{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:TZ7VYTVWYYJMBFWVM56ZFJ4OLK","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":"6322bfb912ca7702f6cfb0af7d365eb81c30d460539bb0556883302bec944cdf","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.AT","submitted_at":"2005-02-19T21:18:51Z","title_canon_sha256":"4fa23cef2fa11314cfdaced277359c26350805da94defb3ca5cddf9ff0bee011"},"schema_version":"1.0","source":{"id":"math/0502417","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0502417","created_at":"2026-05-18T04:38:49Z"},{"alias_kind":"arxiv_version","alias_value":"math/0502417v2","created_at":"2026-05-18T04:38:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0502417","created_at":"2026-05-18T04:38:49Z"},{"alias_kind":"pith_short_12","alias_value":"TZ7VYTVWYYJM","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"TZ7VYTVWYYJMBFWV","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"TZ7VYTVW","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:c91c1079c6e9014a1673e28bad527e3b54c14069db7eb91e9fe27e9d1a59ad69","target":"graph","created_at":"2026-05-18T04:38:49Z","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":"Let A be a graded-commutative, connected k-algebra generated in degree 1. The homotopy Lie algebra g_A is defined to be the Lie algebra of primitives of the Yoneda algebra, Ext_A(k,k). Under certain homological assumptions on A and its quadratic closure, we express g_A as a semi-direct product of the well-understood holonomy Lie algebra h_A with a certain h_A-module. This allows us to compute the homotopy Lie algebra associated to the cohomology ring of the complement of a complex hyperplane arrangement, provided some combinatorial assumptions are satisfied. As an application, we give examples","authors_text":"Alexander I. Suciu, Graham Denham","cross_cats":["math.CO"],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2005-02-19T21:18:51Z","title":"On the homotopy Lie algebra of an arrangement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502417","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:d5aef44d41541c60632e88452f485933eb5f1d4feae4df685f38aba768925539","target":"record","created_at":"2026-05-18T04:38:49Z","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":"6322bfb912ca7702f6cfb0af7d365eb81c30d460539bb0556883302bec944cdf","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.AT","submitted_at":"2005-02-19T21:18:51Z","title_canon_sha256":"4fa23cef2fa11314cfdaced277359c26350805da94defb3ca5cddf9ff0bee011"},"schema_version":"1.0","source":{"id":"math/0502417","kind":"arxiv","version":2}},"canonical_sha256":"9e7f5c4eb6c612c096d5677d92a78e5ab2917dfc46803c7c096b0dd07726faaa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e7f5c4eb6c612c096d5677d92a78e5ab2917dfc46803c7c096b0dd07726faaa","first_computed_at":"2026-05-18T04:38:49.091344Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:49.091344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3mBaCcA/QjrNKjHp8618LRg7fyi2j7tuBi6vT1NZ7UvnxG9XkLCJkcSqfypddI+kkISxqESyEc7OatNhxn2ICw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:49.091771Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0502417","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5aef44d41541c60632e88452f485933eb5f1d4feae4df685f38aba768925539","sha256:c91c1079c6e9014a1673e28bad527e3b54c14069db7eb91e9fe27e9d1a59ad69"],"state_sha256":"c8f0c86b77c2c39e6aaa2166106ca0651107438ffdcb41119d4c99ab7e59528d"}