{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:3EIAC5UQXKYIBJBPTZFLXMBZPH","short_pith_number":"pith:3EIAC5UQ","schema_version":"1.0","canonical_sha256":"d910017690bab080a42f9e4abbb03979d5ea61e6e606f48c5e872bacbe06824c","source":{"kind":"arxiv","id":"2303.14625","version":2},"attestation_state":"computed","paper":{"title":"Non-commutative resolutions for Segre products and Cohen-Macaulay rings of hereditary representation type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RA","math.RT"],"primary_cat":"math.AC","authors_text":"Norihiro Hanihara","submitted_at":"2023-03-26T04:59:09Z","abstract_excerpt":"We study commutative Cohen-Macaulay rings whose Cohen-Macaulay representation theory are controlled by representations of quivers, which we call hereditary representation type. Based on tilting theory and cluster tilting theory, we construct some commutative Cohen-Macaulay rings of hereditary representation type. First we give a general existence theorem of cluster tilting module or non-commutative crepant resolutions on the Segre product of two commutative Gorenstein rings whenever each factor has such an object. As an application we obtain three examples of Gorenstein rings of hereditary rep"},"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":"2303.14625","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2023-03-26T04:59:09Z","cross_cats_sorted":["math.AG","math.RA","math.RT"],"title_canon_sha256":"10d56a5395e489b3275b5d2c85ef21f9af31644dc79b3b6290bb014ec8f9854f","abstract_canon_sha256":"29ebcc763740e0127254b39b0916f0a3e98b2d96cb6db33c28e394c24774dfc4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:16:17.245785Z","signature_b64":"F+bDPyZ3vQQG/mzsBo3fLr4lWW0hWVrEluyeQlEfHycJaT1Md9vr1uwjXn34bd28l0JUC767di+kRwyZ8louBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d910017690bab080a42f9e4abbb03979d5ea61e6e606f48c5e872bacbe06824c","last_reissued_at":"2026-07-05T06:16:17.245286Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:16:17.245286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-commutative resolutions for Segre products and Cohen-Macaulay rings of hereditary representation type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RA","math.RT"],"primary_cat":"math.AC","authors_text":"Norihiro Hanihara","submitted_at":"2023-03-26T04:59:09Z","abstract_excerpt":"We study commutative Cohen-Macaulay rings whose Cohen-Macaulay representation theory are controlled by representations of quivers, which we call hereditary representation type. Based on tilting theory and cluster tilting theory, we construct some commutative Cohen-Macaulay rings of hereditary representation type. First we give a general existence theorem of cluster tilting module or non-commutative crepant resolutions on the Segre product of two commutative Gorenstein rings whenever each factor has such an object. As an application we obtain three examples of Gorenstein rings of hereditary rep"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.14625","kind":"arxiv","version":2},"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/2303.14625/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":"2303.14625","created_at":"2026-07-05T06:16:17.245353+00:00"},{"alias_kind":"arxiv_version","alias_value":"2303.14625v2","created_at":"2026-07-05T06:16:17.245353+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.14625","created_at":"2026-07-05T06:16:17.245353+00:00"},{"alias_kind":"pith_short_12","alias_value":"3EIAC5UQXKYI","created_at":"2026-07-05T06:16:17.245353+00:00"},{"alias_kind":"pith_short_16","alias_value":"3EIAC5UQXKYIBJBP","created_at":"2026-07-05T06:16:17.245353+00:00"},{"alias_kind":"pith_short_8","alias_value":"3EIAC5UQ","created_at":"2026-07-05T06:16:17.245353+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2510.26252","citing_title":"Non-commutative crepant resolutions of toric singularities with divisor class group of rank one","ref_index":5,"is_internal_anchor":false},{"citing_arxiv_id":"2510.26199","citing_title":"Weak del Pezzo surfaces are characterized by the existence of $2$-tilting bundles","ref_index":12,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3EIAC5UQXKYIBJBPTZFLXMBZPH","json":"https://pith.science/pith/3EIAC5UQXKYIBJBPTZFLXMBZPH.json","graph_json":"https://pith.science/api/pith-number/3EIAC5UQXKYIBJBPTZFLXMBZPH/graph.json","events_json":"https://pith.science/api/pith-number/3EIAC5UQXKYIBJBPTZFLXMBZPH/events.json","paper":"https://pith.science/paper/3EIAC5UQ"},"agent_actions":{"view_html":"https://pith.science/pith/3EIAC5UQXKYIBJBPTZFLXMBZPH","download_json":"https://pith.science/pith/3EIAC5UQXKYIBJBPTZFLXMBZPH.json","view_paper":"https://pith.science/paper/3EIAC5UQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2303.14625&json=true","fetch_graph":"https://pith.science/api/pith-number/3EIAC5UQXKYIBJBPTZFLXMBZPH/graph.json","fetch_events":"https://pith.science/api/pith-number/3EIAC5UQXKYIBJBPTZFLXMBZPH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3EIAC5UQXKYIBJBPTZFLXMBZPH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3EIAC5UQXKYIBJBPTZFLXMBZPH/action/storage_attestation","attest_author":"https://pith.science/pith/3EIAC5UQXKYIBJBPTZFLXMBZPH/action/author_attestation","sign_citation":"https://pith.science/pith/3EIAC5UQXKYIBJBPTZFLXMBZPH/action/citation_signature","submit_replication":"https://pith.science/pith/3EIAC5UQXKYIBJBPTZFLXMBZPH/action/replication_record"}},"created_at":"2026-07-05T06:16:17.245353+00:00","updated_at":"2026-07-05T06:16:17.245353+00:00"}