{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:KLXC4UWMQASJIF6KC2LNDJH362","short_pith_number":"pith:KLXC4UWM","schema_version":"1.0","canonical_sha256":"52ee2e52cc80249417ca1696d1a4fbf6b01d598188e948f16f0ba332295dea2d","source":{"kind":"arxiv","id":"1009.0828","version":1},"attestation_state":"computed","paper":{"title":"Equality of ordinary and symbolic powers of Stanley-Reisner ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ngo Viet Trung, Tran Manh Tuan","submitted_at":"2010-09-04T11:40:59Z","abstract_excerpt":"This paper studies properties of simplicial complexes for which the m-th symbolic power of the Stanley-Reisner ideal equals to the m-th ordinary power for a given m > 1. The main results are combinatorial characterizations of such complexes in the two-dimensional case. It turns out that there exist only a finite number of complexes with this property and that these complexes can be described completely. As a consequence we are able to determine all complexes for which the m-th ordinary power of the Stanley-Reisner ideal is Cohen-Macaulay for a given m > 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":"1009.0828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-09-04T11:40:59Z","cross_cats_sorted":[],"title_canon_sha256":"b53c8a36f62097eba36812d94980bb548c325f9655e6c8a0bc5e361ac83f6251","abstract_canon_sha256":"31b0bd4939a7827c9c1bd856c9b91dcb1f09a5a6d5efbe4a8c2b9970b1beb7e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:45.728426Z","signature_b64":"wVTpI1GD6SnADaBxi4TU/VaN0hojCO24NuCv9trAu704W6k/EGrbtzI0jIYfoCaVj4DpIcHnJt1wHlaIxMnPDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52ee2e52cc80249417ca1696d1a4fbf6b01d598188e948f16f0ba332295dea2d","last_reissued_at":"2026-05-18T03:15:45.727487Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:45.727487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equality of ordinary and symbolic powers of Stanley-Reisner ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ngo Viet Trung, Tran Manh Tuan","submitted_at":"2010-09-04T11:40:59Z","abstract_excerpt":"This paper studies properties of simplicial complexes for which the m-th symbolic power of the Stanley-Reisner ideal equals to the m-th ordinary power for a given m > 1. The main results are combinatorial characterizations of such complexes in the two-dimensional case. It turns out that there exist only a finite number of complexes with this property and that these complexes can be described completely. As a consequence we are able to determine all complexes for which the m-th ordinary power of the Stanley-Reisner ideal is Cohen-Macaulay for a given m > 1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0828","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":"1009.0828","created_at":"2026-05-18T03:15:45.727646+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.0828v1","created_at":"2026-05-18T03:15:45.727646+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0828","created_at":"2026-05-18T03:15:45.727646+00:00"},{"alias_kind":"pith_short_12","alias_value":"KLXC4UWMQASJ","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"KLXC4UWMQASJIF6K","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"KLXC4UWM","created_at":"2026-05-18T12:26:09.077623+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/KLXC4UWMQASJIF6KC2LNDJH362","json":"https://pith.science/pith/KLXC4UWMQASJIF6KC2LNDJH362.json","graph_json":"https://pith.science/api/pith-number/KLXC4UWMQASJIF6KC2LNDJH362/graph.json","events_json":"https://pith.science/api/pith-number/KLXC4UWMQASJIF6KC2LNDJH362/events.json","paper":"https://pith.science/paper/KLXC4UWM"},"agent_actions":{"view_html":"https://pith.science/pith/KLXC4UWMQASJIF6KC2LNDJH362","download_json":"https://pith.science/pith/KLXC4UWMQASJIF6KC2LNDJH362.json","view_paper":"https://pith.science/paper/KLXC4UWM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.0828&json=true","fetch_graph":"https://pith.science/api/pith-number/KLXC4UWMQASJIF6KC2LNDJH362/graph.json","fetch_events":"https://pith.science/api/pith-number/KLXC4UWMQASJIF6KC2LNDJH362/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KLXC4UWMQASJIF6KC2LNDJH362/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KLXC4UWMQASJIF6KC2LNDJH362/action/storage_attestation","attest_author":"https://pith.science/pith/KLXC4UWMQASJIF6KC2LNDJH362/action/author_attestation","sign_citation":"https://pith.science/pith/KLXC4UWMQASJIF6KC2LNDJH362/action/citation_signature","submit_replication":"https://pith.science/pith/KLXC4UWMQASJIF6KC2LNDJH362/action/replication_record"}},"created_at":"2026-05-18T03:15:45.727646+00:00","updated_at":"2026-05-18T03:15:45.727646+00:00"}