{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:F2WSFUWC4ILVESBBWBD64AAL6L","short_pith_number":"pith:F2WSFUWC","schema_version":"1.0","canonical_sha256":"2ead22d2c2e217524821b047ee000bf2f4aa3aa54d9de4fc7c3abf2022436c07","source":{"kind":"arxiv","id":"2504.02966","version":2},"attestation_state":"computed","paper":{"title":"On deformation of perfectoid purity in Gorenstein domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Austyn Simpson, Benjamin Baily, Jack Westbrook, Karina Dovgodko","submitted_at":"2025-04-03T18:35:24Z","abstract_excerpt":"If $(R,\\mathfrak{m})$ is a complete local ring of mixed characteristic $(0,p)$ and $R/pR$ is an $F$-pure Gorenstein domain, we find a sufficient condition for $R$ to be perfectoid pure. This condition is related to the Cohen-Macaulayness of the absolute integral closures of Gorenstein local domains of mixed characteristic which are not necessarily excellent. Along the way, we show that the problem of lifting $F$-purity of $R/pR$ to perfectoid purity of $R$ is equivalent to a similar deformation problem for the splinter property."},"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":"2504.02966","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-04-03T18:35:24Z","cross_cats_sorted":[],"title_canon_sha256":"4846c6cb541d81c131f2feefad84bf48da4b1997dba6abdc1d20fdac6773c277","abstract_canon_sha256":"7194028b7164a539e94215b39814cf236eb626463dec802b63a63aa63d50f1cd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:07:23.226152Z","signature_b64":"Od1rEJUfaktRdcZnhVms9vTK7OlXYNEsLlhLaXNNPy3ccPpdvV3KFVfjJ8QmEBSAdvrW4sPLX8MwB8OMPgt8Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ead22d2c2e217524821b047ee000bf2f4aa3aa54d9de4fc7c3abf2022436c07","last_reissued_at":"2026-07-05T11:07:23.225669Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:07:23.225669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On deformation of perfectoid purity in Gorenstein domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Austyn Simpson, Benjamin Baily, Jack Westbrook, Karina Dovgodko","submitted_at":"2025-04-03T18:35:24Z","abstract_excerpt":"If $(R,\\mathfrak{m})$ is a complete local ring of mixed characteristic $(0,p)$ and $R/pR$ is an $F$-pure Gorenstein domain, we find a sufficient condition for $R$ to be perfectoid pure. This condition is related to the Cohen-Macaulayness of the absolute integral closures of Gorenstein local domains of mixed characteristic which are not necessarily excellent. Along the way, we show that the problem of lifting $F$-purity of $R/pR$ to perfectoid purity of $R$ is equivalent to a similar deformation problem for the splinter property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.02966","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.02966/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2504.02966","created_at":"2026-07-05T11:07:23.225723+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.02966v2","created_at":"2026-07-05T11:07:23.225723+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.02966","created_at":"2026-07-05T11:07:23.225723+00:00"},{"alias_kind":"pith_short_12","alias_value":"F2WSFUWC4ILV","created_at":"2026-07-05T11:07:23.225723+00:00"},{"alias_kind":"pith_short_16","alias_value":"F2WSFUWC4ILVESBB","created_at":"2026-07-05T11:07:23.225723+00:00"},{"alias_kind":"pith_short_8","alias_value":"F2WSFUWC","created_at":"2026-07-05T11:07:23.225723+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/F2WSFUWC4ILVESBBWBD64AAL6L","json":"https://pith.science/pith/F2WSFUWC4ILVESBBWBD64AAL6L.json","graph_json":"https://pith.science/api/pith-number/F2WSFUWC4ILVESBBWBD64AAL6L/graph.json","events_json":"https://pith.science/api/pith-number/F2WSFUWC4ILVESBBWBD64AAL6L/events.json","paper":"https://pith.science/paper/F2WSFUWC"},"agent_actions":{"view_html":"https://pith.science/pith/F2WSFUWC4ILVESBBWBD64AAL6L","download_json":"https://pith.science/pith/F2WSFUWC4ILVESBBWBD64AAL6L.json","view_paper":"https://pith.science/paper/F2WSFUWC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.02966&json=true","fetch_graph":"https://pith.science/api/pith-number/F2WSFUWC4ILVESBBWBD64AAL6L/graph.json","fetch_events":"https://pith.science/api/pith-number/F2WSFUWC4ILVESBBWBD64AAL6L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F2WSFUWC4ILVESBBWBD64AAL6L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F2WSFUWC4ILVESBBWBD64AAL6L/action/storage_attestation","attest_author":"https://pith.science/pith/F2WSFUWC4ILVESBBWBD64AAL6L/action/author_attestation","sign_citation":"https://pith.science/pith/F2WSFUWC4ILVESBBWBD64AAL6L/action/citation_signature","submit_replication":"https://pith.science/pith/F2WSFUWC4ILVESBBWBD64AAL6L/action/replication_record"}},"created_at":"2026-07-05T11:07:23.225723+00:00","updated_at":"2026-07-05T11:07:23.225723+00:00"}