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If $\\dim(\\Delta)=1$, we also prove that $S/I_\\Delta^{(2)}$ ($S/I_\\Delta^2$) is clean if and only if $S/I_\\Delta^{(2)}$ ($S/I_\\Delta^2$) is Cohen-Macaulay."},"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":"1505.00634","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-04T13:44:18Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"d25cfa28ec6532be5ff95993454b297b94d5e90503c5b46ddd03e22ffdb3e944","abstract_canon_sha256":"164162d4e001d48d5311e50aa1dd9b3f36a26d0955eca264553a3d746577ba07"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:02.287217Z","signature_b64":"c/8DtngJKAnFmEclfTV1jnragS47fgaW2kWect7ZPqxp7vNCSMBEKmn+zK7lMCYqq3BgirFBR9JHt2FuSB2HDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3207d548b840efe4cab4e41b60e3e94d4e63322463acac882b89ade55c32e3d8","last_reissued_at":"2026-05-18T02:17:02.286472Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:02.286472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The cleanness of (symbolic) powers of Stanley-Reisner ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Ali Soleyman Jahan, Somayeh Bandari","submitted_at":"2015-05-04T13:44:18Z","abstract_excerpt":"Let $\\Delta$ be a pure simplicial complex and $I_\\Delta$ its Stanley-Reisner ideal in a polynomial ring $S$. 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