{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:B6WZ3XSSKAKZFQS7JY33NYPFIV","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":"923c6efe4636b014624331535baa644aa8cb63d8c967782e2d792538dcbb1aa0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-02-16T14:17:28Z","title_canon_sha256":"d5603a29e04af304b2deb2d5dd5f7f1b32f37aaa2a6c10c19d025904733d5368"},"schema_version":"1.0","source":{"id":"1202.3597","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3597","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3597v1","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3597","created_at":"2026-05-18T04:02:12Z"},{"alias_kind":"pith_short_12","alias_value":"B6WZ3XSSKAKZ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B6WZ3XSSKAKZFQS7","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B6WZ3XSS","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:3b14a83a15b506d153dddcac189106911f0f91decd463c71d50d81a329ee4d10","target":"graph","created_at":"2026-05-18T04:02:12Z","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":"Let $R$ be a commutative $F$-algebra, where $F$ is a field of characteristic 0, satisfying the following conditions: $R$ is equidimensional of dimension $n$, every residual field with respect to a maximal ideal is an algebraic extension of $F,$ and $\\Der_F (R)$ is a finitely generated projective $R$-module of rank $n$ such that $R_m\\otimes_R \\Der_F (R)=\\Der_F(R_m)$. We show that the associated graded ring of the ring of differentiable operators, $D(R,F)$, is a commutative Noetherian regular with unity and pure graded dimension equal to $2\\dim(R)$. Moreover, we prove that $D(R,F)$ has weak glob","authors_text":"Luis Nunez-Betancourt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-02-16T14:17:28Z","title":"On certain rings of differentiable type and finiteness properties of local cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3597","kind":"arxiv","version":1},"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:b10de05057f6c7b83ff0ec05d086e14f1482b975fc42248995ed925709c4818a","target":"record","created_at":"2026-05-18T04:02:12Z","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":"923c6efe4636b014624331535baa644aa8cb63d8c967782e2d792538dcbb1aa0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-02-16T14:17:28Z","title_canon_sha256":"d5603a29e04af304b2deb2d5dd5f7f1b32f37aaa2a6c10c19d025904733d5368"},"schema_version":"1.0","source":{"id":"1202.3597","kind":"arxiv","version":1}},"canonical_sha256":"0fad9dde52501592c25f4e37b6e1e54560f449edae374033cbf68d4ffa1ceff3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fad9dde52501592c25f4e37b6e1e54560f449edae374033cbf68d4ffa1ceff3","first_computed_at":"2026-05-18T04:02:12.797205Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:12.797205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mpw8605JgwxogzlWc4vSrbSvWrBQhGwEIIZMvbgG1We2/99xyEvx3g4hGF4INC8DkBQBb6EpVQ9dG7yDN9UaBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:12.797650Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3597","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b10de05057f6c7b83ff0ec05d086e14f1482b975fc42248995ed925709c4818a","sha256:3b14a83a15b506d153dddcac189106911f0f91decd463c71d50d81a329ee4d10"],"state_sha256":"e0b0fd70ec25067dabae1704e9ee2dec6b86d7589ce92a00d25f4b3860133856"}