{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:5VRR5G67ZFDWAKZUCTMTD7TGBU","short_pith_number":"pith:5VRR5G67","schema_version":"1.0","canonical_sha256":"ed631e9bdfc947602b3414d931fe660d1445abc55c450bc5dee1636afb537181","source":{"kind":"arxiv","id":"0901.0256","version":3},"attestation_state":"computed","paper":{"title":"Holonomy Lie algebras and the LCS formula for subarrangements of A_n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Hal Schenck, Paulo Lima-Filho","submitted_at":"2009-01-02T17:09:55Z","abstract_excerpt":"If X is the complement of a hypersurface in P^n, then Kohno showed that the nilpotent completion of the fundamental group is isomorphic to the nilpotent completion of the holonomy Lie algebra of X. When X is the complement of a hyperplane arrangement A, the ranks phi_k of the lower central series quotients of the fundamental group of X are known for isolated examples, and for two special classes: if X is hypersolvable (in which case the quadratic closure of the cohomology ring is Koszul), or if the holonomy Lie algebra decomposes in degree three as a direct product of local components. In this"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0901.0256","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-01-02T17:09:55Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"0349186fb85b603c5ecf867b09a8155c9927cbc77be6781e76353a9d4435443a","abstract_canon_sha256":"d1f6923723b1253dceec40471381e60b96ed83bc8e7998d491638c082ca7855a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:44.020571Z","signature_b64":"MaMjtOaIGC4ZCe3UUFKzK5tPAgJDMKNJjDWpBEGS79oQAFB40ALyXDQfpADO57GGLhox7vUMJxPvIx2l6AfNBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed631e9bdfc947602b3414d931fe660d1445abc55c450bc5dee1636afb537181","last_reissued_at":"2026-05-18T04:03:44.019915Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:44.019915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Holonomy Lie algebras and the LCS formula for subarrangements of A_n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Hal Schenck, Paulo Lima-Filho","submitted_at":"2009-01-02T17:09:55Z","abstract_excerpt":"If X is the complement of a hypersurface in P^n, then Kohno showed that the nilpotent completion of the fundamental group is isomorphic to the nilpotent completion of the holonomy Lie algebra of X. When X is the complement of a hyperplane arrangement A, the ranks phi_k of the lower central series quotients of the fundamental group of X are known for isolated examples, and for two special classes: if X is hypersolvable (in which case the quadratic closure of the cohomology ring is Koszul), or if the holonomy Lie algebra decomposes in degree three as a direct product of local components. In this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.0256","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"0901.0256","created_at":"2026-05-18T04:03:44.020008+00:00"},{"alias_kind":"arxiv_version","alias_value":"0901.0256v3","created_at":"2026-05-18T04:03:44.020008+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.0256","created_at":"2026-05-18T04:03:44.020008+00:00"},{"alias_kind":"pith_short_12","alias_value":"5VRR5G67ZFDW","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"5VRR5G67ZFDWAKZU","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"5VRR5G67","created_at":"2026-05-18T12:25:58.837520+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5VRR5G67ZFDWAKZUCTMTD7TGBU","json":"https://pith.science/pith/5VRR5G67ZFDWAKZUCTMTD7TGBU.json","graph_json":"https://pith.science/api/pith-number/5VRR5G67ZFDWAKZUCTMTD7TGBU/graph.json","events_json":"https://pith.science/api/pith-number/5VRR5G67ZFDWAKZUCTMTD7TGBU/events.json","paper":"https://pith.science/paper/5VRR5G67"},"agent_actions":{"view_html":"https://pith.science/pith/5VRR5G67ZFDWAKZUCTMTD7TGBU","download_json":"https://pith.science/pith/5VRR5G67ZFDWAKZUCTMTD7TGBU.json","view_paper":"https://pith.science/paper/5VRR5G67","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0901.0256&json=true","fetch_graph":"https://pith.science/api/pith-number/5VRR5G67ZFDWAKZUCTMTD7TGBU/graph.json","fetch_events":"https://pith.science/api/pith-number/5VRR5G67ZFDWAKZUCTMTD7TGBU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5VRR5G67ZFDWAKZUCTMTD7TGBU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5VRR5G67ZFDWAKZUCTMTD7TGBU/action/storage_attestation","attest_author":"https://pith.science/pith/5VRR5G67ZFDWAKZUCTMTD7TGBU/action/author_attestation","sign_citation":"https://pith.science/pith/5VRR5G67ZFDWAKZUCTMTD7TGBU/action/citation_signature","submit_replication":"https://pith.science/pith/5VRR5G67ZFDWAKZUCTMTD7TGBU/action/replication_record"}},"created_at":"2026-05-18T04:03:44.020008+00:00","updated_at":"2026-05-18T04:03:44.020008+00:00"}