{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XQTAXUKILCE6ODYFS6G7E7D75C","short_pith_number":"pith:XQTAXUKI","schema_version":"1.0","canonical_sha256":"bc260bd1485889e70f05978df27c7fe8be0524c57ea496d3958f3fbdc56698d2","source":{"kind":"arxiv","id":"1608.00664","version":1},"attestation_state":"computed","paper":{"title":"Integration of 2-term representations up to homotopy via 2-functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Cristian Ortiz, Olivier Brahic","submitted_at":"2016-08-02T01:00:58Z","abstract_excerpt":"Given a representation up to homotopy of a Lie algebroid on a 2-term complex of vector bundles, we define the corresponding holonomy as a strict 2-functor from a Weinstein path 2-groupoid to the gauge 2-groupoid of the underlying 2-term complex. We construct a corresponding transformation 2-groupoid and we prove that the 1-truncation of this 2-groupoid is isomorphic to the Weinstein groupoid of the VB-algebroid associated to a representation up to homotopy. As applications, we describe alternative integration schemes for semi-direct products of Lie 2-algebras and string algebras."},"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":"1608.00664","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-02T01:00:58Z","cross_cats_sorted":[],"title_canon_sha256":"5da89eb584d6de22f758b291f71d29fce7f6de04a28369fc4f35b3f3b311451d","abstract_canon_sha256":"ff73dadb98fcbfb2594803ee21f1b4d78802129b72789330f1d0f2f3c45ed1ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:01.381305Z","signature_b64":"6KMLeRC0WHF6aex8zpnia3+GkAg4YsvJbw5116EYHA40fMzZAspVYKpPphZ2b8z1Shc/WFZaDbWM9HrihEBZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc260bd1485889e70f05978df27c7fe8be0524c57ea496d3958f3fbdc56698d2","last_reissued_at":"2026-05-18T01:10:01.380690Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:01.380690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integration of 2-term representations up to homotopy via 2-functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Cristian Ortiz, Olivier Brahic","submitted_at":"2016-08-02T01:00:58Z","abstract_excerpt":"Given a representation up to homotopy of a Lie algebroid on a 2-term complex of vector bundles, we define the corresponding holonomy as a strict 2-functor from a Weinstein path 2-groupoid to the gauge 2-groupoid of the underlying 2-term complex. We construct a corresponding transformation 2-groupoid and we prove that the 1-truncation of this 2-groupoid is isomorphic to the Weinstein groupoid of the VB-algebroid associated to a representation up to homotopy. As applications, we describe alternative integration schemes for semi-direct products of Lie 2-algebras and string algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00664","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1608.00664","created_at":"2026-05-18T01:10:01.380797+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.00664v1","created_at":"2026-05-18T01:10:01.380797+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00664","created_at":"2026-05-18T01:10:01.380797+00:00"},{"alias_kind":"pith_short_12","alias_value":"XQTAXUKILCE6","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XQTAXUKILCE6ODYF","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XQTAXUKI","created_at":"2026-05-18T12:30:51.357362+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/XQTAXUKILCE6ODYFS6G7E7D75C","json":"https://pith.science/pith/XQTAXUKILCE6ODYFS6G7E7D75C.json","graph_json":"https://pith.science/api/pith-number/XQTAXUKILCE6ODYFS6G7E7D75C/graph.json","events_json":"https://pith.science/api/pith-number/XQTAXUKILCE6ODYFS6G7E7D75C/events.json","paper":"https://pith.science/paper/XQTAXUKI"},"agent_actions":{"view_html":"https://pith.science/pith/XQTAXUKILCE6ODYFS6G7E7D75C","download_json":"https://pith.science/pith/XQTAXUKILCE6ODYFS6G7E7D75C.json","view_paper":"https://pith.science/paper/XQTAXUKI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.00664&json=true","fetch_graph":"https://pith.science/api/pith-number/XQTAXUKILCE6ODYFS6G7E7D75C/graph.json","fetch_events":"https://pith.science/api/pith-number/XQTAXUKILCE6ODYFS6G7E7D75C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XQTAXUKILCE6ODYFS6G7E7D75C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XQTAXUKILCE6ODYFS6G7E7D75C/action/storage_attestation","attest_author":"https://pith.science/pith/XQTAXUKILCE6ODYFS6G7E7D75C/action/author_attestation","sign_citation":"https://pith.science/pith/XQTAXUKILCE6ODYFS6G7E7D75C/action/citation_signature","submit_replication":"https://pith.science/pith/XQTAXUKILCE6ODYFS6G7E7D75C/action/replication_record"}},"created_at":"2026-05-18T01:10:01.380797+00:00","updated_at":"2026-05-18T01:10:01.380797+00:00"}