{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:OCFFIQJ7TLCATUCP6YLVQTLQLC","short_pith_number":"pith:OCFFIQJ7","schema_version":"1.0","canonical_sha256":"708a54413f9ac409d04ff617584d7058b32836222cac8229cff41a4406542bcb","source":{"kind":"arxiv","id":"1502.04978","version":1},"attestation_state":"computed","paper":{"title":"On the associated prime ideals of local cohomology modules defined by a pair of ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kh. Ahmadi Amoli, M. Jahangiri, Z. Habibi","submitted_at":"2015-02-17T17:53:36Z","abstract_excerpt":"Let $I$ and $J$ be two ideals of a commutative Noetherian ring $R$ and $M$ be an $R$-module. For a non-negative integer $n$ it is shown that, if the sets $\\Ass_R(\\Ext^{n} _{R}(R/I,M))$ and $\\Supp_R(\\Ext^{i}_{R}(R/I,H^{j}_{I,J} (M)))$ are finite for all $i \\leq n+1$ and all $j< n$, then so is \\linebreak$\\Ass_R(\\Hom_{R}(R/I,H^{n}_{I,J}(M)))$. We also study the finiteness of $\\Ass_R(\\Ext^{i}_{R}(R/I,H^{n}_{I,J} (M)))$ for $i=1,2$."},"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":"1502.04978","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-02-17T17:53:36Z","cross_cats_sorted":[],"title_canon_sha256":"916d68ea15147e6ddf4a9ef5958743693ea3e91750de4d095bea6b9969197370","abstract_canon_sha256":"5a6dc0a3ffd69e7be57e0bedfaf303f5c17e1ff5814bd06029c955f5b757ce7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:53.378000Z","signature_b64":"UGbyyvjy9QNDhEPOIGQ6mm6ZuZ99y3M9LGvFFdn+gBaMQVIHRvbgxiIq/9zRAOKW1IGRM9x79tQv9GkoSJ+pAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"708a54413f9ac409d04ff617584d7058b32836222cac8229cff41a4406542bcb","last_reissued_at":"2026-05-18T02:26:53.377593Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:53.377593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the associated prime ideals of local cohomology modules defined by a pair of ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kh. Ahmadi Amoli, M. Jahangiri, Z. Habibi","submitted_at":"2015-02-17T17:53:36Z","abstract_excerpt":"Let $I$ and $J$ be two ideals of a commutative Noetherian ring $R$ and $M$ be an $R$-module. For a non-negative integer $n$ it is shown that, if the sets $\\Ass_R(\\Ext^{n} _{R}(R/I,M))$ and $\\Supp_R(\\Ext^{i}_{R}(R/I,H^{j}_{I,J} (M)))$ are finite for all $i \\leq n+1$ and all $j< n$, then so is \\linebreak$\\Ass_R(\\Hom_{R}(R/I,H^{n}_{I,J}(M)))$. We also study the finiteness of $\\Ass_R(\\Ext^{i}_{R}(R/I,H^{n}_{I,J} (M)))$ for $i=1,2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04978","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":"1502.04978","created_at":"2026-05-18T02:26:53.377654+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.04978v1","created_at":"2026-05-18T02:26:53.377654+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04978","created_at":"2026-05-18T02:26:53.377654+00:00"},{"alias_kind":"pith_short_12","alias_value":"OCFFIQJ7TLCA","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"OCFFIQJ7TLCATUCP","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"OCFFIQJ7","created_at":"2026-05-18T12:29:34.919912+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/OCFFIQJ7TLCATUCP6YLVQTLQLC","json":"https://pith.science/pith/OCFFIQJ7TLCATUCP6YLVQTLQLC.json","graph_json":"https://pith.science/api/pith-number/OCFFIQJ7TLCATUCP6YLVQTLQLC/graph.json","events_json":"https://pith.science/api/pith-number/OCFFIQJ7TLCATUCP6YLVQTLQLC/events.json","paper":"https://pith.science/paper/OCFFIQJ7"},"agent_actions":{"view_html":"https://pith.science/pith/OCFFIQJ7TLCATUCP6YLVQTLQLC","download_json":"https://pith.science/pith/OCFFIQJ7TLCATUCP6YLVQTLQLC.json","view_paper":"https://pith.science/paper/OCFFIQJ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.04978&json=true","fetch_graph":"https://pith.science/api/pith-number/OCFFIQJ7TLCATUCP6YLVQTLQLC/graph.json","fetch_events":"https://pith.science/api/pith-number/OCFFIQJ7TLCATUCP6YLVQTLQLC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OCFFIQJ7TLCATUCP6YLVQTLQLC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OCFFIQJ7TLCATUCP6YLVQTLQLC/action/storage_attestation","attest_author":"https://pith.science/pith/OCFFIQJ7TLCATUCP6YLVQTLQLC/action/author_attestation","sign_citation":"https://pith.science/pith/OCFFIQJ7TLCATUCP6YLVQTLQLC/action/citation_signature","submit_replication":"https://pith.science/pith/OCFFIQJ7TLCATUCP6YLVQTLQLC/action/replication_record"}},"created_at":"2026-05-18T02:26:53.377654+00:00","updated_at":"2026-05-18T02:26:53.377654+00:00"}