{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:SKVRTU55VKBS4WR5T5FRBZKME5","short_pith_number":"pith:SKVRTU55","schema_version":"1.0","canonical_sha256":"92ab19d3bdaa832e5a3d9f4b10e54c274b362eae2284da53596c3be6f55a77b1","source":{"kind":"arxiv","id":"1110.3182","version":1},"attestation_state":"computed","paper":{"title":"When will the Stanley depth increase","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Yi-Huang Shen","submitted_at":"2011-10-14T12:12:23Z","abstract_excerpt":"Let $I\\subset S=\\KK[x_1,...,x_n]$ be an ideal generated by squarefree monomials of degree $\\ge d$. If the number of degree $d$ minimal generating monomials $\\mu_d(I)\\le \\min(\\binom{n}{d+1},\\sum_{j=1}^{n-d}\\binom{2j-1}{j})$, then the Stanley depth $\\sdepth_S(I)\\ge d+1$."},"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":"1110.3182","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-10-14T12:12:23Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1effbf641f1f26c26e827daf93a5de1dc9ebf2c6a50f77e84688c6f5ddd3beee","abstract_canon_sha256":"6a01eedac6aa0d01788b394455274919bf46e94feee1eee077a29f6154f56f02"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:57.867097Z","signature_b64":"9PqENO+eJ4jq/z+rpnHd8mGoqm1mCOmg0OweuLGmrgc7ykMG0zUSmkjrK4/5VHGqlYQz2zh0LLyea7x+I8QNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92ab19d3bdaa832e5a3d9f4b10e54c274b362eae2284da53596c3be6f55a77b1","last_reissued_at":"2026-05-18T04:10:57.866547Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:57.866547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"When will the Stanley depth increase","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Yi-Huang Shen","submitted_at":"2011-10-14T12:12:23Z","abstract_excerpt":"Let $I\\subset S=\\KK[x_1,...,x_n]$ be an ideal generated by squarefree monomials of degree $\\ge d$. If the number of degree $d$ minimal generating monomials $\\mu_d(I)\\le \\min(\\binom{n}{d+1},\\sum_{j=1}^{n-d}\\binom{2j-1}{j})$, then the Stanley depth $\\sdepth_S(I)\\ge d+1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3182","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":"1110.3182","created_at":"2026-05-18T04:10:57.866639+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.3182v1","created_at":"2026-05-18T04:10:57.866639+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3182","created_at":"2026-05-18T04:10:57.866639+00:00"},{"alias_kind":"pith_short_12","alias_value":"SKVRTU55VKBS","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"SKVRTU55VKBS4WR5","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"SKVRTU55","created_at":"2026-05-18T12:26:41.206345+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/SKVRTU55VKBS4WR5T5FRBZKME5","json":"https://pith.science/pith/SKVRTU55VKBS4WR5T5FRBZKME5.json","graph_json":"https://pith.science/api/pith-number/SKVRTU55VKBS4WR5T5FRBZKME5/graph.json","events_json":"https://pith.science/api/pith-number/SKVRTU55VKBS4WR5T5FRBZKME5/events.json","paper":"https://pith.science/paper/SKVRTU55"},"agent_actions":{"view_html":"https://pith.science/pith/SKVRTU55VKBS4WR5T5FRBZKME5","download_json":"https://pith.science/pith/SKVRTU55VKBS4WR5T5FRBZKME5.json","view_paper":"https://pith.science/paper/SKVRTU55","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.3182&json=true","fetch_graph":"https://pith.science/api/pith-number/SKVRTU55VKBS4WR5T5FRBZKME5/graph.json","fetch_events":"https://pith.science/api/pith-number/SKVRTU55VKBS4WR5T5FRBZKME5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SKVRTU55VKBS4WR5T5FRBZKME5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SKVRTU55VKBS4WR5T5FRBZKME5/action/storage_attestation","attest_author":"https://pith.science/pith/SKVRTU55VKBS4WR5T5FRBZKME5/action/author_attestation","sign_citation":"https://pith.science/pith/SKVRTU55VKBS4WR5T5FRBZKME5/action/citation_signature","submit_replication":"https://pith.science/pith/SKVRTU55VKBS4WR5T5FRBZKME5/action/replication_record"}},"created_at":"2026-05-18T04:10:57.866639+00:00","updated_at":"2026-05-18T04:10:57.866639+00:00"}