{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LHXEIYWMOBGFFTUPMMTTJN4YAX","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":"3ba11a373651aac0eb72a81d3df0bd96b25dd5726031826c8ce43b11a662551a","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-02-07T14:03:20Z","title_canon_sha256":"8ff70113acfa4c350a5b38050ddc90be6a9bb32b1a897bef6a638d4616dcc8d1"},"schema_version":"1.0","source":{"id":"1402.1641","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.1641","created_at":"2026-05-18T00:56:46Z"},{"alias_kind":"arxiv_version","alias_value":"1402.1641v1","created_at":"2026-05-18T00:56:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.1641","created_at":"2026-05-18T00:56:46Z"},{"alias_kind":"pith_short_12","alias_value":"LHXEIYWMOBGF","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LHXEIYWMOBGFFTUP","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LHXEIYWM","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:a45b4fa74ea51a2943b45cfbe6c30f6dadc6900fd3de4387d9544f6daf039e45","target":"graph","created_at":"2026-05-18T00:56:46Z","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 prove the minimality of the CW-complex structure for complements of hyperplane arrangements in $\\mathbb C^n$ by using the theory of Lefschetz pencils and results on the variation maps within a pencil of hyperplanes. This also provides a method to compute the Betti numbers of complements of arrangements via global polar invariants.","authors_text":"Mihai Tibar","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-02-07T14:03:20Z","title":"Complements of hypersurfaces, variation maps and minimal models of arrangements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1641","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":"sha256:793b427af513c734d22da2ad04acdb6e3ab60591f695d0d547224edd5b2c145c","target":"record","created_at":"2026-05-18T00:56:46Z","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":"3ba11a373651aac0eb72a81d3df0bd96b25dd5726031826c8ce43b11a662551a","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-02-07T14:03:20Z","title_canon_sha256":"8ff70113acfa4c350a5b38050ddc90be6a9bb32b1a897bef6a638d4616dcc8d1"},"schema_version":"1.0","source":{"id":"1402.1641","kind":"arxiv","version":1}},"canonical_sha256":"59ee4462cc704c52ce8f632734b79805deb599cf8ad5ebc0f189858ea0acc44e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59ee4462cc704c52ce8f632734b79805deb599cf8ad5ebc0f189858ea0acc44e","first_computed_at":"2026-05-18T00:56:46.994193Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:46.994193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VFVtgiOj+yZuaX3th0nAIpTTm01x9uu6vuHlWWLQdMa3lYrZSqO5Bud/l6QxsTQ5+NjE2j5UZDCFcJ9vtDgBCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:46.994841Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.1641","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:793b427af513c734d22da2ad04acdb6e3ab60591f695d0d547224edd5b2c145c","sha256:a45b4fa74ea51a2943b45cfbe6c30f6dadc6900fd3de4387d9544f6daf039e45"],"state_sha256":"fd25daa1b88734e80692cf797c9f93a97c14f5b8287dffc496caa969ac437b7c"}