{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DGSD5KI5KI4CLG2WOMUCR2WUFS","short_pith_number":"pith:DGSD5KI5","canonical_record":{"source":{"id":"1409.7899","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-09-28T12:34:41Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"d39a9cb6b928ea4db1956ff970e1a027d04df92ba4b5b18417bd68f61f361e75","abstract_canon_sha256":"90952ee11255ab75a19db3fcfbc59696ce84258f0ce54b2df12d3b4dff591f96"},"schema_version":"1.0"},"canonical_sha256":"19a43ea91d5238259b56732828ead42cbdae2cdd53c29703b9a39729bdd00713","source":{"kind":"arxiv","id":"1409.7899","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7899","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7899v2","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7899","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"pith_short_12","alias_value":"DGSD5KI5KI4C","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DGSD5KI5KI4CLG2W","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DGSD5KI5","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DGSD5KI5KI4CLG2WOMUCR2WUFS","target":"record","payload":{"canonical_record":{"source":{"id":"1409.7899","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-09-28T12:34:41Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"d39a9cb6b928ea4db1956ff970e1a027d04df92ba4b5b18417bd68f61f361e75","abstract_canon_sha256":"90952ee11255ab75a19db3fcfbc59696ce84258f0ce54b2df12d3b4dff591f96"},"schema_version":"1.0"},"canonical_sha256":"19a43ea91d5238259b56732828ead42cbdae2cdd53c29703b9a39729bdd00713","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:21.734238Z","signature_b64":"JEfB6UIYQdL0Zc5e893RUvmTe4HczB4HjBPB3TnXQU/iiCJYNIM4fTtcMA4UiKguhfGUnCmz84+e/m+/xFqkDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19a43ea91d5238259b56732828ead42cbdae2cdd53c29703b9a39729bdd00713","last_reissued_at":"2026-05-18T01:22:21.733537Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:21.733537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.7899","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":"2026-05-18T01:22:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QgPZXZyfhui7HBW6CXtp7VWZU5vxo2febRSUzY3HGkb7WEY6cGungdkuVv+BOObz7aFfZAbGnC0eRP/HtpMsDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:55:25.539691Z"},"content_sha256":"a38946a40db7656253382576120decf5b8d9506c12842c49ee103d6fe05f0dcd","schema_version":"1.0","event_id":"sha256:a38946a40db7656253382576120decf5b8d9506c12842c49ee103d6fe05f0dcd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DGSD5KI5KI4CLG2WOMUCR2WUFS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Integration of Coupling Dirac Structures","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":"2014-09-28T12:34:41Z","abstract_excerpt":"Coupling Dirac structures are Dirac structures defined on the total space of a fibration, generalizing hamiltonian fibrations from symplectic geometry, where one replaces the symplectic structure on the fibers by a Poisson structure.\n  We study the associated Poisson gauge theory, in order to describe the presymplectic groupoid integrating coupling Dirac structures. We find the obstructions to integrability and we give explicit geometric descriptions of the integration."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7899","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":""},"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":"2026-05-18T01:22:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iArK8qEWfj2sS8CjLOLTAhA3ZxHsAR+3CkN5SwBysAiP24PMVpoMIVCokBeTwIBsgEG4R5qQWkLnzlglojDkBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:55:25.540409Z"},"content_sha256":"ed1111ea19243ae6f05076e8cdf13969b8bc525d284a8db2b605c56b36b4dad8","schema_version":"1.0","event_id":"sha256:ed1111ea19243ae6f05076e8cdf13969b8bc525d284a8db2b605c56b36b4dad8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DGSD5KI5KI4CLG2WOMUCR2WUFS/bundle.json","state_url":"https://pith.science/pith/DGSD5KI5KI4CLG2WOMUCR2WUFS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DGSD5KI5KI4CLG2WOMUCR2WUFS/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":"2026-06-10T23:55:25Z","links":{"resolver":"https://pith.science/pith/DGSD5KI5KI4CLG2WOMUCR2WUFS","bundle":"https://pith.science/pith/DGSD5KI5KI4CLG2WOMUCR2WUFS/bundle.json","state":"https://pith.science/pith/DGSD5KI5KI4CLG2WOMUCR2WUFS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DGSD5KI5KI4CLG2WOMUCR2WUFS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DGSD5KI5KI4CLG2WOMUCR2WUFS","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":"90952ee11255ab75a19db3fcfbc59696ce84258f0ce54b2df12d3b4dff591f96","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-09-28T12:34:41Z","title_canon_sha256":"d39a9cb6b928ea4db1956ff970e1a027d04df92ba4b5b18417bd68f61f361e75"},"schema_version":"1.0","source":{"id":"1409.7899","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7899","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7899v2","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7899","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"pith_short_12","alias_value":"DGSD5KI5KI4C","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DGSD5KI5KI4CLG2W","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DGSD5KI5","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:ed1111ea19243ae6f05076e8cdf13969b8bc525d284a8db2b605c56b36b4dad8","target":"graph","created_at":"2026-05-18T01:22:21Z","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":"Coupling Dirac structures are Dirac structures defined on the total space of a fibration, generalizing hamiltonian fibrations from symplectic geometry, where one replaces the symplectic structure on the fibers by a Poisson structure.\n  We study the associated Poisson gauge theory, in order to describe the presymplectic groupoid integrating coupling Dirac structures. We find the obstructions to integrability and we give explicit geometric descriptions of the integration.","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":"2014-09-28T12:34:41Z","title":"Integration of Coupling Dirac Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7899","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:a38946a40db7656253382576120decf5b8d9506c12842c49ee103d6fe05f0dcd","target":"record","created_at":"2026-05-18T01:22:21Z","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":"90952ee11255ab75a19db3fcfbc59696ce84258f0ce54b2df12d3b4dff591f96","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-09-28T12:34:41Z","title_canon_sha256":"d39a9cb6b928ea4db1956ff970e1a027d04df92ba4b5b18417bd68f61f361e75"},"schema_version":"1.0","source":{"id":"1409.7899","kind":"arxiv","version":2}},"canonical_sha256":"19a43ea91d5238259b56732828ead42cbdae2cdd53c29703b9a39729bdd00713","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19a43ea91d5238259b56732828ead42cbdae2cdd53c29703b9a39729bdd00713","first_computed_at":"2026-05-18T01:22:21.733537Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:21.733537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JEfB6UIYQdL0Zc5e893RUvmTe4HczB4HjBPB3TnXQU/iiCJYNIM4fTtcMA4UiKguhfGUnCmz84+e/m+/xFqkDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:21.734238Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.7899","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a38946a40db7656253382576120decf5b8d9506c12842c49ee103d6fe05f0dcd","sha256:ed1111ea19243ae6f05076e8cdf13969b8bc525d284a8db2b605c56b36b4dad8"],"state_sha256":"d2857ebd5c4554bae5ada7b430adfb2e42aab43fdec7e1e43ba459a5f7eca645"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bCqop0wj1ExlHzIBBVulB9PSE7PHPjWYtt2cetq43G9bV/xsTWSj0W9ADF3Ua79CiYDfz1E4+XwFjZYKAHmEAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T23:55:25.544408Z","bundle_sha256":"4995bd63a47766589ab151fc7844b9274fce856399dbbcf8319ae0edb7ce9f81"}}