{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NCJMPDGYZX35LF6DER6TI44ZQ7","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":"8c9c038d7ec898b4de7bdf4f4449e8dfd50301837dedf55c1adf214c97dbb3f4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2025-04-28T17:18:50Z","title_canon_sha256":"0bfa76d112fd23360f3cafcf0b49586da4efad6ba1fbe8433b2b397312b4ba81"},"schema_version":"1.0","source":{"id":"2504.19998","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.19998","created_at":"2026-07-05T10:55:07Z"},{"alias_kind":"arxiv_version","alias_value":"2504.19998v1","created_at":"2026-07-05T10:55:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.19998","created_at":"2026-07-05T10:55:07Z"},{"alias_kind":"pith_short_12","alias_value":"NCJMPDGYZX35","created_at":"2026-07-05T10:55:07Z"},{"alias_kind":"pith_short_16","alias_value":"NCJMPDGYZX35LF6D","created_at":"2026-07-05T10:55:07Z"},{"alias_kind":"pith_short_8","alias_value":"NCJMPDGY","created_at":"2026-07-05T10:55:07Z"}],"graph_snapshots":[{"event_id":"sha256:a4c2824a7274e78392e53aa38306e64aa67ba42243f3a273f9c86f201f7c943f","target":"graph","created_at":"2026-07-05T10:55:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2504.19998/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the homotopy theory of post-Lie algebras. Guided by Koszul duality theory, we consider the graded Lie algebra of coderivations of the cofree conilpotent graded cocommutative cotrialgebra generated by $V$. We show that in the case of $V$ being a shift of an ungraded vector space $W$, Maurer-Cartan elements of this graded Lie algebra are exactly post-Lie algebra structures on $W$. The cohomology of a post-Lie algebra is then defined using Maurer-Cartan twisting. The second cohomology group of a post-Lie algebra has a familiar interpretation as equivalence classes of infin","authors_text":"Andrey Lazarev, Rong Tang, Yunhe Sheng","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2025-04-28T17:18:50Z","title":"Homotopy theory of post-Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.19998","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":"sha256:4ef1150cc0b7647064634e542cc8cab64e62a45083e0f31034a508b7aca62cee","target":"record","created_at":"2026-07-05T10:55:07Z","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":"8c9c038d7ec898b4de7bdf4f4449e8dfd50301837dedf55c1adf214c97dbb3f4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2025-04-28T17:18:50Z","title_canon_sha256":"0bfa76d112fd23360f3cafcf0b49586da4efad6ba1fbe8433b2b397312b4ba81"},"schema_version":"1.0","source":{"id":"2504.19998","kind":"arxiv","version":1}},"canonical_sha256":"6892c78cd8cdf7d597c3247d34739987d2ea802cedcb37e83941a9104a7dd0b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6892c78cd8cdf7d597c3247d34739987d2ea802cedcb37e83941a9104a7dd0b0","first_computed_at":"2026-07-05T10:55:07.469066Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:55:07.469066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dIo1g4fWEFCSlH87K6+oAPbD4MOmKgjwKnVbyXwL/E9DCpXTQJ0HlO7QhRxQgIPZQ5kHZuz0I+zuIuGJHBeMCw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:55:07.469532Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.19998","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ef1150cc0b7647064634e542cc8cab64e62a45083e0f31034a508b7aca62cee","sha256:a4c2824a7274e78392e53aa38306e64aa67ba42243f3a273f9c86f201f7c943f"],"state_sha256":"7e1a16d8d09243c4585b70324dfc94a00e23d9b22facfb77a432aea7274564e4"}