{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:PL6VH2F7W2WAIPYFZYOEMZXGR4","short_pith_number":"pith:PL6VH2F7","schema_version":"1.0","canonical_sha256":"7afd53e8bfb6ac043f05ce1c4666e68f256187ab39cc550a568fca5dee91db7b","source":{"kind":"arxiv","id":"2211.08391","version":1},"attestation_state":"computed","paper":{"title":"Factorization in the Monoid of Integrally Closed Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Emmy Lewis","submitted_at":"2022-11-15T18:38:38Z","abstract_excerpt":"Given a Noetherian ring $A$, the collection of all integrally closed ideals in $A$ which contain a nonzerodivisor, denoted $ic(A)$, forms a cancellative monoid under the operation $I*J=\\overline{IJ}$, the integral closure of the product. The monoid is torsion-free and atomic -- every integrally closed ideal in $A$ containing a nonzerodivisor can be factored in this $*$-product into $*$-irreducible integrally closed ideals. Restricting to the case where $A$ is a polynomial ring and the ideals in question are monomial, we show that there is a surjective homomorphism from the Integral Polytope Gr"},"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":"2211.08391","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2022-11-15T18:38:38Z","cross_cats_sorted":[],"title_canon_sha256":"70df74c1751fc5eca5dbca34da89236e4f7879bf330815155cbe4b46dcb30831","abstract_canon_sha256":"5edd26d65328e2bf10d78369c299890a99bed651694e63f17bdaecc653e5fa30"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:16:28.784555Z","signature_b64":"EkpmE6s01do2EpZh3ikkBMHrwJT2rItCywIKzbFmljrRaFVxPvmXaFco4qOazmAMZ4NesjSmt60MG/qrYZfyDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7afd53e8bfb6ac043f05ce1c4666e68f256187ab39cc550a568fca5dee91db7b","last_reissued_at":"2026-07-05T05:16:28.784132Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:16:28.784132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Factorization in the Monoid of Integrally Closed Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Emmy Lewis","submitted_at":"2022-11-15T18:38:38Z","abstract_excerpt":"Given a Noetherian ring $A$, the collection of all integrally closed ideals in $A$ which contain a nonzerodivisor, denoted $ic(A)$, forms a cancellative monoid under the operation $I*J=\\overline{IJ}$, the integral closure of the product. The monoid is torsion-free and atomic -- every integrally closed ideal in $A$ containing a nonzerodivisor can be factored in this $*$-product into $*$-irreducible integrally closed ideals. Restricting to the case where $A$ is a polynomial ring and the ideals in question are monomial, we show that there is a surjective homomorphism from the Integral Polytope Gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.08391","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.08391/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2211.08391","created_at":"2026-07-05T05:16:28.784192+00:00"},{"alias_kind":"arxiv_version","alias_value":"2211.08391v1","created_at":"2026-07-05T05:16:28.784192+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.08391","created_at":"2026-07-05T05:16:28.784192+00:00"},{"alias_kind":"pith_short_12","alias_value":"PL6VH2F7W2WA","created_at":"2026-07-05T05:16:28.784192+00:00"},{"alias_kind":"pith_short_16","alias_value":"PL6VH2F7W2WAIPYF","created_at":"2026-07-05T05:16:28.784192+00:00"},{"alias_kind":"pith_short_8","alias_value":"PL6VH2F7","created_at":"2026-07-05T05:16:28.784192+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/PL6VH2F7W2WAIPYFZYOEMZXGR4","json":"https://pith.science/pith/PL6VH2F7W2WAIPYFZYOEMZXGR4.json","graph_json":"https://pith.science/api/pith-number/PL6VH2F7W2WAIPYFZYOEMZXGR4/graph.json","events_json":"https://pith.science/api/pith-number/PL6VH2F7W2WAIPYFZYOEMZXGR4/events.json","paper":"https://pith.science/paper/PL6VH2F7"},"agent_actions":{"view_html":"https://pith.science/pith/PL6VH2F7W2WAIPYFZYOEMZXGR4","download_json":"https://pith.science/pith/PL6VH2F7W2WAIPYFZYOEMZXGR4.json","view_paper":"https://pith.science/paper/PL6VH2F7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2211.08391&json=true","fetch_graph":"https://pith.science/api/pith-number/PL6VH2F7W2WAIPYFZYOEMZXGR4/graph.json","fetch_events":"https://pith.science/api/pith-number/PL6VH2F7W2WAIPYFZYOEMZXGR4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PL6VH2F7W2WAIPYFZYOEMZXGR4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PL6VH2F7W2WAIPYFZYOEMZXGR4/action/storage_attestation","attest_author":"https://pith.science/pith/PL6VH2F7W2WAIPYFZYOEMZXGR4/action/author_attestation","sign_citation":"https://pith.science/pith/PL6VH2F7W2WAIPYFZYOEMZXGR4/action/citation_signature","submit_replication":"https://pith.science/pith/PL6VH2F7W2WAIPYFZYOEMZXGR4/action/replication_record"}},"created_at":"2026-07-05T05:16:28.784192+00:00","updated_at":"2026-07-05T05:16:28.784192+00:00"}