{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:55GB54O7YCDBF5LWLKILNXLCSV","short_pith_number":"pith:55GB54O7","canonical_record":{"source":{"id":"1612.02026","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-12-06T21:18:45Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"27b67987647c243e6938560037d56eb1da26223f3bda6ef288ae9911cb9e077c","abstract_canon_sha256":"0ff2b9963aa3fe2f11f3b154344096fdcc5ace64bee286bdb56b07a2bbc83b76"},"schema_version":"1.0"},"canonical_sha256":"ef4c1ef1dfc08612f5765a90b6dd62955dda0e00b5239c71459c1cf0aecb9131","source":{"kind":"arxiv","id":"1612.02026","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:55GB54O7YCDBF5LWLKILNXLCSV","target":"record","payload":{"canonical_record":{"source":{"id":"1612.02026","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-12-06T21:18:45Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"27b67987647c243e6938560037d56eb1da26223f3bda6ef288ae9911cb9e077c","abstract_canon_sha256":"0ff2b9963aa3fe2f11f3b154344096fdcc5ace64bee286bdb56b07a2bbc83b76"},"schema_version":"1.0"},"canonical_sha256":"ef4c1ef1dfc08612f5765a90b6dd62955dda0e00b5239c71459c1cf0aecb9131","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:54.698053Z","signature_b64":"t2Ad+L2QUl6umdFEkSUaAeuFMOgBFKX5bqcPT9tWzWrAxUzEAfdZjhrfyzKms79ddek+1NYcJMCrJoq43PQYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef4c1ef1dfc08612f5765a90b6dd62955dda0e00b5239c71459c1cf0aecb9131","last_reissued_at":"2026-05-18T00:37:54.697578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:54.697578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.02026","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":"2026-05-18T00:37:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XLhZfh+z4biChj+MEi7kUvQbVgUUsbrw5Wdii9Q+Hfl3Ubt6PKxNYJVcnM8Gts+FLge9gFFtFzHS6yVnJEfjDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T06:39:36.066888Z"},"content_sha256":"59e9bf62865eb91ae756fb9a7d35e490c5354fc0895335bae3732ec842a6968f","schema_version":"1.0","event_id":"sha256:59e9bf62865eb91ae756fb9a7d35e490c5354fc0895335bae3732ec842a6968f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:55GB54O7YCDBF5LWLKILNXLCSV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On homotopy Lie bialgebroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.QA","authors_text":"Alexander A. Voronov, Denis Bashkirov","submitted_at":"2016-12-06T21:18:45Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02026","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":"2026-05-18T00:37:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LuiktyDr+SOQMIB7ZgXE006PTfQXeTWrrk2fJYx1qp15t3jzVIVrPUJWtFSMrQAgxJ8yZFUVgj1nqqbi/86MCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T06:39:36.067218Z"},"content_sha256":"d30d737608a5a1b30c3a045b71afdf26bbd8a18d54be2d6b8057ba8e04831eab","schema_version":"1.0","event_id":"sha256:d30d737608a5a1b30c3a045b71afdf26bbd8a18d54be2d6b8057ba8e04831eab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/55GB54O7YCDBF5LWLKILNXLCSV/bundle.json","state_url":"https://pith.science/pith/55GB54O7YCDBF5LWLKILNXLCSV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/55GB54O7YCDBF5LWLKILNXLCSV/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":"2026-06-29T06:39:36Z","links":{"resolver":"https://pith.science/pith/55GB54O7YCDBF5LWLKILNXLCSV","bundle":"https://pith.science/pith/55GB54O7YCDBF5LWLKILNXLCSV/bundle.json","state":"https://pith.science/pith/55GB54O7YCDBF5LWLKILNXLCSV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/55GB54O7YCDBF5LWLKILNXLCSV/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jzY12TG4gCA4l+4nF+wEbcVEiTl8nbM73czfhwEZQ7XAV/hayjUNfWb54lZH5VloFsZce1W8UFonrywHijFKAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T06:39:36.069164Z","bundle_sha256":"f7648c55e75cf8da6fe9ea27ceb2c6a7dba85f504c4a3d55b5e1a96db967cb70"}}