{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:55GB54O7YCDBF5LWLKILNXLCSV","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":"0ff2b9963aa3fe2f11f3b154344096fdcc5ace64bee286bdb56b07a2bbc83b76","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-12-06T21:18:45Z","title_canon_sha256":"27b67987647c243e6938560037d56eb1da26223f3bda6ef288ae9911cb9e077c"},"schema_version":"1.0","source":{"id":"1612.02026","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02026","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02026v2","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02026","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"pith_short_12","alias_value":"55GB54O7YCDB","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"55GB54O7YCDBF5LW","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"55GB54O7","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:d30d737608a5a1b30c3a045b71afdf26bbd8a18d54be2d6b8057ba8e04831eab","target":"graph","created_at":"2026-05-18T00:37:54Z","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":"A well-known result of A. Vaintrob characterizes Lie algebroids and their morphisms in terms of homological vector fields on supermanifolds. We give an interpretation of Lie bialgebroids and their morphisms in terms of odd symplectic dg-manifolds, building on the approach of D. Roytenberg. This extends naturally to the homotopy Lie case and leads to the notion of $L_\\infty$-bialgebroids and $L_\\infty$-morphisms between them.","authors_text":"Alexander A. Voronov, Denis Bashkirov","cross_cats":["math-ph","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-12-06T21:18:45Z","title":"On homotopy Lie bialgebroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02026","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":"sha256:59e9bf62865eb91ae756fb9a7d35e490c5354fc0895335bae3732ec842a6968f","target":"record","created_at":"2026-05-18T00:37:54Z","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":"0ff2b9963aa3fe2f11f3b154344096fdcc5ace64bee286bdb56b07a2bbc83b76","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-12-06T21:18:45Z","title_canon_sha256":"27b67987647c243e6938560037d56eb1da26223f3bda6ef288ae9911cb9e077c"},"schema_version":"1.0","source":{"id":"1612.02026","kind":"arxiv","version":2}},"canonical_sha256":"ef4c1ef1dfc08612f5765a90b6dd62955dda0e00b5239c71459c1cf0aecb9131","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef4c1ef1dfc08612f5765a90b6dd62955dda0e00b5239c71459c1cf0aecb9131","first_computed_at":"2026-05-18T00:37:54.697578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:54.697578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t2Ad+L2QUl6umdFEkSUaAeuFMOgBFKX5bqcPT9tWzWrAxUzEAfdZjhrfyzKms79ddek+1NYcJMCrJoq43PQYAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:54.698053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.02026","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59e9bf62865eb91ae756fb9a7d35e490c5354fc0895335bae3732ec842a6968f","sha256:d30d737608a5a1b30c3a045b71afdf26bbd8a18d54be2d6b8057ba8e04831eab"],"state_sha256":"94ad98c6ec8735d2a07918746722cae344688a13bf6cc18a54dd7cbb5339a7fd"}