{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FGPCYD7TQDPYMLG7DFIYPLW6XR","short_pith_number":"pith:FGPCYD7T","schema_version":"1.0","canonical_sha256":"299e2c0ff380df862cdf195187aedebc69d8618b920655d706305504373aad77","source":{"kind":"arxiv","id":"1611.02292","version":3},"attestation_state":"computed","paper":{"title":"On higher Dirac structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.SG","authors_text":"Henrique Bursztyn, Nicolas Martinez Alba, Roberto Rubio","submitted_at":"2016-11-07T21:00:13Z","abstract_excerpt":"We study higher-order analogues of Dirac structures, extending the multisymplectic structures that arise in field theory. We define higher Dirac structures as involutive subbundles of $TM+\\wedge^k TM^*$ satisfying a weak version of the usual lagrangian condition (which agrees with it only when $k=1$). Higher Dirac structures transversal to $TM$ recover the higher Poisson structures introduced in [8] as the infinitesimal counterparts of multisymplectic groupoids. We describe the leafwise geometry underlying an involutive isotropic subbundle in terms of a distinguished 1-cocycle in a natural dif"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1611.02292","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2016-11-07T21:00:13Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"7234279ba9f2e127d260d4792fbe5be3c0e2211739e18442d5979070d3e64b29","abstract_canon_sha256":"c30f69690855284b12fd1a4216b0a105a627bc899cb1a8171d70935151adb20f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:42.322812Z","signature_b64":"+V82TKRx3ew6VvgrkkVxTpKNALhC3DxetnqcT6YQe6Qtnv5J05AcIMEQoqj5BPpo2JKF37XAVvYB5H/wOO6ZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"299e2c0ff380df862cdf195187aedebc69d8618b920655d706305504373aad77","last_reissued_at":"2026-05-17T23:39:42.322137Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:42.322137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On higher Dirac structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.SG","authors_text":"Henrique Bursztyn, Nicolas Martinez Alba, Roberto Rubio","submitted_at":"2016-11-07T21:00:13Z","abstract_excerpt":"We study higher-order analogues of Dirac structures, extending the multisymplectic structures that arise in field theory. We define higher Dirac structures as involutive subbundles of $TM+\\wedge^k TM^*$ satisfying a weak version of the usual lagrangian condition (which agrees with it only when $k=1$). Higher Dirac structures transversal to $TM$ recover the higher Poisson structures introduced in [8] as the infinitesimal counterparts of multisymplectic groupoids. We describe the leafwise geometry underlying an involutive isotropic subbundle in terms of a distinguished 1-cocycle in a natural dif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02292","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1611.02292","created_at":"2026-05-17T23:39:42.322240+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.02292v3","created_at":"2026-05-17T23:39:42.322240+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02292","created_at":"2026-05-17T23:39:42.322240+00:00"},{"alias_kind":"pith_short_12","alias_value":"FGPCYD7TQDPY","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FGPCYD7TQDPYMLG7","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FGPCYD7T","created_at":"2026-05-18T12:30:15.759754+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FGPCYD7TQDPYMLG7DFIYPLW6XR","json":"https://pith.science/pith/FGPCYD7TQDPYMLG7DFIYPLW6XR.json","graph_json":"https://pith.science/api/pith-number/FGPCYD7TQDPYMLG7DFIYPLW6XR/graph.json","events_json":"https://pith.science/api/pith-number/FGPCYD7TQDPYMLG7DFIYPLW6XR/events.json","paper":"https://pith.science/paper/FGPCYD7T"},"agent_actions":{"view_html":"https://pith.science/pith/FGPCYD7TQDPYMLG7DFIYPLW6XR","download_json":"https://pith.science/pith/FGPCYD7TQDPYMLG7DFIYPLW6XR.json","view_paper":"https://pith.science/paper/FGPCYD7T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.02292&json=true","fetch_graph":"https://pith.science/api/pith-number/FGPCYD7TQDPYMLG7DFIYPLW6XR/graph.json","fetch_events":"https://pith.science/api/pith-number/FGPCYD7TQDPYMLG7DFIYPLW6XR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FGPCYD7TQDPYMLG7DFIYPLW6XR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FGPCYD7TQDPYMLG7DFIYPLW6XR/action/storage_attestation","attest_author":"https://pith.science/pith/FGPCYD7TQDPYMLG7DFIYPLW6XR/action/author_attestation","sign_citation":"https://pith.science/pith/FGPCYD7TQDPYMLG7DFIYPLW6XR/action/citation_signature","submit_replication":"https://pith.science/pith/FGPCYD7TQDPYMLG7DFIYPLW6XR/action/replication_record"}},"created_at":"2026-05-17T23:39:42.322240+00:00","updated_at":"2026-05-17T23:39:42.322240+00:00"}