{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NX2IFMBVYBPJFED3SRVXRE42MP","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":"c3b9092efe309511055d8e75bab2c73bd8e96a1d9f9d1421868f3c10debbe3a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-04T13:32:24Z","title_canon_sha256":"d00b7c2751c5b151c8c6a41b3717268b9772914dca80db068b5d1eee1beec3e4"},"schema_version":"1.0","source":{"id":"1310.1261","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1261","created_at":"2026-05-18T02:54:14Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1261v3","created_at":"2026-05-18T02:54:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1261","created_at":"2026-05-18T02:54:14Z"},{"alias_kind":"pith_short_12","alias_value":"NX2IFMBVYBPJ","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NX2IFMBVYBPJFED3","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NX2IFMBV","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:ea0024aab086085620b6c13ac08933d1c7c845b48f268daced45def1a8f8e81d","target":"graph","created_at":"2026-05-18T02:54:14Z","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 generalize an algorithm by Goward for principalization of monomial ideals in nonsingular varieties to work on any scheme of finite type over a field. The normal crossings condition considered by Goward is weakened to the condition that components of the generating divisors meet as complete intersections. This leads to a substantial generalization of the notion of monomial scheme; we call the resulting schemes `c.i. monomial'. We prove that c.i. monomial schemes in arbitrarily singular varieties can be principalized by a sequence of blow-ups at codimension 2 c.i. monomial centers.","authors_text":"Corey Harris","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-04T13:32:24Z","title":"Monomial principalization in the singular setting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1261","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:c14e4518ae63aac13b1d418e2906dfa76ba2b1c661a9d64814ea3d1a1342ddc9","target":"record","created_at":"2026-05-18T02:54:14Z","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":"c3b9092efe309511055d8e75bab2c73bd8e96a1d9f9d1421868f3c10debbe3a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-04T13:32:24Z","title_canon_sha256":"d00b7c2751c5b151c8c6a41b3717268b9772914dca80db068b5d1eee1beec3e4"},"schema_version":"1.0","source":{"id":"1310.1261","kind":"arxiv","version":3}},"canonical_sha256":"6df482b035c05e92907b946b78939a63f36022c7bf48e8e03fe17a72f80c02d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6df482b035c05e92907b946b78939a63f36022c7bf48e8e03fe17a72f80c02d8","first_computed_at":"2026-05-18T02:54:14.099323Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:14.099323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mGQS1iBJjXczFX478eDRoo7Zoln6nZlS093BNSrN3ji6Q/emb7wV+qEuXma9rvd8Xd9sM8qIQH4tsgrV4pyACQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:14.099787Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1261","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c14e4518ae63aac13b1d418e2906dfa76ba2b1c661a9d64814ea3d1a1342ddc9","sha256:ea0024aab086085620b6c13ac08933d1c7c845b48f268daced45def1a8f8e81d"],"state_sha256":"5a2311eae802d57c1e4ad877d585a4e9d8ceb05e24acdc8ce3ebf7abbb26b1e4"}