28T19:15:01Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"fa8e0b41efd6d36dbec49845c3fba4afb59b2d4ca984535676c33e6e15d1fe81","abstract_canon_sha256":"2692be77db19208a719fad498ec987fe8a47938064b81c7192de4f82c21e0fc5"},"schema_version":"1.0"},"canonical_sha256":"fe9e623f793ca190b74483dad622360db48a29485306e5786d1012341c3d05f3","source":{"kind":"arxiv","id":"1311.7398","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7398","created_at":"2026-05-18T03:05:56Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7398v1","created_at":"2026-05-18T03:05:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7398","created_at":"2026-05-18T03:05:56Z"},{"alias_kind":"pith_short_12","alias_value":"72PGEP3ZHSQZ","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"72PGEP3ZHSQZBN2E","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"72PGEP3Z","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:72PGEP3ZHSQZBN2EQPNNMIRWBW","target":"record","payload":{"canonical_record":{"source":{"id":"1311.7398","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-11-28T19:15:01Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"fa8e0b41efd6d36dbec49845c3fba4afb59b2d4ca984535676c33e6e15d1fe81","abstract_canon_sha256":"2692be77db19208a719fad498ec987fe8a47938064b81c7192de4f82c21e0fc5"},"schema_version":"1.0"},"canonical_sha256":"fe9e623f793ca190b74483dad622360db48a29485306e5786d1012341c3d05f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:56.410178Z","signature_b64":"2KsLprcLSESUNMe0Ag6JBogb/zqTkf1Jy1hRxKyHV/Uhea5lRQOlS8b1VG5mS0BMycFZAPmdGc9wz2LtTX/zAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe9e623f793ca190b74483dad622360db48a29485306e5786d1012341c3d05f3","last_reissued_at":"2026-05-18T03:05:56.409578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:56.409578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.7398","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":"2026-05-18T03:05:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PpDvIr21jYHN7IzbMdKCZff4sWMQzrW8ZiTP2+WOInjcKhx2Wfe15wO2QjwNfcXQY3cFWNF7oSbYAZ/hcsxoCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:07:19.877768Z"},"content_sha256":"2331e9040632e15a3cca4a1c3961370282612359c956ca405f070bcdc87a8f1c","schema_version":"1.0","event_id":"sha256:2331e9040632e15a3cca4a1c3961370282612359c956ca405f070bcdc87a8f1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:72PGEP3ZHSQZBN2EQPNNMIRWBW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Integrability and Reduction of Hamiltonian Actions on Dirac Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Olivier Brahic, Rui Loja Fernandes","submitted_at":"2013-11-28T19:15:01Z","abstract_excerpt":"For a Hamiltonian, proper and free action of a Lie group $G$ on a Dirac manifold $(M,L)$, with a regular moment map $\\mu:M\\to \\mathfrak{g}^*$, the manifolds $M/G$, $\\mu^{-1}(0)$ and $\\mu^{-1}(0)/G$ all have natural induced Dirac structures. If $(M,L)$ is an integrable Dirac structure, we show that $M/G$ is always integrable, but $\\mu^{-1}(0)$ and $\\mu^{-1}(0)/G$ may fail to be integrable, and we describe the obstructions to their integrability."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7398","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":"2026-05-18T03:05:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JU2Vrmp9fGlp7noIqJ4l/SUsZ5Zt/VS9rubRI9mqcHTEvjZkF4y8S+EOhfV9rx2dlLzr8Hf+aABxZGW/J9MEDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:07:19.878615Z"},"content_sha256":"2c49308c4647ee87bc9162e0d60d151c0212630360cd6ec962fefd5043ca7c0a","schema_version":"1.0","event_id":"sha256:2c49308c4647ee87bc9162e0d60d151c0212630360cd6ec962fefd5043ca7c0a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/72PGEP3ZHSQZBN2EQPNNMIRWBW/bundle.json","state_url":"https://pith.science/pith/72PGEP3ZHSQZBN2EQPNNMIRWBW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/72PGEP3ZHSQZBN2EQPNNMIRWBW/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":"2026-06-11T02:07:19Z","links":{"resolver":"https://pith.science/pith/72PGEP3ZHSQZBN2EQPNNMIRWBW","bundle":"https://pith.science/pith/72PGEP3ZHSQZBN2EQPNNMIRWBW/bundle.json","state":"https://pith.science/pith/72PGEP3ZHSQZBN2EQPNNMIRWBW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/72PGEP3ZHSQZBN2EQPNNMIRWBW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:72PGEP3ZHSQZBN2EQPNNMIRWBW","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":"2692be77db19208a719fad498ec987fe8a47938064b81c7192de4f82c21e0fc5","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-11-28T19:15:01Z","title_canon_sha256":"fa8e0b41efd6d36dbec49845c3fba4afb59b2d4ca984535676c33e6e15d1fe81"},"schema_version":"1.0","source":{"id":"1311.7398","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7398","created_at":"2026-05-18T03:05:56Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7398v1","created_at":"2026-05-18T03:05:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7398","created_at":"2026-05-18T03:05:56Z"},{"alias_kind":"pith_short_12","alias_value":"72PGEP3ZHSQZ","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"72PGEP3ZHSQZBN2E","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"72PGEP3Z","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:2c49308c4647ee87bc9162e0d60d151c0212630360cd6ec962fefd5043ca7c0a","target":"graph","created_at":"2026-05-18T03:05:56Z","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":"For a Hamiltonian, proper and free action of a Lie group $G$ on a Dirac manifold $(M,L)$, with a regular moment map $\\mu:M\\to \\mathfrak{g}^*$, the manifolds $M/G$, $\\mu^{-1}(0)$ and $\\mu^{-1}(0)/G$ all have natural induced Dirac structures. If $(M,L)$ is an integrable Dirac structure, we show that $M/G$ is always integrable, but $\\mu^{-1}(0)$ and $\\mu^{-1}(0)/G$ may fail to be integrable, and we describe the obstructions to their integrability.","authors_text":"Olivier Brahic, Rui Loja Fernandes","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-11-28T19:15:01Z","title":"Integrability and Reduction of Hamiltonian Actions on Dirac Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7398","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":"sha256:2331e9040632e15a3cca4a1c3961370282612359c956ca405f070bcdc87a8f1c","target":"record","created_at":"2026-05-18T03:05:56Z","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":"2692be77db19208a719fad498ec987fe8a47938064b81c7192de4f82c21e0fc5","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-11-28T19:15:01Z","title_canon_sha256":"fa8e0b41efd6d36dbec49845c3fba4afb59b2d4ca984535676c33e6e15d1fe81"},"schema_version":"1.0","source":{"id":"1311.7398","kind":"arxiv","version":1}},"canonical_sha256":"fe9e623f793ca190b74483dad622360db48a29485306e5786d1012341c3d05f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe9e623f793ca190b74483dad622360db48a29485306e5786d1012341c3d05f3","first_computed_at":"2026-05-18T03:05:56.409578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:56.409578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2KsLprcLSESUNMe0Ag6JBogb/zqTkf1Jy1hRxKyHV/Uhea5lRQOlS8b1VG5mS0BMycFZAPmdGc9wz2LtTX/zAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:56.410178Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.7398","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2331e9040632e15a3cca4a1c3961370282612359c956ca405f070bcdc87a8f1c","sha256:2c49308c4647ee87bc9162e0d60d151c0212630360cd6ec962fefd5043ca7c0a"],"state_sha256":"8e5c1c1052ab3e5acad7832c6e986b6029ac95275dead31512621fca090a121c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BgItzdWzfR2PeAlXJVK6/yQ2VSH3Yo2TYlp2RzN7H4rLbEYo0BJ+OPSS7pFxbU58SOlEqCJDKt/8HBSifxJ5Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T02:07:19.882039Z","bundle_sha256":"da40468e683e01c986233efd6e454abeadc65c8821f5319ab2999cb8052bffb6"}}