{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NDFSATRGTNMGPGW2MNVDPWW4Z7","short_pith_number":"pith:NDFSATRG","canonical_record":{"source":{"id":"1103.5380","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-28T14:44:53Z","cross_cats_sorted":["math.AC","math.RT"],"title_canon_sha256":"670a7ae90b1f6415c4fa6d93af2e1d68c37d97c9b6efc21f55118fdd5fcd2e04","abstract_canon_sha256":"5239f360aed6260d8fde294170617f97c3b85fa14cb59ad135c17a4c2904d1fa"},"schema_version":"1.0"},"canonical_sha256":"68cb204e269b58679ada636a37dadccff92a834c5165e939dcc64d000fd49349","source":{"kind":"arxiv","id":"1103.5380","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.5380","created_at":"2026-05-18T04:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"1103.5380v3","created_at":"2026-05-18T04:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.5380","created_at":"2026-05-18T04:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"NDFSATRGTNMG","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NDFSATRGTNMGPGW2","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NDFSATRG","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NDFSATRGTNMGPGW2MNVDPWW4Z7","target":"record","payload":{"canonical_record":{"source":{"id":"1103.5380","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-28T14:44:53Z","cross_cats_sorted":["math.AC","math.RT"],"title_canon_sha256":"670a7ae90b1f6415c4fa6d93af2e1d68c37d97c9b6efc21f55118fdd5fcd2e04","abstract_canon_sha256":"5239f360aed6260d8fde294170617f97c3b85fa14cb59ad135c17a4c2904d1fa"},"schema_version":"1.0"},"canonical_sha256":"68cb204e269b58679ada636a37dadccff92a834c5165e939dcc64d000fd49349","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:05.381445Z","signature_b64":"zxZe6rNq/WOaQU9oqZf1UqZJAAx3KWrwhlk2Hv/CHxVomIQkhF9seVVGFOdxnADo04Zmp8tA8xB7il+qINGUAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68cb204e269b58679ada636a37dadccff92a834c5165e939dcc64d000fd49349","last_reissued_at":"2026-05-18T04:15:05.380764Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:05.380764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.5380","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:15:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+tAEYtRtJIHehpm1lZ7OACrGCDdXAfIF1nDlDRjIpR064m1cL2WjP2h6YWJ8uu/5xjrcVd78qeP5Xy/h7ig0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T03:17:41.522275Z"},"content_sha256":"454795e5491e14549b0d63555c94a2f038ff476177a068c9258ef877520d9ee7","schema_version":"1.0","event_id":"sha256:454795e5491e14549b0d63555c94a2f038ff476177a068c9258ef877520d9ee7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NDFSATRGTNMGPGW2MNVDPWW4Z7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-commutative crepant resolutions: scenes from categorical geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.RT"],"primary_cat":"math.AG","authors_text":"Graham J. Leuschke","submitted_at":"2011-03-28T14:44:53Z","abstract_excerpt":"Non-commutative crepant resolutions are algebraic objects defined by Van den Bergh to realize an equivalence of derived categories in birational geometry. They are motivated by tilting theory, the McKay correspondence, and the minimal model program, and have applications to string theory and representation theory. In this expository article I situate Van den Bergh's definition within these contexts and describe some of the current research in the area."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5380","kind":"arxiv","version":3},"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":"2026-05-18T04:15:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GPDBulKuagGbUns9OMTuoCtpLM9CYZ8xVNH/6i7uzq6wAVh7WZCXzn9URplhZDirO317R9RrnFFkT1+m71YXDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T03:17:41.522654Z"},"content_sha256":"263f30f5eb14d4eb0fd68011b70d1208befe0491db9794b5efe7a76afd4548e0","schema_version":"1.0","event_id":"sha256:263f30f5eb14d4eb0fd68011b70d1208befe0491db9794b5efe7a76afd4548e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NDFSATRGTNMGPGW2MNVDPWW4Z7/bundle.json","state_url":"https://pith.science/pith/NDFSATRGTNMGPGW2MNVDPWW4Z7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NDFSATRGTNMGPGW2MNVDPWW4Z7/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":"2026-07-02T03:17:41Z","links":{"resolver":"https://pith.science/pith/NDFSATRGTNMGPGW2MNVDPWW4Z7","bundle":"https://pith.science/pith/NDFSATRGTNMGPGW2MNVDPWW4Z7/bundle.json","state":"https://pith.science/pith/NDFSATRGTNMGPGW2MNVDPWW4Z7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NDFSATRGTNMGPGW2MNVDPWW4Z7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NDFSATRGTNMGPGW2MNVDPWW4Z7","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":"5239f360aed6260d8fde294170617f97c3b85fa14cb59ad135c17a4c2904d1fa","cross_cats_sorted":["math.AC","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-28T14:44:53Z","title_canon_sha256":"670a7ae90b1f6415c4fa6d93af2e1d68c37d97c9b6efc21f55118fdd5fcd2e04"},"schema_version":"1.0","source":{"id":"1103.5380","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.5380","created_at":"2026-05-18T04:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"1103.5380v3","created_at":"2026-05-18T04:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.5380","created_at":"2026-05-18T04:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"NDFSATRGTNMG","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NDFSATRGTNMGPGW2","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NDFSATRG","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:263f30f5eb14d4eb0fd68011b70d1208befe0491db9794b5efe7a76afd4548e0","target":"graph","created_at":"2026-05-18T04:15:05Z","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":"Non-commutative crepant resolutions are algebraic objects defined by Van den Bergh to realize an equivalence of derived categories in birational geometry. They are motivated by tilting theory, the McKay correspondence, and the minimal model program, and have applications to string theory and representation theory. In this expository article I situate Van den Bergh's definition within these contexts and describe some of the current research in the area.","authors_text":"Graham J. Leuschke","cross_cats":["math.AC","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-28T14:44:53Z","title":"Non-commutative crepant resolutions: scenes from categorical geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5380","kind":"arxiv","version":3},"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":"sha256:454795e5491e14549b0d63555c94a2f038ff476177a068c9258ef877520d9ee7","target":"record","created_at":"2026-05-18T04:15:05Z","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":"5239f360aed6260d8fde294170617f97c3b85fa14cb59ad135c17a4c2904d1fa","cross_cats_sorted":["math.AC","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-28T14:44:53Z","title_canon_sha256":"670a7ae90b1f6415c4fa6d93af2e1d68c37d97c9b6efc21f55118fdd5fcd2e04"},"schema_version":"1.0","source":{"id":"1103.5380","kind":"arxiv","version":3}},"canonical_sha256":"68cb204e269b58679ada636a37dadccff92a834c5165e939dcc64d000fd49349","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68cb204e269b58679ada636a37dadccff92a834c5165e939dcc64d000fd49349","first_computed_at":"2026-05-18T04:15:05.380764Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:05.380764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zxZe6rNq/WOaQU9oqZf1UqZJAAx3KWrwhlk2Hv/CHxVomIQkhF9seVVGFOdxnADo04Zmp8tA8xB7il+qINGUAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:05.381445Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.5380","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:454795e5491e14549b0d63555c94a2f038ff476177a068c9258ef877520d9ee7","sha256:263f30f5eb14d4eb0fd68011b70d1208befe0491db9794b5efe7a76afd4548e0"],"state_sha256":"b490da5c6461c3fc0df5712043be1d31dfff500bcb2fac90fc21a2c26753f698"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uAj7lZ9TroZ4HHhWVicBSJQUKDz9Te1zYtrJGK6a+EHCUpwRNQ2o+AzB8160T2VHj04dBuKUn9vexaLOry4pAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T03:17:41.524783Z","bundle_sha256":"84c81284c78e1bdf5a11d44fb355a234cc362990aca1b302df6b7d8b8a165944"}}