{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:AOJCBT5LF5UBR4GILL6ZUQNHXT","short_pith_number":"pith:AOJCBT5L","schema_version":"1.0","canonical_sha256":"039220cfab2f6818f0c85afd9a41a7bcdaaf563d1d49203da347623b0f87414e","source":{"kind":"arxiv","id":"1711.05534","version":2},"attestation_state":"computed","paper":{"title":"Stable Under Specialization Sets and Cofiniteness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Hossein Faridian, Kamran Divaani-Aazar, Massoud Tousi","submitted_at":"2017-11-15T12:39:59Z","abstract_excerpt":"Let $R$ be a commutative noetherian ring, and $\\mathcal{Z}$ a stable under specialization subset of $\\Spec(R)$. We introduce a notion of $\\mathcal{Z}$-cofiniteness and study its main properties. In the case $\\dim(\\mathcal{Z})\\leq 1$, or $\\dim(R)\\leq 2$, or $R$ is semilocal with $\\cd(\\mathcal{Z},R) \\leq 1$, we show that the category of $\\mathcal{Z}$-cofinite $R$-modules is abelian. Also, in each of these cases, we prove that the local cohomology module $H^{i}_{\\mathcal{Z}}(X)$ is $\\mathcal{Z}$-cofinite for every homologically left-bounded $R$-complex $X$ whose homology modules are finitely gene"},"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":"1711.05534","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-11-15T12:39:59Z","cross_cats_sorted":[],"title_canon_sha256":"455f71d7b062a700d5a3cdc584b68739eb1740baec435a229192b23739242bd5","abstract_canon_sha256":"cabcdd71f2eace1cd6485da95059b6b67b3878f1613d326a0e38869330b17b5b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:27.081141Z","signature_b64":"qDOj0HiIXmwl6I5GZ5H7HJUp1asAcS5woyDGHEDOCwpoY4tpiM+NX+L0qFb98WZtxyF8R+s4ZV4/WYEnmdFMCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"039220cfab2f6818f0c85afd9a41a7bcdaaf563d1d49203da347623b0f87414e","last_reissued_at":"2026-05-18T00:17:27.080554Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:27.080554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stable Under Specialization Sets and Cofiniteness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Hossein Faridian, Kamran Divaani-Aazar, Massoud Tousi","submitted_at":"2017-11-15T12:39:59Z","abstract_excerpt":"Let $R$ be a commutative noetherian ring, and $\\mathcal{Z}$ a stable under specialization subset of $\\Spec(R)$. We introduce a notion of $\\mathcal{Z}$-cofiniteness and study its main properties. In the case $\\dim(\\mathcal{Z})\\leq 1$, or $\\dim(R)\\leq 2$, or $R$ is semilocal with $\\cd(\\mathcal{Z},R) \\leq 1$, we show that the category of $\\mathcal{Z}$-cofinite $R$-modules is abelian. Also, in each of these cases, we prove that the local cohomology module $H^{i}_{\\mathcal{Z}}(X)$ is $\\mathcal{Z}$-cofinite for every homologically left-bounded $R$-complex $X$ whose homology modules are finitely gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05534","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":""},"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":"1711.05534","created_at":"2026-05-18T00:17:27.080660+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.05534v2","created_at":"2026-05-18T00:17:27.080660+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05534","created_at":"2026-05-18T00:17:27.080660+00:00"},{"alias_kind":"pith_short_12","alias_value":"AOJCBT5LF5UB","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"AOJCBT5LF5UBR4GI","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"AOJCBT5L","created_at":"2026-05-18T12:31:05.417338+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/AOJCBT5LF5UBR4GILL6ZUQNHXT","json":"https://pith.science/pith/AOJCBT5LF5UBR4GILL6ZUQNHXT.json","graph_json":"https://pith.science/api/pith-number/AOJCBT5LF5UBR4GILL6ZUQNHXT/graph.json","events_json":"https://pith.science/api/pith-number/AOJCBT5LF5UBR4GILL6ZUQNHXT/events.json","paper":"https://pith.science/paper/AOJCBT5L"},"agent_actions":{"view_html":"https://pith.science/pith/AOJCBT5LF5UBR4GILL6ZUQNHXT","download_json":"https://pith.science/pith/AOJCBT5LF5UBR4GILL6ZUQNHXT.json","view_paper":"https://pith.science/paper/AOJCBT5L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.05534&json=true","fetch_graph":"https://pith.science/api/pith-number/AOJCBT5LF5UBR4GILL6ZUQNHXT/graph.json","fetch_events":"https://pith.science/api/pith-number/AOJCBT5LF5UBR4GILL6ZUQNHXT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AOJCBT5LF5UBR4GILL6ZUQNHXT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AOJCBT5LF5UBR4GILL6ZUQNHXT/action/storage_attestation","attest_author":"https://pith.science/pith/AOJCBT5LF5UBR4GILL6ZUQNHXT/action/author_attestation","sign_citation":"https://pith.science/pith/AOJCBT5LF5UBR4GILL6ZUQNHXT/action/citation_signature","submit_replication":"https://pith.science/pith/AOJCBT5LF5UBR4GILL6ZUQNHXT/action/replication_record"}},"created_at":"2026-05-18T00:17:27.080660+00:00","updated_at":"2026-05-18T00:17:27.080660+00:00"}