{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FQO5MTYT6AHF22ON575JB27Y3Q","short_pith_number":"pith:FQO5MTYT","schema_version":"1.0","canonical_sha256":"2c1dd64f13f00e5d69cdeffa90ebf8dc19c2070fe03666af2eda7a457ed63046","source":{"kind":"arxiv","id":"1603.00334","version":1},"attestation_state":"computed","paper":{"title":"Finite F-type and F-abundant modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Hailong Dao, Tony Se","submitted_at":"2016-03-01T16:02:31Z","abstract_excerpt":"In this note we introduce and study basic properties of two types of modules over a commutative noetherian ring $R$ of positive prime characteristic. The first is the category of modules of finite $F$-type. These objects include reflexive ideals representing torsion elements in the divisor class group of $R$. The second class is what we call $F$-abundant modules. These include, for example, the ring $R$ itself and the canonical module when $R$ has positive splitting dimension. We prove various facts about these two categories and how they are related, for example that $\\mathrm{Hom}_R(M,N)$ is "},"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":"1603.00334","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-03-01T16:02:31Z","cross_cats_sorted":[],"title_canon_sha256":"952bb7c1d9bfa53535958b50a8e4540d56d3241367825f8752fb6924c757a2d8","abstract_canon_sha256":"f70ecee0ba0a22c2ae8215cea678cbeb59dabffbe8db5d917f4667d19e9c1775"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:45.327268Z","signature_b64":"bMhejyqyFiTp5ooqCD8doJv0Z2nyS63lqwx9Fnqda94EzTErnILc2kMhIUm0EmptgtEUyX9BjLaZtwYid/k9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c1dd64f13f00e5d69cdeffa90ebf8dc19c2070fe03666af2eda7a457ed63046","last_reissued_at":"2026-05-18T01:19:45.326757Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:45.326757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite F-type and F-abundant modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Hailong Dao, Tony Se","submitted_at":"2016-03-01T16:02:31Z","abstract_excerpt":"In this note we introduce and study basic properties of two types of modules over a commutative noetherian ring $R$ of positive prime characteristic. The first is the category of modules of finite $F$-type. These objects include reflexive ideals representing torsion elements in the divisor class group of $R$. The second class is what we call $F$-abundant modules. These include, for example, the ring $R$ itself and the canonical module when $R$ has positive splitting dimension. We prove various facts about these two categories and how they are related, for example that $\\mathrm{Hom}_R(M,N)$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00334","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":"1603.00334","created_at":"2026-05-18T01:19:45.326848+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.00334v1","created_at":"2026-05-18T01:19:45.326848+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00334","created_at":"2026-05-18T01:19:45.326848+00:00"},{"alias_kind":"pith_short_12","alias_value":"FQO5MTYT6AHF","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FQO5MTYT6AHF22ON","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FQO5MTYT","created_at":"2026-05-18T12:30:15.759754+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/FQO5MTYT6AHF22ON575JB27Y3Q","json":"https://pith.science/pith/FQO5MTYT6AHF22ON575JB27Y3Q.json","graph_json":"https://pith.science/api/pith-number/FQO5MTYT6AHF22ON575JB27Y3Q/graph.json","events_json":"https://pith.science/api/pith-number/FQO5MTYT6AHF22ON575JB27Y3Q/events.json","paper":"https://pith.science/paper/FQO5MTYT"},"agent_actions":{"view_html":"https://pith.science/pith/FQO5MTYT6AHF22ON575JB27Y3Q","download_json":"https://pith.science/pith/FQO5MTYT6AHF22ON575JB27Y3Q.json","view_paper":"https://pith.science/paper/FQO5MTYT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.00334&json=true","fetch_graph":"https://pith.science/api/pith-number/FQO5MTYT6AHF22ON575JB27Y3Q/graph.json","fetch_events":"https://pith.science/api/pith-number/FQO5MTYT6AHF22ON575JB27Y3Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FQO5MTYT6AHF22ON575JB27Y3Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FQO5MTYT6AHF22ON575JB27Y3Q/action/storage_attestation","attest_author":"https://pith.science/pith/FQO5MTYT6AHF22ON575JB27Y3Q/action/author_attestation","sign_citation":"https://pith.science/pith/FQO5MTYT6AHF22ON575JB27Y3Q/action/citation_signature","submit_replication":"https://pith.science/pith/FQO5MTYT6AHF22ON575JB27Y3Q/action/replication_record"}},"created_at":"2026-05-18T01:19:45.326848+00:00","updated_at":"2026-05-18T01:19:45.326848+00:00"}