{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:S56S5P2S64TVTGSNRIQ6GEQC64","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":"c2c33f56dd5482f1f06d1547a1deb0b2245644b9d43a047f72f358b3a4969348","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-11T18:38:04Z","title_canon_sha256":"5c466a43176e52974cf9f4ebeebcd1fa77b5487f6d929633775f38e88f9a82de"},"schema_version":"1.0","source":{"id":"1112.2383","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2383","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2383v2","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2383","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"S56S5P2S64TV","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"S56S5P2S64TVTGSN","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"S56S5P2S","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:a87a8766dcce1954b98c506c0a7c91ab6eba078d26e617c4613bff8b320d1317","target":"graph","created_at":"2026-05-18T03:52:12Z","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":"A singularity in characteristic zero is said to be of dense F-pure type if its modulo p reduction is locally F-split for infinitely many p. We prove that if $x \\in X$ is an isolated log canonical singularity with $\\mu(x \\in X) \\le 2$ (see Definition 1.4 for the definition of the invariant $\\mu$), then it is of dense F-pure type. As a corollary, we prove the equivalence of log canonicity and being of dense F-pure type in the case of three-dimensional isolated singularities.","authors_text":"Osamu Fujino, Shunsuke Takagi","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-11T18:38:04Z","title":"On the F-purity of isolated log canonical singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2383","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":"sha256:6c734bd0324e88a0333d4ef0963643b8463d6cacf6c4b3a7573002f7256fdbf7","target":"record","created_at":"2026-05-18T03:52:12Z","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":"c2c33f56dd5482f1f06d1547a1deb0b2245644b9d43a047f72f358b3a4969348","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-11T18:38:04Z","title_canon_sha256":"5c466a43176e52974cf9f4ebeebcd1fa77b5487f6d929633775f38e88f9a82de"},"schema_version":"1.0","source":{"id":"1112.2383","kind":"arxiv","version":2}},"canonical_sha256":"977d2ebf52f727599a4d8a21e31202f72a3fe7764d8871f1da544ba634a4282d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"977d2ebf52f727599a4d8a21e31202f72a3fe7764d8871f1da544ba634a4282d","first_computed_at":"2026-05-18T03:52:12.041744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:12.041744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dd7QRd+3NAY+AgpNEpl7FmD1RQ/cspeeeUmdLtsc0y+UGDSvwwOXXTI5R0N8qkuvSP05o4n5iufgdtqNroIQCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:12.042531Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2383","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c734bd0324e88a0333d4ef0963643b8463d6cacf6c4b3a7573002f7256fdbf7","sha256:a87a8766dcce1954b98c506c0a7c91ab6eba078d26e617c4613bff8b320d1317"],"state_sha256":"9b13acf1f04ade87d90d6d40078d80d9f39ea1093915cfb471788cf79590f465"}