{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MK7Z4RSUIWQCHGN3Y3LDURTKCG","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":"22bc6434bd0dc44d97ff4375f2719d826de05bd78355236caa270cb413a768b2","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-01T16:10:15Z","title_canon_sha256":"194f962a29da4ce54a4a7be3b122b77501e77519a26447c24285841403700f45"},"schema_version":"1.0","source":{"id":"1607.00300","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00300","created_at":"2026-05-18T01:11:37Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00300v1","created_at":"2026-05-18T01:11:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00300","created_at":"2026-05-18T01:11:37Z"},{"alias_kind":"pith_short_12","alias_value":"MK7Z4RSUIWQC","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MK7Z4RSUIWQCHGN3","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MK7Z4RSU","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:5f90565039b8d4d606dea1ef6eca8833298aab41a986c13ba19e443a433b9217","target":"graph","created_at":"2026-05-18T01:11:37Z","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 generalize a result on the Heisenberg Lie algebra that gives restrictions to possible Lie bialgebra cobrackets on 2-step nilpotent algebras with some additional properties. For the class of 2-step nilpotent Lie algebras coming from graphs, we describe these extra properties in a very easy graph-combinatorial way. We exhibit applications for $\\mathfrak f_n$, the free 2-step nilpotent Lie algebra.","authors_text":"A. Patricia Jancsa, Marco A. Farinati","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-01T16:10:15Z","title":"Lie bialgebra structures on 2-step nilpotent graph algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00300","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":"sha256:5f46afbba70978b5ca4bf3aed2b43cdc41e0d34dc02f70452349f4900815aac1","target":"record","created_at":"2026-05-18T01:11:37Z","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":"22bc6434bd0dc44d97ff4375f2719d826de05bd78355236caa270cb413a768b2","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-01T16:10:15Z","title_canon_sha256":"194f962a29da4ce54a4a7be3b122b77501e77519a26447c24285841403700f45"},"schema_version":"1.0","source":{"id":"1607.00300","kind":"arxiv","version":1}},"canonical_sha256":"62bf9e465445a02399bbc6d63a466a1182ae373eef3310897d3a1f8710d3c88b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62bf9e465445a02399bbc6d63a466a1182ae373eef3310897d3a1f8710d3c88b","first_computed_at":"2026-05-18T01:11:37.725401Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:37.725401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4KktRoI5UEHm6c9OjZpj4fkGVeeOxqJHyO4ZuAy3enKWHMjfOZBaYka0d4yhTus1ChjQNc5HAj/2nSJdufbgDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:37.725762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.00300","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f46afbba70978b5ca4bf3aed2b43cdc41e0d34dc02f70452349f4900815aac1","sha256:5f90565039b8d4d606dea1ef6eca8833298aab41a986c13ba19e443a433b9217"],"state_sha256":"e63ec88e05bd635c05951c2aa646be3878e7d20d0ea4aaec44953669e5f686ab"}