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Nhan ({Comm. Algebra, 36 (2008), 1527-1536). For a subset $S\\subseteq \\Spec R$ we set $S_{{\\ge}k}={\\p\\in S\\mid\\dim(R/\\p){\\ge}k}$. We first prove in this paper that $\\Ass_R(H^j_I(N))_{\\ge k}$ is a finite set for all $j{\\le}r$}. Let $\\fN=\\oplus_{n\\ge 0}N_n$ be a finitely generated graded $\\fR$-module, where $\\fR$ is a finitely generated standard"},"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":"1211.1477","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-11-07T07:58:43Z","cross_cats_sorted":[],"title_canon_sha256":"ce70128bb3c995e1b94307ef97b7270901d756730dce3edc097e2e82bda5c29b","abstract_canon_sha256":"1528bf1cdb2fbc4465c6324922eec741141c47096497148bcb0be00b777bdf92"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:20.893228Z","signature_b64":"LZVRl/U8hslCPxuKG/eNUOjtU9HYOg9o0az3OVpo0Dms/errFRzuFXXKkXzWK9QSwFF9GZV9H9NcaguDyQwZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50b9f7546e1a789b4d4f0fe1284ee79ead69f5bf5ca53b31e6d9e69e32a09c85","last_reissued_at":"2026-05-18T03:41:20.892819Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:20.892819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the finiteness and stability of certain sets of associated primes ideals of local cohomology modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Nguyen Tu Cuong, Nguyen Van Hoang","submitted_at":"2012-11-07T07:58:43Z","abstract_excerpt":"Let $(R,\\frak{m})$ be a Noetherian local ring, $I$ an ideal of $R$ and $N$ a finitely generated $R$-module. Let $k{\\ge}-1$ be an integer and $ r=\\depth_k(I,N)$ the length of a maximal $N$-sequence in dimension $>k$ in $I$ defined by M. Brodmann and L. T. Nhan ({Comm. Algebra, 36 (2008), 1527-1536). For a subset $S\\subseteq \\Spec R$ we set $S_{{\\ge}k}={\\p\\in S\\mid\\dim(R/\\p){\\ge}k}$. We first prove in this paper that $\\Ass_R(H^j_I(N))_{\\ge k}$ is a finite set for all $j{\\le}r$}. Let $\\fN=\\oplus_{n\\ge 0}N_n$ be a finitely generated graded $\\fR$-module, where $\\fR$ is a finitely generated standard"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1477","kind":"arxiv","version":1},"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":"1211.1477","created_at":"2026-05-18T03:41:20.892882+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.1477v1","created_at":"2026-05-18T03:41:20.892882+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1477","created_at":"2026-05-18T03:41:20.892882+00:00"},{"alias_kind":"pith_short_12","alias_value":"KC47OVDODJ4J","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"KC47OVDODJ4JWTKP","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"KC47OVDO","created_at":"2026-05-18T12:27:11.947152+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/KC47OVDODJ4JWTKPB7QSQTXHT2","json":"https://pith.science/pith/KC47OVDODJ4JWTKPB7QSQTXHT2.json","graph_json":"https://pith.science/api/pith-number/KC47OVDODJ4JWTKPB7QSQTXHT2/graph.json","events_json":"https://pith.science/api/pith-number/KC47OVDODJ4JWTKPB7QSQTXHT2/events.json","paper":"https://pith.science/paper/KC47OVDO"},"agent_actions":{"view_html":"https://pith.science/pith/KC47OVDODJ4JWTKPB7QSQTXHT2","download_json":"https://pith.science/pith/KC47OVDODJ4JWTKPB7QSQTXHT2.json","view_paper":"https://pith.science/paper/KC47OVDO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.1477&json=true","fetch_graph":"https://pith.science/api/pith-number/KC47OVDODJ4JWTKPB7QSQTXHT2/graph.json","fetch_events":"https://pith.science/api/pith-number/KC47OVDODJ4JWTKPB7QSQTXHT2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KC47OVDODJ4JWTKPB7QSQTXHT2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KC47OVDODJ4JWTKPB7QSQTXHT2/action/storage_attestation","attest_author":"https://pith.science/pith/KC47OVDODJ4JWTKPB7QSQTXHT2/action/author_attestation","sign_citation":"https://pith.science/pith/KC47OVDODJ4JWTKPB7QSQTXHT2/action/citation_signature","submit_replication":"https://pith.science/pith/KC47OVDODJ4JWTKPB7QSQTXHT2/action/replication_record"}},"created_at":"2026-05-18T03:41:20.892882+00:00","updated_at":"2026-05-18T03:41:20.892882+00:00"}