{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SDM7S4PVPZVDR2XV3LYJWNF3YH","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":"21b3538db8a0916c1668fc7f0b3d2c5fecd3ff10c00fb4683b6692b4351ed9ab","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-16T18:54:39Z","title_canon_sha256":"00caa66844892bcd710cd65a7dce45adcfaeeec1d1043242284ab83ece2b1e57"},"schema_version":"1.0","source":{"id":"1302.3987","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3987","created_at":"2026-05-18T01:20:18Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3987v2","created_at":"2026-05-18T01:20:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3987","created_at":"2026-05-18T01:20:18Z"},{"alias_kind":"pith_short_12","alias_value":"SDM7S4PVPZVD","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SDM7S4PVPZVDR2XV","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SDM7S4PV","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:653dd2b552d45a1cc2399e0cf6ce7512680ab5b81e45f5177db96031304dc1be","target":"graph","created_at":"2026-05-18T01:20:18Z","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 show in this paper that the correspondence between $2$-term representations up to homotopy and $\\mathcal{VB}$-algebroids, established by Gracia-Saz and Mehta, holds also at the level of morphisms. This correspondence is hence an equivalence of categories. As an application, we study foliations and distributions on a Lie algebroid, that are compatible both with the linear structure and the Lie algebroid structure. In particular, we show how infinitesimal ideal systems in a Lie algebroid $A$ are related with subrepresentations of the adjoint representation of $A$.","authors_text":"Cristian Ortiz, Madeleine Jotz Lean, Thiago Drummond","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-16T18:54:39Z","title":"VB-algebroid morphisms and representations up to homotopy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3987","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":"sha256:2be28ea7d1be8c9034d1ed23cf94e5f0487f2fd484901aa5b16412146d4cea7d","target":"record","created_at":"2026-05-18T01:20:18Z","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":"21b3538db8a0916c1668fc7f0b3d2c5fecd3ff10c00fb4683b6692b4351ed9ab","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-16T18:54:39Z","title_canon_sha256":"00caa66844892bcd710cd65a7dce45adcfaeeec1d1043242284ab83ece2b1e57"},"schema_version":"1.0","source":{"id":"1302.3987","kind":"arxiv","version":2}},"canonical_sha256":"90d9f971f57e6a38eaf5daf09b34bbc1eca4bcf9783ddf6bb091e321a3eb5c5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90d9f971f57e6a38eaf5daf09b34bbc1eca4bcf9783ddf6bb091e321a3eb5c5c","first_computed_at":"2026-05-18T01:20:18.071618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:18.071618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F6BiOvP79tZUmH78mHjWRPTpENWOny0ys8lGy94YAvekfYnMM4rV8g2NCYf4w7XRAAdfkQoFCSRJVkwgshCFCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:18.072194Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3987","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2be28ea7d1be8c9034d1ed23cf94e5f0487f2fd484901aa5b16412146d4cea7d","sha256:653dd2b552d45a1cc2399e0cf6ce7512680ab5b81e45f5177db96031304dc1be"],"state_sha256":"8b08709ab48e6e4ac2d8c8a3d2caf35adffe856b3a8fcd82c1830acb7b1708c4"}