{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5KLUMZXBLIDRLGEFI7H7HKBKWG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"18d1fe7c47f9185a88a34977aacf3c9d4a39bda4a326772d77db3780e0222680","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-03-08T17:51:10Z","title_canon_sha256":"f1e5de2f50405a201b011010f688b9f660897f72ae29e3cb30a872a73d7caa50"},"schema_version":"1.0","source":{"id":"1803.03229","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03229","created_at":"2026-05-18T00:06:16Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03229v2","created_at":"2026-05-18T00:06:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03229","created_at":"2026-05-18T00:06:16Z"},{"alias_kind":"pith_short_12","alias_value":"5KLUMZXBLIDR","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5KLUMZXBLIDRLGEF","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5KLUMZXB","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:4683f18de152643c78d6eb3cc69a3eddc31701190d9ba45426bf7ddbae8ffc6c","target":"graph","created_at":"2026-05-18T00:06:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove a $p$-adic analog of Kunz's theorem: a $p$-adically complete noetherian ring is regular exactly when it admits a faithfully flat map to a perfectoid ring. This result is deduced from a more precise statement on detecting finiteness of projective dimension of finitely generated modules over noetherian rings via maps to perfectoid rings. We also establish a version of the $p$-adic Kunz's theorem where the flatness hypothesis is relaxed to almost flatness.","authors_text":"Bhargav Bhatt, Linquan Ma, Srikanth B. Iyengar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-03-08T17:51:10Z","title":"Regular rings and perfect(oid) algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03229","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d3433d7a969d3f5da6c5048eea80303d566d630946104266300ab27df6fd6105","target":"record","created_at":"2026-05-18T00:06:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"18d1fe7c47f9185a88a34977aacf3c9d4a39bda4a326772d77db3780e0222680","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-03-08T17:51:10Z","title_canon_sha256":"f1e5de2f50405a201b011010f688b9f660897f72ae29e3cb30a872a73d7caa50"},"schema_version":"1.0","source":{"id":"1803.03229","kind":"arxiv","version":2}},"canonical_sha256":"ea974666e15a0715988547cff3a82ab1b6c04885ae4e8955d0db5ccbce8025a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea974666e15a0715988547cff3a82ab1b6c04885ae4e8955d0db5ccbce8025a2","first_computed_at":"2026-05-18T00:06:16.156985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:16.156985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CTgNrkIWAeNeFaGJ5f+gZ+oLyKzTCIkONxzXF6lOszJkFi2Y4D/7LI4EnN3niYO2c7PJEJiJmh1p0D+8ixTDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:16.157605Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03229","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3433d7a969d3f5da6c5048eea80303d566d630946104266300ab27df6fd6105","sha256:4683f18de152643c78d6eb3cc69a3eddc31701190d9ba45426bf7ddbae8ffc6c"],"state_sha256":"e8a02afd7a95228beb35370acbc4ecdea9d72e7b92ed8ab8555d819d99c5e0c3"}