{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:5QBE6CTDNMXUHD6EXTFB5S3SHA","short_pith_number":"pith:5QBE6CTD","schema_version":"1.0","canonical_sha256":"ec024f0a636b2f438fc4bcca1ecb72382c3ecaa9aa2cf1d5bc8f2ae3ca124ea5","source":{"kind":"arxiv","id":"2512.11600","version":2},"attestation_state":"computed","paper":{"title":"Equivalence classes of Wakamatsu tilting modules and preenveloping and precovering subcategories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"An equivalence relation on Wakamatsu tilting modules extends the Mantese-Reiten theorems to arbitrary associative rings.","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ali Mahin Fallah, Kamran Divaani-Aazar, Massoud Tousi","submitted_at":"2025-12-12T14:35:19Z","abstract_excerpt":"Let R be an associative ring with identity. We introduce an equivalence relation on the class of Wakamatsu tilting right R modules. By using this equivalence relation, we extend the Mantese Reiten theorems from the setting of Artin algebras to that of arbitrary associative rings."},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2512.11600","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-12-12T14:35:19Z","cross_cats_sorted":[],"title_canon_sha256":"5ba4d60ea55623875f0674b194c2e52e944512db1d95dbe2c724eb78226c15cc","abstract_canon_sha256":"aadbd82e20189a4a7fb005b944bae15260f9a4ea5c736119370d674006479f97"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:11.551377Z","signature_b64":"ZlzFau4/gnC/Rb5vLkwtcwJs3OmyfLYKOKYw9KONbbhtjAVpPu6wUFiGDdUrjHDyvnwVhkj8VWv8Gf1jH3MJAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec024f0a636b2f438fc4bcca1ecb72382c3ecaa9aa2cf1d5bc8f2ae3ca124ea5","last_reissued_at":"2026-05-18T03:10:11.550705Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:11.550705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equivalence classes of Wakamatsu tilting modules and preenveloping and precovering subcategories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"An equivalence relation on Wakamatsu tilting modules extends the Mantese-Reiten theorems to arbitrary associative rings.","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ali Mahin Fallah, Kamran Divaani-Aazar, Massoud Tousi","submitted_at":"2025-12-12T14:35:19Z","abstract_excerpt":"Let R be an associative ring with identity. We introduce an equivalence relation on the class of Wakamatsu tilting right R modules. By using this equivalence relation, we extend the Mantese Reiten theorems from the setting of Artin algebras to that of arbitrary associative rings."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We introduce an equivalence relation on the class of Wakamatsu tilting right R modules. By using this equivalence relation, we extend the Mantese Reiten theorems from the setting of Artin algebras to that of arbitrary associative rings.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The introduced equivalence relation on Wakamatsu tilting modules preserves the properties needed for the Mantese-Reiten theorems to hold without extra conditions on the arbitrary associative ring R.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"An equivalence relation on Wakamatsu tilting modules extends Mantese-Reiten theorems from Artin algebras to arbitrary associative rings.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"An equivalence relation on Wakamatsu tilting modules extends the Mantese-Reiten theorems to arbitrary associative rings.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1e7fb05b7096c7494f2f201d8c9f59c336912bf8784acd814b1d845c3a2b820b"},"source":{"id":"2512.11600","kind":"arxiv","version":2},"verdict":{"id":"56cd08c6-9f4b-49b2-92c5-b88743482612","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T22:28:12.886151Z","strongest_claim":"We introduce an equivalence relation on the class of Wakamatsu tilting right R modules. By using this equivalence relation, we extend the Mantese Reiten theorems from the setting of Artin algebras to that of arbitrary associative rings.","one_line_summary":"An equivalence relation on Wakamatsu tilting modules extends Mantese-Reiten theorems from Artin algebras to arbitrary associative rings.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The introduced equivalence relation on Wakamatsu tilting modules preserves the properties needed for the Mantese-Reiten theorems to hold without extra conditions on the arbitrary associative ring R.","pith_extraction_headline":"An equivalence relation on Wakamatsu tilting modules extends the Mantese-Reiten theorems to arbitrary associative rings."},"references":{"count":28,"sample":[{"doi":"","year":1992,"title":"F. W. Anderson and K. R. Fuller,Rings and categories of modules, (2nd ed.), Graduate Texts in Mathematics, 13, New York, Springer-Verlag, (1992)","work_id":"f67a63cd-f0e5-481e-b1ae-0202d6bd1999","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2013,"title":"Angeleri H¨ ugel,Infinite dimensional tilting theory, Advances in representation theory of algebras, EMS Series of Congress Reports, Z¨ urich, (2013), 1–37","work_id":"5a2d56c4-1af7-414b-9278-f2101ad9aa81","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2000,"title":"Angeleri H¨ ugel,Finitely cotilting modules, Commun","work_id":"1b9e2044-52d8-4085-b841-62c4cc5aa853","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2006,"title":"I. Assem, D. Simson and A. Skowro´ nski,Elements of the representation theory of associative algebras, vol. 1: Techniques of representation theory, London Mathematical Society Student Texts,65, Cambri","work_id":"cc5d6b38-086a-41ff-ad33-03e9a446ae17","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1978,"title":"Auslander,Functors and morphisms determined by objects, Represent","work_id":"700df358-8b2d-498e-a6d2-e6502d6a6c94","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":28,"snapshot_sha256":"e17f661d0d7e1b00aa5e4eaee96fe37214f8c5dd7c7ef5dbfad76890efe70be2","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"24f09250b3dd8eaab0bf7de7d1155b867126817852c67d880c08b501537f4c5f"},"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":"2512.11600","created_at":"2026-05-18T03:10:11.550807+00:00"},{"alias_kind":"arxiv_version","alias_value":"2512.11600v2","created_at":"2026-05-18T03:10:11.550807+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.11600","created_at":"2026-05-18T03:10:11.550807+00:00"},{"alias_kind":"pith_short_12","alias_value":"5QBE6CTDNMXU","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"5QBE6CTDNMXUHD6E","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"5QBE6CTD","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5QBE6CTDNMXUHD6EXTFB5S3SHA","json":"https://pith.science/pith/5QBE6CTDNMXUHD6EXTFB5S3SHA.json","graph_json":"https://pith.science/api/pith-number/5QBE6CTDNMXUHD6EXTFB5S3SHA/graph.json","events_json":"https://pith.science/api/pith-number/5QBE6CTDNMXUHD6EXTFB5S3SHA/events.json","paper":"https://pith.science/paper/5QBE6CTD"},"agent_actions":{"view_html":"https://pith.science/pith/5QBE6CTDNMXUHD6EXTFB5S3SHA","download_json":"https://pith.science/pith/5QBE6CTDNMXUHD6EXTFB5S3SHA.json","view_paper":"https://pith.science/paper/5QBE6CTD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2512.11600&json=true","fetch_graph":"https://pith.science/api/pith-number/5QBE6CTDNMXUHD6EXTFB5S3SHA/graph.json","fetch_events":"https://pith.science/api/pith-number/5QBE6CTDNMXUHD6EXTFB5S3SHA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5QBE6CTDNMXUHD6EXTFB5S3SHA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5QBE6CTDNMXUHD6EXTFB5S3SHA/action/storage_attestation","attest_author":"https://pith.science/pith/5QBE6CTDNMXUHD6EXTFB5S3SHA/action/author_attestation","sign_citation":"https://pith.science/pith/5QBE6CTDNMXUHD6EXTFB5S3SHA/action/citation_signature","submit_replication":"https://pith.science/pith/5QBE6CTDNMXUHD6EXTFB5S3SHA/action/replication_record"}},"created_at":"2026-05-18T03:10:11.550807+00:00","updated_at":"2026-05-18T03:10:11.550807+00:00"}