{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:CXX3T4EOINV4J2U65SX353SAV4","short_pith_number":"pith:CXX3T4EO","schema_version":"1.0","canonical_sha256":"15efb9f08e436bc4ea9eecafbeee40af230bc98df43b0a63c6afd7120337e392","source":{"kind":"arxiv","id":"1302.5837","version":1},"attestation_state":"computed","paper":{"title":"Stanley depth of weakly polymatroidal ideals and squarefree monomial ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"S. A. Seyed Fakhari","submitted_at":"2013-02-23T18:57:19Z","abstract_excerpt":"Let $I$ be a weakly polymatroidal ideal or a squarefree monomial ideal of a polynomial ring $S$. In this paper we provide a lower bound for the Stanley depth of $I$ and $S/I$. In particular we prove that if $I$ is a squarefree monomial ideal which is generated in a single degree, then ${\\rm sdepth}(I)\\geq n-\\ell(I)+1$ and ${\\rm sdepth}(S/I)\\geq n-\\ell(I)$, where $\\ell(I)$ denotes the analytic spread of $I$. This proves a conjecture of the author in a special case."},"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":"1302.5837","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-02-23T18:57:19Z","cross_cats_sorted":[],"title_canon_sha256":"525fd838f9befbe949dbf61f2ca4e57dc116a97787948539151a381e605fd19e","abstract_canon_sha256":"6aafcf4e03f400bfa8c4a4fdc407752340c2ab019e9791c9d0bb486f2134ee2c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:43.539254Z","signature_b64":"u6+LRHjax6/QNySUYUthuAUn/SE9PyCKLmnnr3JuQt6KEaeU1TVBdMbrGD7ST3wAJ/l3jmkw3kEX5b1S9Y/BDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15efb9f08e436bc4ea9eecafbeee40af230bc98df43b0a63c6afd7120337e392","last_reissued_at":"2026-05-18T03:32:43.538418Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:43.538418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stanley depth of weakly polymatroidal ideals and squarefree monomial ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"S. A. Seyed Fakhari","submitted_at":"2013-02-23T18:57:19Z","abstract_excerpt":"Let $I$ be a weakly polymatroidal ideal or a squarefree monomial ideal of a polynomial ring $S$. In this paper we provide a lower bound for the Stanley depth of $I$ and $S/I$. In particular we prove that if $I$ is a squarefree monomial ideal which is generated in a single degree, then ${\\rm sdepth}(I)\\geq n-\\ell(I)+1$ and ${\\rm sdepth}(S/I)\\geq n-\\ell(I)$, where $\\ell(I)$ denotes the analytic spread of $I$. This proves a conjecture of the author in a special case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5837","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":""},"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":"1302.5837","created_at":"2026-05-18T03:32:43.538569+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.5837v1","created_at":"2026-05-18T03:32:43.538569+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5837","created_at":"2026-05-18T03:32:43.538569+00:00"},{"alias_kind":"pith_short_12","alias_value":"CXX3T4EOINV4","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"CXX3T4EOINV4J2U6","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"CXX3T4EO","created_at":"2026-05-18T12:27:40.988391+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/CXX3T4EOINV4J2U65SX353SAV4","json":"https://pith.science/pith/CXX3T4EOINV4J2U65SX353SAV4.json","graph_json":"https://pith.science/api/pith-number/CXX3T4EOINV4J2U65SX353SAV4/graph.json","events_json":"https://pith.science/api/pith-number/CXX3T4EOINV4J2U65SX353SAV4/events.json","paper":"https://pith.science/paper/CXX3T4EO"},"agent_actions":{"view_html":"https://pith.science/pith/CXX3T4EOINV4J2U65SX353SAV4","download_json":"https://pith.science/pith/CXX3T4EOINV4J2U65SX353SAV4.json","view_paper":"https://pith.science/paper/CXX3T4EO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.5837&json=true","fetch_graph":"https://pith.science/api/pith-number/CXX3T4EOINV4J2U65SX353SAV4/graph.json","fetch_events":"https://pith.science/api/pith-number/CXX3T4EOINV4J2U65SX353SAV4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CXX3T4EOINV4J2U65SX353SAV4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CXX3T4EOINV4J2U65SX353SAV4/action/storage_attestation","attest_author":"https://pith.science/pith/CXX3T4EOINV4J2U65SX353SAV4/action/author_attestation","sign_citation":"https://pith.science/pith/CXX3T4EOINV4J2U65SX353SAV4/action/citation_signature","submit_replication":"https://pith.science/pith/CXX3T4EOINV4J2U65SX353SAV4/action/replication_record"}},"created_at":"2026-05-18T03:32:43.538569+00:00","updated_at":"2026-05-18T03:32:43.538569+00:00"}