{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4AWYOTVOF7OZG24SLPZC76MUVT","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":"25e71a8ba5eda41199a0248220607186bde81b8707196e81490fe4b5ed2c42ba","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-20T22:12:40Z","title_canon_sha256":"abaccccfa49f38c1533b7fcd944eaaa41580dffa55010391699e3fbe4811c99d"},"schema_version":"1.0","source":{"id":"1507.05667","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05667","created_at":"2026-05-18T01:22:01Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05667v3","created_at":"2026-05-18T01:22:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05667","created_at":"2026-05-18T01:22:01Z"},{"alias_kind":"pith_short_12","alias_value":"4AWYOTVOF7OZ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4AWYOTVOF7OZG24S","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4AWYOTVO","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:8eebe20198e8125f1565c700894255068c8fd4baa56d4cc102b292cbc3a8cb14","target":"graph","created_at":"2026-05-18T01:22:01Z","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 $\\mathcal A\\subset\\mathbb P^{k-1}$ be a rank $k$ arrangement of $n$ hyperplanes, with the property that any $k$ of the defining linear forms are linearly independent (i.e., $\\mathcal A$ is called $k-$generic). We show that for any $j=0,\\ldots,k-2$, the subspace arrangement with defining ideal generated by the $(n-j)-$fold products of the defining linear forms of $\\mathcal A$ is a set-theoretic complete intersection, which is equivalent to saying that star configurations have this property.","authors_text":"Stefan Tohaneanu","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-20T22:12:40Z","title":"Star Configurations are Set-Theoretic Complete Intersections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05667","kind":"arxiv","version":3},"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":"sha256:52149b1cc727f83aa5cf65bbe63e842ba96c41fa706cefbefa34bacf25ee949e","target":"record","created_at":"2026-05-18T01:22:01Z","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":"25e71a8ba5eda41199a0248220607186bde81b8707196e81490fe4b5ed2c42ba","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-20T22:12:40Z","title_canon_sha256":"abaccccfa49f38c1533b7fcd944eaaa41580dffa55010391699e3fbe4811c99d"},"schema_version":"1.0","source":{"id":"1507.05667","kind":"arxiv","version":3}},"canonical_sha256":"e02d874eae2fdd936b925bf22ff994acc7b3261172f55e7248709e0173e7d203","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e02d874eae2fdd936b925bf22ff994acc7b3261172f55e7248709e0173e7d203","first_computed_at":"2026-05-18T01:22:01.230068Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:01.230068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iIv9OiNrx0Et+KkDUsrn4iVSesInTr+k1rtWeSKAIux+Na6mJhLeaIypfelBB8H1lRyYKFzvL/GIG0lPvQzOBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:01.230572Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05667","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52149b1cc727f83aa5cf65bbe63e842ba96c41fa706cefbefa34bacf25ee949e","sha256:8eebe20198e8125f1565c700894255068c8fd4baa56d4cc102b292cbc3a8cb14"],"state_sha256":"1a4351f4748d040bbb5c65af82169f187f67a46d611449c6d748b04ff48e5795"}