{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:625SY2VN3ORB2WGRW7FC2ZM3EF","short_pith_number":"pith:625SY2VN","schema_version":"1.0","canonical_sha256":"f6bb2c6aaddba21d58d1b7ca2d659b21462127fdde04e561f8b3c0926e7c1bb7","source":{"kind":"arxiv","id":"math/0507238","version":2},"attestation_state":"computed","paper":{"title":"Monomial ideals via square-free monomial ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Sara Faridi","submitted_at":"2005-07-12T16:32:24Z","abstract_excerpt":"We study monomial ideals using the operation polarization to first turn them into square-free monomial ideals. We focus on monomial ideals whose polarization produce simplicial trees, and show that many of the properties of simplicial trees hold for such ideals.This includes Cohen-Macaulayness of the Rees ring, and being sequentially Cohen-Macaulay. The appendix is an independent study of primary decomposition in a sequentially Cohen-Macaulay module. We demonstrate how every submodule appearing in the filtration of a sequentially Cohen-Macaulay module can be described in terms of the primary d"},"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":"math/0507238","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2005-07-12T16:32:24Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"acd6542c8d8326dd5b7d6038c285660f50c28cbc3f483ed8b4d33c71eefcffd2","abstract_canon_sha256":"e41c609e19bc808c29653399cd6e7c160a47647874cdec7fe0bc1ff5ed1d6eec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:55.687444Z","signature_b64":"/KS6KWHK/3z9jnFZ8DZB/Jib1XOEAbl4wBW7gzGwOYdVCDumMGdECgakoAc9fAdFx/39rsJ6Nv6xCG5xI62pCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6bb2c6aaddba21d58d1b7ca2d659b21462127fdde04e561f8b3c0926e7c1bb7","last_reissued_at":"2026-05-18T00:48:55.686609Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:55.686609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Monomial ideals via square-free monomial ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Sara Faridi","submitted_at":"2005-07-12T16:32:24Z","abstract_excerpt":"We study monomial ideals using the operation polarization to first turn them into square-free monomial ideals. We focus on monomial ideals whose polarization produce simplicial trees, and show that many of the properties of simplicial trees hold for such ideals.This includes Cohen-Macaulayness of the Rees ring, and being sequentially Cohen-Macaulay. The appendix is an independent study of primary decomposition in a sequentially Cohen-Macaulay module. We demonstrate how every submodule appearing in the filtration of a sequentially Cohen-Macaulay module can be described in terms of the primary d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0507238","kind":"arxiv","version":2},"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":"math/0507238","created_at":"2026-05-18T00:48:55.686746+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0507238v2","created_at":"2026-05-18T00:48:55.686746+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0507238","created_at":"2026-05-18T00:48:55.686746+00:00"},{"alias_kind":"pith_short_12","alias_value":"625SY2VN3ORB","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"625SY2VN3ORB2WGR","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"625SY2VN","created_at":"2026-05-18T12:25:53.335082+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/625SY2VN3ORB2WGRW7FC2ZM3EF","json":"https://pith.science/pith/625SY2VN3ORB2WGRW7FC2ZM3EF.json","graph_json":"https://pith.science/api/pith-number/625SY2VN3ORB2WGRW7FC2ZM3EF/graph.json","events_json":"https://pith.science/api/pith-number/625SY2VN3ORB2WGRW7FC2ZM3EF/events.json","paper":"https://pith.science/paper/625SY2VN"},"agent_actions":{"view_html":"https://pith.science/pith/625SY2VN3ORB2WGRW7FC2ZM3EF","download_json":"https://pith.science/pith/625SY2VN3ORB2WGRW7FC2ZM3EF.json","view_paper":"https://pith.science/paper/625SY2VN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0507238&json=true","fetch_graph":"https://pith.science/api/pith-number/625SY2VN3ORB2WGRW7FC2ZM3EF/graph.json","fetch_events":"https://pith.science/api/pith-number/625SY2VN3ORB2WGRW7FC2ZM3EF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/625SY2VN3ORB2WGRW7FC2ZM3EF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/625SY2VN3ORB2WGRW7FC2ZM3EF/action/storage_attestation","attest_author":"https://pith.science/pith/625SY2VN3ORB2WGRW7FC2ZM3EF/action/author_attestation","sign_citation":"https://pith.science/pith/625SY2VN3ORB2WGRW7FC2ZM3EF/action/citation_signature","submit_replication":"https://pith.science/pith/625SY2VN3ORB2WGRW7FC2ZM3EF/action/replication_record"}},"created_at":"2026-05-18T00:48:55.686746+00:00","updated_at":"2026-05-18T00:48:55.686746+00:00"}