{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:KBRX4DFSXTEIM4NRDA6T6GDK46","short_pith_number":"pith:KBRX4DFS","canonical_record":{"source":{"id":"math/0211064","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2002-11-04T18:13:29Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"8037f3040d5cfd8a1905666fb8be0c0d19d3abb096b950bb6e2fa0931ede2c8d","abstract_canon_sha256":"a912f9851c35e83e75b4e78f362ac598f3eb3f784335680f131078f80f4964b6"},"schema_version":"1.0"},"canonical_sha256":"50637e0cb2bcc88671b1183d3f186ae7b0ce534d613351b37c43cba130685be6","source":{"kind":"arxiv","id":"math/0211064","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0211064","created_at":"2026-07-04T15:43:27Z"},{"alias_kind":"arxiv_version","alias_value":"math/0211064v2","created_at":"2026-07-04T15:43:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0211064","created_at":"2026-07-04T15:43:27Z"},{"alias_kind":"pith_short_12","alias_value":"KBRX4DFSXTEI","created_at":"2026-07-04T15:43:27Z"},{"alias_kind":"pith_short_16","alias_value":"KBRX4DFSXTEIM4NR","created_at":"2026-07-04T15:43:27Z"},{"alias_kind":"pith_short_8","alias_value":"KBRX4DFS","created_at":"2026-07-04T15:43:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:KBRX4DFSXTEIM4NRDA6T6GDK46","target":"record","payload":{"canonical_record":{"source":{"id":"math/0211064","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2002-11-04T18:13:29Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"8037f3040d5cfd8a1905666fb8be0c0d19d3abb096b950bb6e2fa0931ede2c8d","abstract_canon_sha256":"a912f9851c35e83e75b4e78f362ac598f3eb3f784335680f131078f80f4964b6"},"schema_version":"1.0"},"canonical_sha256":"50637e0cb2bcc88671b1183d3f186ae7b0ce534d613351b37c43cba130685be6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:43:27.173602Z","signature_b64":"kq5G8lN728h7Q22JGK2s6GCOkm59mFXamA0/BLkHJ08Bznj5k5Tiim5Cx5uAWWTZ9qDEtRbeTg9cie2SzukQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50637e0cb2bcc88671b1183d3f186ae7b0ce534d613351b37c43cba130685be6","last_reissued_at":"2026-07-04T15:43:27.173179Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:43:27.173179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0211064","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":"2026-07-04T15:43:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XgPu2Kk5vlTGItTWfQtF5wqBggnPIrTu6P0C2arQR98+u+R8+vQ7I8pocB1u5mLCboRw+q02mhJIul8mJtUfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T15:52:11.185627Z"},"content_sha256":"4472989d28663f8d903f422ba1429998b7feccdc011aa76b8a0aa14c6a9aa422","schema_version":"1.0","event_id":"sha256:4472989d28663f8d903f422ba1429998b7feccdc011aa76b8a0aa14c6a9aa422"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:KBRX4DFSXTEIM4NRDA6T6GDK46","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-commutative crepant resolutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RA","authors_text":"Michel Van den Bergh","submitted_at":"2002-11-04T18:13:29Z","abstract_excerpt":"We introduce the notion of a ``non-commutative crepant'' resolution of a singularity and show that it exists in certain cases. We also give some evidence for an extension of a conjecture by Bondal and Orlov, stating that different crepant resolutions of a Gorenstein singularity have the same derived category."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0211064","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/math/0211064/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:43:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hrrEa06Auv63td8I2/LaWGe/mJTXNawwMMTKN5Ugrwm7WAil/7ABbw9KYxHfmxznX3ZP8zpfN+vXClmcSGIBCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T15:52:11.186505Z"},"content_sha256":"d76bd94d5fbf6cde4156392d4593cdbddddc8ab0b1f401c2c8da94c91f73b06f","schema_version":"1.0","event_id":"sha256:d76bd94d5fbf6cde4156392d4593cdbddddc8ab0b1f401c2c8da94c91f73b06f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KBRX4DFSXTEIM4NRDA6T6GDK46/bundle.json","state_url":"https://pith.science/pith/KBRX4DFSXTEIM4NRDA6T6GDK46/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KBRX4DFSXTEIM4NRDA6T6GDK46/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":"2026-08-08T15:52:11Z","links":{"resolver":"https://pith.science/pith/KBRX4DFSXTEIM4NRDA6T6GDK46","bundle":"https://pith.science/pith/KBRX4DFSXTEIM4NRDA6T6GDK46/bundle.json","state":"https://pith.science/pith/KBRX4DFSXTEIM4NRDA6T6GDK46/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KBRX4DFSXTEIM4NRDA6T6GDK46/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:KBRX4DFSXTEIM4NRDA6T6GDK46","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":"a912f9851c35e83e75b4e78f362ac598f3eb3f784335680f131078f80f4964b6","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2002-11-04T18:13:29Z","title_canon_sha256":"8037f3040d5cfd8a1905666fb8be0c0d19d3abb096b950bb6e2fa0931ede2c8d"},"schema_version":"1.0","source":{"id":"math/0211064","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0211064","created_at":"2026-07-04T15:43:27Z"},{"alias_kind":"arxiv_version","alias_value":"math/0211064v2","created_at":"2026-07-04T15:43:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0211064","created_at":"2026-07-04T15:43:27Z"},{"alias_kind":"pith_short_12","alias_value":"KBRX4DFSXTEI","created_at":"2026-07-04T15:43:27Z"},{"alias_kind":"pith_short_16","alias_value":"KBRX4DFSXTEIM4NR","created_at":"2026-07-04T15:43:27Z"},{"alias_kind":"pith_short_8","alias_value":"KBRX4DFS","created_at":"2026-07-04T15:43:27Z"}],"graph_snapshots":[{"event_id":"sha256:d76bd94d5fbf6cde4156392d4593cdbddddc8ab0b1f401c2c8da94c91f73b06f","target":"graph","created_at":"2026-07-04T15:43:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0211064/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the notion of a ``non-commutative crepant'' resolution of a singularity and show that it exists in certain cases. We also give some evidence for an extension of a conjecture by Bondal and Orlov, stating that different crepant resolutions of a Gorenstein singularity have the same derived category.","authors_text":"Michel Van den Bergh","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2002-11-04T18:13:29Z","title":"Non-commutative crepant resolutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0211064","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":"sha256:4472989d28663f8d903f422ba1429998b7feccdc011aa76b8a0aa14c6a9aa422","target":"record","created_at":"2026-07-04T15:43:27Z","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":"a912f9851c35e83e75b4e78f362ac598f3eb3f784335680f131078f80f4964b6","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2002-11-04T18:13:29Z","title_canon_sha256":"8037f3040d5cfd8a1905666fb8be0c0d19d3abb096b950bb6e2fa0931ede2c8d"},"schema_version":"1.0","source":{"id":"math/0211064","kind":"arxiv","version":2}},"canonical_sha256":"50637e0cb2bcc88671b1183d3f186ae7b0ce534d613351b37c43cba130685be6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50637e0cb2bcc88671b1183d3f186ae7b0ce534d613351b37c43cba130685be6","first_computed_at":"2026-07-04T15:43:27.173179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:43:27.173179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kq5G8lN728h7Q22JGK2s6GCOkm59mFXamA0/BLkHJ08Bznj5k5Tiim5Cx5uAWWTZ9qDEtRbeTg9cie2SzukQDw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:43:27.173602Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0211064","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4472989d28663f8d903f422ba1429998b7feccdc011aa76b8a0aa14c6a9aa422","sha256:d76bd94d5fbf6cde4156392d4593cdbddddc8ab0b1f401c2c8da94c91f73b06f"],"state_sha256":"5d272f0c95ea7b8b03222c687737ceeba51091a5de3c81d0a9be29c5774d5e37"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cTT9MKvOnluZeDFP9h6cupIb+I+e1k4IdvPeM6Il826Uh5wazwr/UTAJ4PjZG2yIniLrr6pnI8lzAgtFusRnBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T15:52:11.196399Z","bundle_sha256":"1aae76e45d9ef5ee8f33000c0b83bbc3d9177d81a9fb96224218a5d62d84c30b"}}