{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:U2MIZLZBRWL45K2GALEKZGV2WQ","short_pith_number":"pith:U2MIZLZB","schema_version":"1.0","canonical_sha256":"a6988caf218d97ceab4602c8ac9abab421feb28d79e6bb6907c3527b33bb1aaf","source":{"kind":"arxiv","id":"0911.2659","version":2},"attestation_state":"computed","paper":{"title":"Non-commutative desingularization of determinantal varieties, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Graham J. Leuschke, Michel Van den Bergh, Ragnar-Olaf Buchweitz","submitted_at":"2009-11-13T19:38:44Z","abstract_excerpt":"We show that determinantal varieties defined by maximal minors of a generic matrix have a non-commutative desingularization, in that we construct a maximal Cohen-Macaulay module over such a variety whose endomorphism ring is Cohen-Macaulay and has finite global dimension. In the case of the determinant of a square matrix, this gives a non-commutative crepant resolution."},"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":"0911.2659","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-11-13T19:38:44Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"8b888a3911c61856dcb588426475fee99f7a19ed1438ab21c6471f802ea9fd48","abstract_canon_sha256":"7801d58cdcf91a4ae0ffd92255a35ed7522611b7bb9fe22dece7f59c7d5d5d86"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:47.858756Z","signature_b64":"CD77USTbEv4CCfKbRtFprMAB4OZkgSGXE/GkB/HS7Kb2Z3FgxdcO2IK9r669Ca7SF47UB/fZPXw/TD7sCB5FBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6988caf218d97ceab4602c8ac9abab421feb28d79e6bb6907c3527b33bb1aaf","last_reissued_at":"2026-05-18T02:10:47.858007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:47.858007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-commutative desingularization of determinantal varieties, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Graham J. Leuschke, Michel Van den Bergh, Ragnar-Olaf Buchweitz","submitted_at":"2009-11-13T19:38:44Z","abstract_excerpt":"We show that determinantal varieties defined by maximal minors of a generic matrix have a non-commutative desingularization, in that we construct a maximal Cohen-Macaulay module over such a variety whose endomorphism ring is Cohen-Macaulay and has finite global dimension. In the case of the determinant of a square matrix, this gives a non-commutative crepant resolution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2659","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":""},"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":"0911.2659","created_at":"2026-05-18T02:10:47.858120+00:00"},{"alias_kind":"arxiv_version","alias_value":"0911.2659v2","created_at":"2026-05-18T02:10:47.858120+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.2659","created_at":"2026-05-18T02:10:47.858120+00:00"},{"alias_kind":"pith_short_12","alias_value":"U2MIZLZBRWL4","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"U2MIZLZBRWL45K2G","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"U2MIZLZB","created_at":"2026-05-18T12:26:02.257875+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/U2MIZLZBRWL45K2GALEKZGV2WQ","json":"https://pith.science/pith/U2MIZLZBRWL45K2GALEKZGV2WQ.json","graph_json":"https://pith.science/api/pith-number/U2MIZLZBRWL45K2GALEKZGV2WQ/graph.json","events_json":"https://pith.science/api/pith-number/U2MIZLZBRWL45K2GALEKZGV2WQ/events.json","paper":"https://pith.science/paper/U2MIZLZB"},"agent_actions":{"view_html":"https://pith.science/pith/U2MIZLZBRWL45K2GALEKZGV2WQ","download_json":"https://pith.science/pith/U2MIZLZBRWL45K2GALEKZGV2WQ.json","view_paper":"https://pith.science/paper/U2MIZLZB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0911.2659&json=true","fetch_graph":"https://pith.science/api/pith-number/U2MIZLZBRWL45K2GALEKZGV2WQ/graph.json","fetch_events":"https://pith.science/api/pith-number/U2MIZLZBRWL45K2GALEKZGV2WQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U2MIZLZBRWL45K2GALEKZGV2WQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U2MIZLZBRWL45K2GALEKZGV2WQ/action/storage_attestation","attest_author":"https://pith.science/pith/U2MIZLZBRWL45K2GALEKZGV2WQ/action/author_attestation","sign_citation":"https://pith.science/pith/U2MIZLZBRWL45K2GALEKZGV2WQ/action/citation_signature","submit_replication":"https://pith.science/pith/U2MIZLZBRWL45K2GALEKZGV2WQ/action/replication_record"}},"created_at":"2026-05-18T02:10:47.858120+00:00","updated_at":"2026-05-18T02:10:47.858120+00:00"}