{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:C27MA2YU7ZPYVJ26DVOTX6675Q","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":"487e01814f70bae723fb5eea9fe4c8bf6d25153218a3a0f31474092d9d754883","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-07-26T23:17:16Z","title_canon_sha256":"feb1a5964ed99e6e9c2b245a04b198c53f5e0baf9f7932c3c1da784abb8892d8"},"schema_version":"1.0","source":{"id":"1607.07913","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07913","created_at":"2026-05-18T01:10:22Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07913v1","created_at":"2026-05-18T01:10:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07913","created_at":"2026-05-18T01:10:22Z"},{"alias_kind":"pith_short_12","alias_value":"C27MA2YU7ZPY","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C27MA2YU7ZPYVJ26","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C27MA2YU","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:982ab43a0af5d12cd391e7f669a4545031d0bcb05c3eb9e78043499672b52a4c","target":"graph","created_at":"2026-05-18T01:10:22Z","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":"The $n$-Lie bialgebras are studied. In Section 2, the $n$-Lie coalgebra with rank $r$ is defined, and the structure of it is discussed. In Section 3, the $n$-Lie bialgebra is introduced. A triple $(L, \\mu, \\Delta)$ is an $n$-Lie bialgebra if and only if $\\Delta$ is a conformal $1$-cocycle on the $n$-Lie algebra $L$ associated to $L$-modules $(L^{\\otimes n}, \\rho_s^{\\mu})$, $1\\leq s\\leq n$, and the structure of $n$-Lie bialgebras is investigated by the structural constants. In Section 4, two-dimensional extension of finite dimensional $n$-Lie bialgebras are studied. For an $m$ dimensional $n$-L","authors_text":"Lixin Lin, Ruipu Bai, Weiwei Guo, Yang Zhang","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-07-26T23:17:16Z","title":"n-Lie bialgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07913","kind":"arxiv","version":1},"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":"sha256:62372d536092d471397aef932aa7ce8956490ab550f5847973931c095489e91c","target":"record","created_at":"2026-05-18T01:10:22Z","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":"487e01814f70bae723fb5eea9fe4c8bf6d25153218a3a0f31474092d9d754883","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-07-26T23:17:16Z","title_canon_sha256":"feb1a5964ed99e6e9c2b245a04b198c53f5e0baf9f7932c3c1da784abb8892d8"},"schema_version":"1.0","source":{"id":"1607.07913","kind":"arxiv","version":1}},"canonical_sha256":"16bec06b14fe5f8aa75e1d5d3bfbdfec320991da8f8e6a0f08ec30b7ec31b8c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16bec06b14fe5f8aa75e1d5d3bfbdfec320991da8f8e6a0f08ec30b7ec31b8c7","first_computed_at":"2026-05-18T01:10:22.954795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:22.954795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EWX8qZYwmfAEBrpWRj1uROjIXeQX6WctBFjQA4MzItIgKeXMmmqGg4HJ+1frmcXL1g/sSZ8hmKNQzL3q07EOCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:22.955404Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.07913","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62372d536092d471397aef932aa7ce8956490ab550f5847973931c095489e91c","sha256:982ab43a0af5d12cd391e7f669a4545031d0bcb05c3eb9e78043499672b52a4c"],"state_sha256":"546c25f2d464b0b9b5dee38f0643776cbb1566eed7a84bc4945a6d3407b102c9"}