{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:6A3C3GOUP7JBJHPS46446VXVEJ","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":"93d03b28159dcb2b59fa630f442da0bce9835512e30f1355055ee118a6cee1fd","cross_cats_sorted":["math.KT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-01-02T23:02:32Z","title_canon_sha256":"b4ddde394283febddb4fc97fa78c9b02a0d38c839e0ee6551c969c2a6af4d612"},"schema_version":"1.0","source":{"id":"2501.01567","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.01567","created_at":"2026-07-05T10:12:24Z"},{"alias_kind":"arxiv_version","alias_value":"2501.01567v2","created_at":"2026-07-05T10:12:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.01567","created_at":"2026-07-05T10:12:24Z"},{"alias_kind":"pith_short_12","alias_value":"6A3C3GOUP7JB","created_at":"2026-07-05T10:12:24Z"},{"alias_kind":"pith_short_16","alias_value":"6A3C3GOUP7JBJHPS","created_at":"2026-07-05T10:12:24Z"},{"alias_kind":"pith_short_8","alias_value":"6A3C3GOU","created_at":"2026-07-05T10:12:24Z"}],"graph_snapshots":[{"event_id":"sha256:13a6cede688677422567d8ca5d44533aca62e28b7443698a69c9456949f8612d","target":"graph","created_at":"2026-07-05T10:12:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.01567/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We take a fresh look at the relationship between $K$-regularity and regularity of schemes, proving two results in this direction. First, we show that $K_2$-regular affine algebras over fields of characteristic zero are normal. Second, we improve on Vorst's $K$-regularity bound in the case of local complete intersections; this is related to recent work on higher du Bois singularities.","authors_text":"Charles A. Weibel, Christian Haesemeyer","cross_cats":["math.KT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-01-02T23:02:32Z","title":"$K_2$-regularity and normality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.01567","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:f454437654bdf73a7e20a18045e6a74481d425d814a6ebaecb9189537e129620","target":"record","created_at":"2026-07-05T10:12:24Z","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":"93d03b28159dcb2b59fa630f442da0bce9835512e30f1355055ee118a6cee1fd","cross_cats_sorted":["math.KT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-01-02T23:02:32Z","title_canon_sha256":"b4ddde394283febddb4fc97fa78c9b02a0d38c839e0ee6551c969c2a6af4d612"},"schema_version":"1.0","source":{"id":"2501.01567","kind":"arxiv","version":2}},"canonical_sha256":"f0362d99d47fd2149df2e7b9cf56f522793a56548349effe092f3a6b484daca3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0362d99d47fd2149df2e7b9cf56f522793a56548349effe092f3a6b484daca3","first_computed_at":"2026-07-05T10:12:24.773598Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:12:24.773598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s2qLmSU66652rcRRYW9ATxbRD2lpiFDozX6ViifKEfNSBBF0fEdRrmzBAJBG0Dh49nWfVajfCbbwJehKGEnjAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:12:24.774066Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.01567","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f454437654bdf73a7e20a18045e6a74481d425d814a6ebaecb9189537e129620","sha256:13a6cede688677422567d8ca5d44533aca62e28b7443698a69c9456949f8612d"],"state_sha256":"f579d78964592c6efba031d65613057c92055ab9b55395e700388e4f40dee83c"}