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In this article we show that the iterated socles are integral over $I$, with reduction number one, provided $s \\leq \\text{o}(I_1(\\varphi_d))-1$, where $\\text{o}(I_1(\\varphi_d))$ is the order o"},"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":"1409.5481","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-09-18T22:31:31Z","cross_cats_sorted":[],"title_canon_sha256":"35e11f8864aff2926357833b005bc8d561272916d288af83fa6286bed7d49e6b","abstract_canon_sha256":"2adff6659455f13cfa0515ebe28727870984c647f92df9560cc438460dcf65aa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:27.400171Z","signature_b64":"F9lRNLAYeqqliDgmw9F6mqz2EiGCzRQklORZ8RlKLFXErUyDjzaq/8G9Dv1HGa/gc0YV2bfrlC507nWAfP35Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bb674eef22799aa798f9acfe2662d3ed49bd3ddc4f0053e762520163a0479fe","last_reissued_at":"2026-05-18T02:42:27.399338Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:27.399338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Iterated socles and integral dependence in regular rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Alberto Corso, Bernd Ulrich, Claudia Polini, Craig Huneke, Shiro Goto","submitted_at":"2014-09-18T22:31:31Z","abstract_excerpt":"Let $R$ be a formal power series ring over a field, with maximal ideal $\\mathfrak m$, and let $I$ be an ideal of $R$ such that $R/I$ is Artinian. 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