{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:OIYJBGMOG34UMCM6YRLKDOZ7EF","short_pith_number":"pith:OIYJBGMO","schema_version":"1.0","canonical_sha256":"723090998e36f946099ec456a1bb3f215ba9029839a7155ee58e33d3f520ed67","source":{"kind":"arxiv","id":"2412.19625","version":1},"attestation_state":"computed","paper":{"title":"Reflexive modules and Auslander-type conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CT","math.RA"],"primary_cat":"math.RT","authors_text":"Norihiro Hanihara","submitted_at":"2024-12-27T13:02:12Z","abstract_excerpt":"We study the category $\\mathop{\\mathrm{ref}}\\Lambda$ of reflexive modules over a two-sided Noetherian ring $\\Lambda$. We show that the category $\\mathop{\\mathrm{ref}}\\Lambda$ is quasi-abelian if and only if $\\Lambda$ satisfies certain Auslander-type condition on the minimal injective resolution of the ring itself. Furthermore, we establish a Morita theorem which characterizes the category of reflexive modules among quasi-abelian categories in terms of generator-cogenerators."},"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":"2412.19625","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-12-27T13:02:12Z","cross_cats_sorted":["math.AC","math.CT","math.RA"],"title_canon_sha256":"870fbb53c4ca8432d8326c3318e1951ce5e51fb3160d002faa9625e4f642d670","abstract_canon_sha256":"f84bbd200500713f637436ed9bd78c1d0aca22b99b161e12b6626537642e1e92"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:54:38.860490Z","signature_b64":"h4x1NpKCgztnloyYjWA7cYVqZ5xpy8rmAp8lYglGPYyvdpko1Rx7fifn/CylQ9fWue07nL/fbH6IP9qemKdUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"723090998e36f946099ec456a1bb3f215ba9029839a7155ee58e33d3f520ed67","last_reissued_at":"2026-07-05T09:54:38.860076Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:54:38.860076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reflexive modules and Auslander-type conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CT","math.RA"],"primary_cat":"math.RT","authors_text":"Norihiro Hanihara","submitted_at":"2024-12-27T13:02:12Z","abstract_excerpt":"We study the category $\\mathop{\\mathrm{ref}}\\Lambda$ of reflexive modules over a two-sided Noetherian ring $\\Lambda$. We show that the category $\\mathop{\\mathrm{ref}}\\Lambda$ is quasi-abelian if and only if $\\Lambda$ satisfies certain Auslander-type condition on the minimal injective resolution of the ring itself. Furthermore, we establish a Morita theorem which characterizes the category of reflexive modules among quasi-abelian categories in terms of generator-cogenerators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.19625","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.19625/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2412.19625","created_at":"2026-07-05T09:54:38.860131+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.19625v1","created_at":"2026-07-05T09:54:38.860131+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.19625","created_at":"2026-07-05T09:54:38.860131+00:00"},{"alias_kind":"pith_short_12","alias_value":"OIYJBGMOG34U","created_at":"2026-07-05T09:54:38.860131+00:00"},{"alias_kind":"pith_short_16","alias_value":"OIYJBGMOG34UMCM6","created_at":"2026-07-05T09:54:38.860131+00:00"},{"alias_kind":"pith_short_8","alias_value":"OIYJBGMO","created_at":"2026-07-05T09:54:38.860131+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.10901","citing_title":"Spherical modules and the Auslander--Gorenstein condition for Auslander--Yoneda algebras","ref_index":29,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OIYJBGMOG34UMCM6YRLKDOZ7EF","json":"https://pith.science/pith/OIYJBGMOG34UMCM6YRLKDOZ7EF.json","graph_json":"https://pith.science/api/pith-number/OIYJBGMOG34UMCM6YRLKDOZ7EF/graph.json","events_json":"https://pith.science/api/pith-number/OIYJBGMOG34UMCM6YRLKDOZ7EF/events.json","paper":"https://pith.science/paper/OIYJBGMO"},"agent_actions":{"view_html":"https://pith.science/pith/OIYJBGMOG34UMCM6YRLKDOZ7EF","download_json":"https://pith.science/pith/OIYJBGMOG34UMCM6YRLKDOZ7EF.json","view_paper":"https://pith.science/paper/OIYJBGMO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.19625&json=true","fetch_graph":"https://pith.science/api/pith-number/OIYJBGMOG34UMCM6YRLKDOZ7EF/graph.json","fetch_events":"https://pith.science/api/pith-number/OIYJBGMOG34UMCM6YRLKDOZ7EF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OIYJBGMOG34UMCM6YRLKDOZ7EF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OIYJBGMOG34UMCM6YRLKDOZ7EF/action/storage_attestation","attest_author":"https://pith.science/pith/OIYJBGMOG34UMCM6YRLKDOZ7EF/action/author_attestation","sign_citation":"https://pith.science/pith/OIYJBGMOG34UMCM6YRLKDOZ7EF/action/citation_signature","submit_replication":"https://pith.science/pith/OIYJBGMOG34UMCM6YRLKDOZ7EF/action/replication_record"}},"created_at":"2026-07-05T09:54:38.860131+00:00","updated_at":"2026-07-05T09:54:38.860131+00:00"}