{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:CMOVEHS4Z5CXVMPINKBIEZSNDW","short_pith_number":"pith:CMOVEHS4","schema_version":"1.0","canonical_sha256":"131d521e5ccf457ab1e86a8282664d1da58dbf0fa1cb5372f77249a0d4ead1e8","source":{"kind":"arxiv","id":"0809.2194","version":1},"attestation_state":"computed","paper":{"title":"Arithmetical ranks of Stanley-Reisner ideals of simplicial complexes with a cone","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Margherita Barile, Naoki Terai","submitted_at":"2008-09-12T12:18:33Z","abstract_excerpt":"When a cone is added to a simplicial complex $\\Delta$ over one of its faces, we investigate the relation between the arithmetical ranks of the Stanley-Reisner ideals of the original simplicial complex and the new simplicial complex $\\Delta'$. In particular, we show that the arithmetical rank of the Stanley-Reisner ideal of $\\Delta'$ equals the projective dimension of the Stanley-Reisner ring of $\\Delta'$ if the corresponding equality holds for $\\Delta$."},"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":"0809.2194","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2008-09-12T12:18:33Z","cross_cats_sorted":[],"title_canon_sha256":"47aec029425fc7d4ec750845bfc68ecb8d25344b3c613bbc57de6afc7e989b87","abstract_canon_sha256":"1cbde8b433ef84dfe617de63b9f2b7ec638410408ebace4361f3110253a24e75"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:28.450575Z","signature_b64":"KhBpRvPQkBhm3SMg5ucjMpLPukVRvqSDKDo5GWtUGzKgqiT+P8AT8XnWit5trvWycufI1LxPSB30acGqxI+LBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"131d521e5ccf457ab1e86a8282664d1da58dbf0fa1cb5372f77249a0d4ead1e8","last_reissued_at":"2026-05-18T04:28:28.450081Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:28.450081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Arithmetical ranks of Stanley-Reisner ideals of simplicial complexes with a cone","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Margherita Barile, Naoki Terai","submitted_at":"2008-09-12T12:18:33Z","abstract_excerpt":"When a cone is added to a simplicial complex $\\Delta$ over one of its faces, we investigate the relation between the arithmetical ranks of the Stanley-Reisner ideals of the original simplicial complex and the new simplicial complex $\\Delta'$. In particular, we show that the arithmetical rank of the Stanley-Reisner ideal of $\\Delta'$ equals the projective dimension of the Stanley-Reisner ring of $\\Delta'$ if the corresponding equality holds for $\\Delta$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.2194","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":"0809.2194","created_at":"2026-05-18T04:28:28.450145+00:00"},{"alias_kind":"arxiv_version","alias_value":"0809.2194v1","created_at":"2026-05-18T04:28:28.450145+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.2194","created_at":"2026-05-18T04:28:28.450145+00:00"},{"alias_kind":"pith_short_12","alias_value":"CMOVEHS4Z5CX","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"CMOVEHS4Z5CXVMPI","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"CMOVEHS4","created_at":"2026-05-18T12:25:57.157939+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/CMOVEHS4Z5CXVMPINKBIEZSNDW","json":"https://pith.science/pith/CMOVEHS4Z5CXVMPINKBIEZSNDW.json","graph_json":"https://pith.science/api/pith-number/CMOVEHS4Z5CXVMPINKBIEZSNDW/graph.json","events_json":"https://pith.science/api/pith-number/CMOVEHS4Z5CXVMPINKBIEZSNDW/events.json","paper":"https://pith.science/paper/CMOVEHS4"},"agent_actions":{"view_html":"https://pith.science/pith/CMOVEHS4Z5CXVMPINKBIEZSNDW","download_json":"https://pith.science/pith/CMOVEHS4Z5CXVMPINKBIEZSNDW.json","view_paper":"https://pith.science/paper/CMOVEHS4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0809.2194&json=true","fetch_graph":"https://pith.science/api/pith-number/CMOVEHS4Z5CXVMPINKBIEZSNDW/graph.json","fetch_events":"https://pith.science/api/pith-number/CMOVEHS4Z5CXVMPINKBIEZSNDW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CMOVEHS4Z5CXVMPINKBIEZSNDW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CMOVEHS4Z5CXVMPINKBIEZSNDW/action/storage_attestation","attest_author":"https://pith.science/pith/CMOVEHS4Z5CXVMPINKBIEZSNDW/action/author_attestation","sign_citation":"https://pith.science/pith/CMOVEHS4Z5CXVMPINKBIEZSNDW/action/citation_signature","submit_replication":"https://pith.science/pith/CMOVEHS4Z5CXVMPINKBIEZSNDW/action/replication_record"}},"created_at":"2026-05-18T04:28:28.450145+00:00","updated_at":"2026-05-18T04:28:28.450145+00:00"}