{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7FGBJ3KWK2VB3SXU6KF23VJ6NH","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":"2c0ab9536fd449c25e1bf14e5f1b1972c697c3dd0f9cf4a495c1d235ae09bfbb","cross_cats_sorted":["math.KT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-09-08T19:22:49Z","title_canon_sha256":"b06803c7b9eb86ce22877244f1b319acce3033af666550d97a87d1738dc7a381"},"schema_version":"1.0","source":{"id":"1609.02540","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02540","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02540v2","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02540","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"pith_short_12","alias_value":"7FGBJ3KWK2VB","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7FGBJ3KWK2VB3SXU","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7FGBJ3KW","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:b6636aa531ad67af3072303d3475198fda899d37d140ec6d6784aa1ad3805523","target":"graph","created_at":"2026-05-18T00:20:57Z","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":"Over a field of characteristic zero we prove two formality conditions. We prove that a dg Lie algebra is formal if and only if its universal enveloping algebra is formal. We also prove that a commutative dg algebra is formal as a dg associative algebra if and only if it is formal as a commutative dg algebra. We present some consequences of these theorems in rational homotopy theory.","authors_text":"Bashar Saleh","cross_cats":["math.KT","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-09-08T19:22:49Z","title":"Non-commutative formality implies commutative and Lie formality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02540","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":"sha256:9e9233113d5e267f5ac8c44c7d3c6e914bdbfc61bbd6d165d2c971200b2d16cf","target":"record","created_at":"2026-05-18T00:20:57Z","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":"2c0ab9536fd449c25e1bf14e5f1b1972c697c3dd0f9cf4a495c1d235ae09bfbb","cross_cats_sorted":["math.KT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-09-08T19:22:49Z","title_canon_sha256":"b06803c7b9eb86ce22877244f1b319acce3033af666550d97a87d1738dc7a381"},"schema_version":"1.0","source":{"id":"1609.02540","kind":"arxiv","version":2}},"canonical_sha256":"f94c14ed5656aa1dcaf4f28badd53e69fc4b0da3f6c55d74af3180df6948a00a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f94c14ed5656aa1dcaf4f28badd53e69fc4b0da3f6c55d74af3180df6948a00a","first_computed_at":"2026-05-18T00:20:57.237155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:57.237155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AePW9pMFhpwKPKGDVxhBLdpnUbbchQ1v+LhzbKtxLlN40Br0PFs+udTE7jb/JykZrctoaZqPdf8AyzUYNhVlCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:57.237754Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.02540","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e9233113d5e267f5ac8c44c7d3c6e914bdbfc61bbd6d165d2c971200b2d16cf","sha256:b6636aa531ad67af3072303d3475198fda899d37d140ec6d6784aa1ad3805523"],"state_sha256":"91defe0312fbb1ada811b1645036b35aa99d9bfdd42f78154b38df42b9e97090"}