{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LCDE2F4FY5OYEBIUTMIUU7JEER","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":"1bf731762360b470e4e42f6254d2d24c576430d1d9e3603bc6e3b0a8bffa1a0c","cross_cats_sorted":["math.CT","math.MP","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-07T02:59:30Z","title_canon_sha256":"ff87b52cd81c7d10eea70aaf00a3177555f9259e1b3b8919a763237b29a9c042"},"schema_version":"1.0","source":{"id":"1109.1344","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1344","created_at":"2026-05-18T03:26:41Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1344v4","created_at":"2026-05-18T03:26:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1344","created_at":"2026-05-18T03:26:41Z"},{"alias_kind":"pith_short_12","alias_value":"LCDE2F4FY5OY","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LCDE2F4FY5OYEBIU","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LCDE2F4F","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:46624fdb1194e6fc77729ded94053cff238db059b2589340ae1d2b1752ebfca0","target":"graph","created_at":"2026-05-18T03:26:41Z","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":"In this paper, we study Lie 2-bialgebras, with special attention to coboundary ones, with the help of the cohomology theory of $L_\\infty$-algebras with coefficients in $L_\\infty$-modules. We construct examples of strict Lie 2-bialgebras from left-symmetric algebras and symplectic Lie algebras.","authors_text":"Chenchang Zhu, Chengming Bai, Yunhe Sheng","cross_cats":["math.CT","math.MP","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-07T02:59:30Z","title":"Lie 2-bialgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1344","kind":"arxiv","version":4},"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:c5e3c75eb0772a9a8ebd175ad85c71ebfb783f1d140f171ec47b10a103f8f966","target":"record","created_at":"2026-05-18T03:26:41Z","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":"1bf731762360b470e4e42f6254d2d24c576430d1d9e3603bc6e3b0a8bffa1a0c","cross_cats_sorted":["math.CT","math.MP","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-07T02:59:30Z","title_canon_sha256":"ff87b52cd81c7d10eea70aaf00a3177555f9259e1b3b8919a763237b29a9c042"},"schema_version":"1.0","source":{"id":"1109.1344","kind":"arxiv","version":4}},"canonical_sha256":"58864d1785c75d8205149b114a7d24247b41f3898c7dbba3b5ec2dd66ec3d510","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58864d1785c75d8205149b114a7d24247b41f3898c7dbba3b5ec2dd66ec3d510","first_computed_at":"2026-05-18T03:26:41.373481Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:41.373481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OTvge/5vWpu0Zs30t2AMVoZY+Z6U4FX8HK+XIE0irKNSxOi9PSm7WcOI6WxyAaJnvm82vKqyN+omqLDctSA1Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:41.374190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.1344","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5e3c75eb0772a9a8ebd175ad85c71ebfb783f1d140f171ec47b10a103f8f966","sha256:46624fdb1194e6fc77729ded94053cff238db059b2589340ae1d2b1752ebfca0"],"state_sha256":"3f23ef5958e054b63223b15270cd34902fc506cfb2c07ce087b2cc10b88d450a"}