{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:U2MIZLZBRWL45K2GALEKZGV2WQ","short_pith_number":"pith:U2MIZLZB","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"},"canonical_sha256":"a6988caf218d97ceab4602c8ac9abab421feb28d79e6bb6907c3527b33bb1aaf","source":{"kind":"arxiv","id":"0911.2659","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.2659","created_at":"2026-05-18T02:10:47Z"},{"alias_kind":"arxiv_version","alias_value":"0911.2659v2","created_at":"2026-05-18T02:10:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.2659","created_at":"2026-05-18T02:10:47Z"},{"alias_kind":"pith_short_12","alias_value":"U2MIZLZBRWL4","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"U2MIZLZBRWL45K2G","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"U2MIZLZB","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:U2MIZLZBRWL45K2GALEKZGV2WQ","target":"record","payload":{"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"},"canonical_sha256":"a6988caf218d97ceab4602c8ac9abab421feb28d79e6bb6907c3527b33bb1aaf","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"},"source_kind":"arxiv","source_id":"0911.2659","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:10:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"orj6OfigS6M/K03bS6k8C8Fv+d4n721ksSQfqVnTqN68LUyhFWukMRGqYL0MOfZMinoHIGeWbfp3tmhUNz8PAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T01:53:42.499184Z"},"content_sha256":"b4ab91b4731622994dc1d514f885f0a175b5eb7ba50bdea38b12e8f37faebf5c","schema_version":"1.0","event_id":"sha256:b4ab91b4731622994dc1d514f885f0a175b5eb7ba50bdea38b12e8f37faebf5c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:U2MIZLZBRWL45K2GALEKZGV2WQ","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:10:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B8U7OalEnufnSenW6fUAvMqA6dYa3UX+q3kGmqwr6NOu1dQpHUaFg/68vdEghzcbiF7esDDoMJLjA2WKeIekDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T01:53:42.499552Z"},"content_sha256":"c526f02f0e73e7f5b5639d6bc3ee076de3f3a3cf253ad20fb5e8251dcaac456d","schema_version":"1.0","event_id":"sha256:c526f02f0e73e7f5b5639d6bc3ee076de3f3a3cf253ad20fb5e8251dcaac456d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U2MIZLZBRWL45K2GALEKZGV2WQ/bundle.json","state_url":"https://pith.science/pith/U2MIZLZBRWL45K2GALEKZGV2WQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U2MIZLZBRWL45K2GALEKZGV2WQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-02T01:53:42Z","links":{"resolver":"https://pith.science/pith/U2MIZLZBRWL45K2GALEKZGV2WQ","bundle":"https://pith.science/pith/U2MIZLZBRWL45K2GALEKZGV2WQ/bundle.json","state":"https://pith.science/pith/U2MIZLZBRWL45K2GALEKZGV2WQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U2MIZLZBRWL45K2GALEKZGV2WQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:U2MIZLZBRWL45K2GALEKZGV2WQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7801d58cdcf91a4ae0ffd92255a35ed7522611b7bb9fe22dece7f59c7d5d5d86","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-11-13T19:38:44Z","title_canon_sha256":"8b888a3911c61856dcb588426475fee99f7a19ed1438ab21c6471f802ea9fd48"},"schema_version":"1.0","source":{"id":"0911.2659","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.2659","created_at":"2026-05-18T02:10:47Z"},{"alias_kind":"arxiv_version","alias_value":"0911.2659v2","created_at":"2026-05-18T02:10:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.2659","created_at":"2026-05-18T02:10:47Z"},{"alias_kind":"pith_short_12","alias_value":"U2MIZLZBRWL4","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"U2MIZLZBRWL45K2G","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"U2MIZLZB","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:c526f02f0e73e7f5b5639d6bc3ee076de3f3a3cf253ad20fb5e8251dcaac456d","target":"graph","created_at":"2026-05-18T02:10:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Graham J. Leuschke, Michel Van den Bergh, Ragnar-Olaf Buchweitz","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-11-13T19:38:44Z","title":"Non-commutative desingularization of determinantal varieties, I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2659","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b4ab91b4731622994dc1d514f885f0a175b5eb7ba50bdea38b12e8f37faebf5c","target":"record","created_at":"2026-05-18T02:10:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7801d58cdcf91a4ae0ffd92255a35ed7522611b7bb9fe22dece7f59c7d5d5d86","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-11-13T19:38:44Z","title_canon_sha256":"8b888a3911c61856dcb588426475fee99f7a19ed1438ab21c6471f802ea9fd48"},"schema_version":"1.0","source":{"id":"0911.2659","kind":"arxiv","version":2}},"canonical_sha256":"a6988caf218d97ceab4602c8ac9abab421feb28d79e6bb6907c3527b33bb1aaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6988caf218d97ceab4602c8ac9abab421feb28d79e6bb6907c3527b33bb1aaf","first_computed_at":"2026-05-18T02:10:47.858007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:10:47.858007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CD77USTbEv4CCfKbRtFprMAB4OZkgSGXE/GkB/HS7Kb2Z3FgxdcO2IK9r669Ca7SF47UB/fZPXw/TD7sCB5FBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:10:47.858756Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.2659","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4ab91b4731622994dc1d514f885f0a175b5eb7ba50bdea38b12e8f37faebf5c","sha256:c526f02f0e73e7f5b5639d6bc3ee076de3f3a3cf253ad20fb5e8251dcaac456d"],"state_sha256":"c77e2ad9fec6e122936c8901245a0d8d3c311836440b06eeda8f2f1555b8fa14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0GXyrCXG1LcmSOl1NIPLUqhPB9EZVXPzmGEm5d1cSWASAM3jifZSj+t1y8Sjx072R0OmkvxjTiN12Tc4XbPnAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T01:53:42.501680Z","bundle_sha256":"a0832679dbef139befc909a47cac4f09c44fae1e1fd5af2dee2357390821e952"}}