{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:C5MBLKLVOXJ5SLTHY4KTME3PO2","short_pith_number":"pith:C5MBLKLV","schema_version":"1.0","canonical_sha256":"175815a97575d3d92e67c71536136f76ae281a173a09bcab8ef78849e9e5fbe4","source":{"kind":"arxiv","id":"1408.4255","version":2},"attestation_state":"computed","paper":{"title":"Lcm-lattices and Stanley depth: a first computational approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Bogdan Ichim, Julio Jos\\'e Moyano-Fern\\'andez, Lukas Katth\\\"an","submitted_at":"2014-08-19T08:54:46Z","abstract_excerpt":"Let $\\mathbb{K}$ be a field, and let $S=\\mathbb{K}[X_1, ..., X_n]$ be the polynomial ring. Let $I$ be a monomial ideal of $S$ with up to 5 generators. In this paper, we present a computational experiment which allows us to prove that $\\mathrm{depth}_S S/I = \\mathrm{sdepth}_S S/I < \\mathrm{sdepth}_S I$. This shows that the Stanley conjecture is true for $S/I$ and $I$, if $I$ can be generated by at most 5 monomials. The result also brings additional computational evidence for a conjecture made by Herzog."},"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":"1408.4255","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-08-19T08:54:46Z","cross_cats_sorted":[],"title_canon_sha256":"c904743d432db470c01e2127616c235ecd9075a1aa0127888c5e72d642614173","abstract_canon_sha256":"e14e4a8fe226b2ad07b35a026307852c852a383febd56ac014a53ee63f86796e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:21.192658Z","signature_b64":"zRgEx6TUzko218/7BKmetSt946NFVAI/22dzQ4a6n0dGMBs9/lw6Zuo2TG3XxyNLvFWD8YhGX7BGHigWa7RfDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"175815a97575d3d92e67c71536136f76ae281a173a09bcab8ef78849e9e5fbe4","last_reissued_at":"2026-05-18T01:20:21.191920Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:21.191920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lcm-lattices and Stanley depth: a first computational approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Bogdan Ichim, Julio Jos\\'e Moyano-Fern\\'andez, Lukas Katth\\\"an","submitted_at":"2014-08-19T08:54:46Z","abstract_excerpt":"Let $\\mathbb{K}$ be a field, and let $S=\\mathbb{K}[X_1, ..., X_n]$ be the polynomial ring. Let $I$ be a monomial ideal of $S$ with up to 5 generators. In this paper, we present a computational experiment which allows us to prove that $\\mathrm{depth}_S S/I = \\mathrm{sdepth}_S S/I < \\mathrm{sdepth}_S I$. This shows that the Stanley conjecture is true for $S/I$ and $I$, if $I$ can be generated by at most 5 monomials. The result also brings additional computational evidence for a conjecture made by Herzog."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4255","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":"1408.4255","created_at":"2026-05-18T01:20:21.192041+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.4255v2","created_at":"2026-05-18T01:20:21.192041+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4255","created_at":"2026-05-18T01:20:21.192041+00:00"},{"alias_kind":"pith_short_12","alias_value":"C5MBLKLVOXJ5","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"C5MBLKLVOXJ5SLTH","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"C5MBLKLV","created_at":"2026-05-18T12:28:22.404517+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/C5MBLKLVOXJ5SLTHY4KTME3PO2","json":"https://pith.science/pith/C5MBLKLVOXJ5SLTHY4KTME3PO2.json","graph_json":"https://pith.science/api/pith-number/C5MBLKLVOXJ5SLTHY4KTME3PO2/graph.json","events_json":"https://pith.science/api/pith-number/C5MBLKLVOXJ5SLTHY4KTME3PO2/events.json","paper":"https://pith.science/paper/C5MBLKLV"},"agent_actions":{"view_html":"https://pith.science/pith/C5MBLKLVOXJ5SLTHY4KTME3PO2","download_json":"https://pith.science/pith/C5MBLKLVOXJ5SLTHY4KTME3PO2.json","view_paper":"https://pith.science/paper/C5MBLKLV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.4255&json=true","fetch_graph":"https://pith.science/api/pith-number/C5MBLKLVOXJ5SLTHY4KTME3PO2/graph.json","fetch_events":"https://pith.science/api/pith-number/C5MBLKLVOXJ5SLTHY4KTME3PO2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C5MBLKLVOXJ5SLTHY4KTME3PO2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C5MBLKLVOXJ5SLTHY4KTME3PO2/action/storage_attestation","attest_author":"https://pith.science/pith/C5MBLKLVOXJ5SLTHY4KTME3PO2/action/author_attestation","sign_citation":"https://pith.science/pith/C5MBLKLVOXJ5SLTHY4KTME3PO2/action/citation_signature","submit_replication":"https://pith.science/pith/C5MBLKLVOXJ5SLTHY4KTME3PO2/action/replication_record"}},"created_at":"2026-05-18T01:20:21.192041+00:00","updated_at":"2026-05-18T01:20:21.192041+00:00"}