{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:EQDCSUPWWZ52M4UZAB32SHQCUE","short_pith_number":"pith:EQDCSUPW","schema_version":"1.0","canonical_sha256":"24062951f6b67ba672990077a91e02a134b2b12db0a67b157f595c44cddfd96e","source":{"kind":"arxiv","id":"1706.01024","version":2},"attestation_state":"computed","paper":{"title":"Stability properties of powers of ideals over regular local rings of small dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Amir Mafi, J\\\"urgen Herzog","submitted_at":"2017-06-04T04:51:57Z","abstract_excerpt":"Let $(R,\\mathfrak{m})$ be a regular local ring or a polynomial ring over a field, and let $I$ be an ideal of $R$ which we assume to be graded if $R$ is a polynomial ring. Let astab$(I)$ resp. $\\overline{\\rm astab}(I)$ be the smallest integer $n$ for which Ass$(I^n)$ resp. Ass$(\\overline{I^n})$ stabilize, and dstab$(I)$ be the smallest integer $n$ for which depth$(I^n)$ stabilizes. Here $\\overline{I^n}$ denotes the integral closure of $I^n$. We show that astab$(I)=\\overline{\\rm astab}(I)={\\rm dstab}(I)$ if dim$\\,R\\leq 2$, while already in dimension $3$, astab$(I)$ and $\\overline{\\rm astab}(I)$ "},"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":"1706.01024","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-06-04T04:51:57Z","cross_cats_sorted":[],"title_canon_sha256":"14ffc84a4de73a247bc552e87653182ce6f49da7e75e6612e2c49749b7c3e458","abstract_canon_sha256":"c40e21fc9e2496f1e519203da38e71f1b1a4683f7e6c78de2cbfc59ea4dfe6d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:06.889393Z","signature_b64":"v1exi7bbblBcbKK41FYNEoLqYnUglzZVSuj8pTTFY1lNCfeArIu3/H9B5HkhDYthNKWSJCYsmt/AC/yQe2MkBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24062951f6b67ba672990077a91e02a134b2b12db0a67b157f595c44cddfd96e","last_reissued_at":"2026-05-18T00:20:06.888706Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:06.888706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability properties of powers of ideals over regular local rings of small dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Amir Mafi, J\\\"urgen Herzog","submitted_at":"2017-06-04T04:51:57Z","abstract_excerpt":"Let $(R,\\mathfrak{m})$ be a regular local ring or a polynomial ring over a field, and let $I$ be an ideal of $R$ which we assume to be graded if $R$ is a polynomial ring. Let astab$(I)$ resp. $\\overline{\\rm astab}(I)$ be the smallest integer $n$ for which Ass$(I^n)$ resp. Ass$(\\overline{I^n})$ stabilize, and dstab$(I)$ be the smallest integer $n$ for which depth$(I^n)$ stabilizes. Here $\\overline{I^n}$ denotes the integral closure of $I^n$. We show that astab$(I)=\\overline{\\rm astab}(I)={\\rm dstab}(I)$ if dim$\\,R\\leq 2$, while already in dimension $3$, astab$(I)$ and $\\overline{\\rm astab}(I)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01024","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":"1706.01024","created_at":"2026-05-18T00:20:06.888806+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.01024v2","created_at":"2026-05-18T00:20:06.888806+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.01024","created_at":"2026-05-18T00:20:06.888806+00:00"},{"alias_kind":"pith_short_12","alias_value":"EQDCSUPWWZ52","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"EQDCSUPWWZ52M4UZ","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"EQDCSUPW","created_at":"2026-05-18T12:31:12.930513+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/EQDCSUPWWZ52M4UZAB32SHQCUE","json":"https://pith.science/pith/EQDCSUPWWZ52M4UZAB32SHQCUE.json","graph_json":"https://pith.science/api/pith-number/EQDCSUPWWZ52M4UZAB32SHQCUE/graph.json","events_json":"https://pith.science/api/pith-number/EQDCSUPWWZ52M4UZAB32SHQCUE/events.json","paper":"https://pith.science/paper/EQDCSUPW"},"agent_actions":{"view_html":"https://pith.science/pith/EQDCSUPWWZ52M4UZAB32SHQCUE","download_json":"https://pith.science/pith/EQDCSUPWWZ52M4UZAB32SHQCUE.json","view_paper":"https://pith.science/paper/EQDCSUPW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.01024&json=true","fetch_graph":"https://pith.science/api/pith-number/EQDCSUPWWZ52M4UZAB32SHQCUE/graph.json","fetch_events":"https://pith.science/api/pith-number/EQDCSUPWWZ52M4UZAB32SHQCUE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EQDCSUPWWZ52M4UZAB32SHQCUE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EQDCSUPWWZ52M4UZAB32SHQCUE/action/storage_attestation","attest_author":"https://pith.science/pith/EQDCSUPWWZ52M4UZAB32SHQCUE/action/author_attestation","sign_citation":"https://pith.science/pith/EQDCSUPWWZ52M4UZAB32SHQCUE/action/citation_signature","submit_replication":"https://pith.science/pith/EQDCSUPWWZ52M4UZAB32SHQCUE/action/replication_record"}},"created_at":"2026-05-18T00:20:06.888806+00:00","updated_at":"2026-05-18T00:20:06.888806+00:00"}