{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:Y3AEWIHSANA2KARM67ECQFKMYL","short_pith_number":"pith:Y3AEWIHS","schema_version":"1.0","canonical_sha256":"c6c04b20f20341a5022cf7c828154cc2c01a31f9a4c3834b7080429c4f8f36d0","source":{"kind":"arxiv","id":"1810.10217","version":1},"attestation_state":"computed","paper":{"title":"Extension functors of generalized local cohomology modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Alireza Vahidi, Elham Hoseinzade, Faisal Hassani","submitted_at":"2018-10-24T07:15:39Z","abstract_excerpt":"Let $R$ be a commutative Noetherian ring with non-zero identity, $\\mathfrak{a}$ an ideal of $R$, $M$ a finitely generated $R$--module, and $X$ an arbitrary $R$--module. In this paper, for non-negative integers $s, t$ and a finitely generated $R$--module $N$, we study the membership of $\\operatorname{Ext}_{R}^{s}(N, \\operatorname{H}^{t}_{\\mathfrak{a}}(M, X))$ in Serre subcategories of the category of $R$--modules and present some upper bounds for the injective dimension and the Bass numbers of $\\operatorname{H}^{t}_{\\mathfrak{a}}(M, X)$. We also give some results on cofiniteness and minimaxness"},"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":"1810.10217","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-10-24T07:15:39Z","cross_cats_sorted":[],"title_canon_sha256":"580eea8f40a8e0950c3b69ca575a8cfb6786489e1993c76aa8e88100b1668a17","abstract_canon_sha256":"5112afc48ce503d1796871502567b431dec96fa4609458ba2f8240eb7d8505cc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:23.869851Z","signature_b64":"BkohnwUMTYFLuZKnNYNmEDAqQCkQekeg1mU08h4i9N0QZxB6TkwmfZyJiZpeQutwzCydaYuP93qR9oNyv25GBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6c04b20f20341a5022cf7c828154cc2c01a31f9a4c3834b7080429c4f8f36d0","last_reissued_at":"2026-05-18T00:02:23.869170Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:23.869170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extension functors of generalized local cohomology modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Alireza Vahidi, Elham Hoseinzade, Faisal Hassani","submitted_at":"2018-10-24T07:15:39Z","abstract_excerpt":"Let $R$ be a commutative Noetherian ring with non-zero identity, $\\mathfrak{a}$ an ideal of $R$, $M$ a finitely generated $R$--module, and $X$ an arbitrary $R$--module. In this paper, for non-negative integers $s, t$ and a finitely generated $R$--module $N$, we study the membership of $\\operatorname{Ext}_{R}^{s}(N, \\operatorname{H}^{t}_{\\mathfrak{a}}(M, X))$ in Serre subcategories of the category of $R$--modules and present some upper bounds for the injective dimension and the Bass numbers of $\\operatorname{H}^{t}_{\\mathfrak{a}}(M, X)$. We also give some results on cofiniteness and minimaxness"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10217","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":"1810.10217","created_at":"2026-05-18T00:02:23.869269+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.10217v1","created_at":"2026-05-18T00:02:23.869269+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10217","created_at":"2026-05-18T00:02:23.869269+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y3AEWIHSANA2","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y3AEWIHSANA2KARM","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y3AEWIHS","created_at":"2026-05-18T12:33:04.347982+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/Y3AEWIHSANA2KARM67ECQFKMYL","json":"https://pith.science/pith/Y3AEWIHSANA2KARM67ECQFKMYL.json","graph_json":"https://pith.science/api/pith-number/Y3AEWIHSANA2KARM67ECQFKMYL/graph.json","events_json":"https://pith.science/api/pith-number/Y3AEWIHSANA2KARM67ECQFKMYL/events.json","paper":"https://pith.science/paper/Y3AEWIHS"},"agent_actions":{"view_html":"https://pith.science/pith/Y3AEWIHSANA2KARM67ECQFKMYL","download_json":"https://pith.science/pith/Y3AEWIHSANA2KARM67ECQFKMYL.json","view_paper":"https://pith.science/paper/Y3AEWIHS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.10217&json=true","fetch_graph":"https://pith.science/api/pith-number/Y3AEWIHSANA2KARM67ECQFKMYL/graph.json","fetch_events":"https://pith.science/api/pith-number/Y3AEWIHSANA2KARM67ECQFKMYL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y3AEWIHSANA2KARM67ECQFKMYL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y3AEWIHSANA2KARM67ECQFKMYL/action/storage_attestation","attest_author":"https://pith.science/pith/Y3AEWIHSANA2KARM67ECQFKMYL/action/author_attestation","sign_citation":"https://pith.science/pith/Y3AEWIHSANA2KARM67ECQFKMYL/action/citation_signature","submit_replication":"https://pith.science/pith/Y3AEWIHSANA2KARM67ECQFKMYL/action/replication_record"}},"created_at":"2026-05-18T00:02:23.869269+00:00","updated_at":"2026-05-18T00:02:23.869269+00:00"}