{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XG6XP3DKECMH35XNZ6UGNZZYCU","short_pith_number":"pith:XG6XP3DK","schema_version":"1.0","canonical_sha256":"b9bd77ec6a20987df6edcfa866e7381534113090561d10a542cbb5fa0f716ba4","source":{"kind":"arxiv","id":"1503.03736","version":2},"attestation_state":"computed","paper":{"title":"On the Stanley depth and size of monomial ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"S. A. Seyed Fakhari","submitted_at":"2015-03-12T14:23:27Z","abstract_excerpt":"Let $\\mathbb{K}$ be a field and $S=\\mathbb{K}[x_1,...,x_n]$ be the polynomial ring in $n$ variables over the field $\\mathbb{K}$. For every monomial ideal $I\\subset S$, We provide a recursive formula to determine a lower bound for the Stanley depth of $S/I$. We use this formula to prove the inequality ${\\rm sdepth}(S/I)\\geq {\\rm size}(I)$ for a particular class of monomial ideals."},"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":"1503.03736","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-03-12T14:23:27Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"eb39aa4b6c57fea860aa07a9776e879734826128fff5c020d6a2d5881bbf60e7","abstract_canon_sha256":"6bfa7777aebf00e44e2ae22ec00eaf06e6c19d3b45e1d548d99a2f4e225e2e39"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:49.170058Z","signature_b64":"uZZ68w/5bXShI/JM2oGhWuFl9AyfdG0zIrNDXyGpzNsIW7L8eYFtqe8AfVFxVObQa8WC97K0lMZGO2GujSwqAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9bd77ec6a20987df6edcfa866e7381534113090561d10a542cbb5fa0f716ba4","last_reissued_at":"2026-05-18T02:20:49.169374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:49.169374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Stanley depth and size of monomial ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"S. A. Seyed Fakhari","submitted_at":"2015-03-12T14:23:27Z","abstract_excerpt":"Let $\\mathbb{K}$ be a field and $S=\\mathbb{K}[x_1,...,x_n]$ be the polynomial ring in $n$ variables over the field $\\mathbb{K}$. For every monomial ideal $I\\subset S$, We provide a recursive formula to determine a lower bound for the Stanley depth of $S/I$. We use this formula to prove the inequality ${\\rm sdepth}(S/I)\\geq {\\rm size}(I)$ for a particular class of monomial ideals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03736","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":"1503.03736","created_at":"2026-05-18T02:20:49.169468+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.03736v2","created_at":"2026-05-18T02:20:49.169468+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03736","created_at":"2026-05-18T02:20:49.169468+00:00"},{"alias_kind":"pith_short_12","alias_value":"XG6XP3DKECMH","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XG6XP3DKECMH35XN","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XG6XP3DK","created_at":"2026-05-18T12:29:50.041715+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/XG6XP3DKECMH35XNZ6UGNZZYCU","json":"https://pith.science/pith/XG6XP3DKECMH35XNZ6UGNZZYCU.json","graph_json":"https://pith.science/api/pith-number/XG6XP3DKECMH35XNZ6UGNZZYCU/graph.json","events_json":"https://pith.science/api/pith-number/XG6XP3DKECMH35XNZ6UGNZZYCU/events.json","paper":"https://pith.science/paper/XG6XP3DK"},"agent_actions":{"view_html":"https://pith.science/pith/XG6XP3DKECMH35XNZ6UGNZZYCU","download_json":"https://pith.science/pith/XG6XP3DKECMH35XNZ6UGNZZYCU.json","view_paper":"https://pith.science/paper/XG6XP3DK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.03736&json=true","fetch_graph":"https://pith.science/api/pith-number/XG6XP3DKECMH35XNZ6UGNZZYCU/graph.json","fetch_events":"https://pith.science/api/pith-number/XG6XP3DKECMH35XNZ6UGNZZYCU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XG6XP3DKECMH35XNZ6UGNZZYCU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XG6XP3DKECMH35XNZ6UGNZZYCU/action/storage_attestation","attest_author":"https://pith.science/pith/XG6XP3DKECMH35XNZ6UGNZZYCU/action/author_attestation","sign_citation":"https://pith.science/pith/XG6XP3DKECMH35XNZ6UGNZZYCU/action/citation_signature","submit_replication":"https://pith.science/pith/XG6XP3DKECMH35XNZ6UGNZZYCU/action/replication_record"}},"created_at":"2026-05-18T02:20:49.169468+00:00","updated_at":"2026-05-18T02:20:49.169468+00:00"}