{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6IKM37MKXJ52ZHLUF7O3VMLLXJ","short_pith_number":"pith:6IKM37MK","canonical_record":{"source":{"id":"1802.09092","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-02-25T21:52:38Z","cross_cats_sorted":[],"title_canon_sha256":"bdc8a6337c8e82b65fedcc420559ff3f3d9dec9bb6b646c8b7d139a791649d29","abstract_canon_sha256":"83e9f2f424ed08f464db15a12f3140a0d85093b997c450ffb5b6f1c449f5ad58"},"schema_version":"1.0"},"canonical_sha256":"f214cdfd8aba7bac9d742fddbab16bba78eb7644c4f7e69b51ac63d405ba9db4","source":{"kind":"arxiv","id":"1802.09092","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.09092","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1802.09092v3","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.09092","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"6IKM37MKXJ52","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6IKM37MKXJ52ZHLU","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6IKM37MK","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6IKM37MKXJ52ZHLUF7O3VMLLXJ","target":"record","payload":{"canonical_record":{"source":{"id":"1802.09092","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-02-25T21:52:38Z","cross_cats_sorted":[],"title_canon_sha256":"bdc8a6337c8e82b65fedcc420559ff3f3d9dec9bb6b646c8b7d139a791649d29","abstract_canon_sha256":"83e9f2f424ed08f464db15a12f3140a0d85093b997c450ffb5b6f1c449f5ad58"},"schema_version":"1.0"},"canonical_sha256":"f214cdfd8aba7bac9d742fddbab16bba78eb7644c4f7e69b51ac63d405ba9db4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:58.285232Z","signature_b64":"jXNb59PMnfzdpepoPtIqgAA+o4pkJOcDutFPQbS10z/orXDvV0/wUmRjjNSHqRGPjOPfwSsd139WqWnhbG0aCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f214cdfd8aba7bac9d742fddbab16bba78eb7644c4f7e69b51ac63d405ba9db4","last_reissued_at":"2026-05-17T23:41:58.284736Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:58.284736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.09092","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":"2026-05-17T23:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Eo+VAAAEyOLpYfDOSazo5pNCLy/kwYJuI8ijuRW28dK7Oj/imZgGTUXEuHgiFCiif0OROAa8Hr8MqqcfftivBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T12:05:38.361279Z"},"content_sha256":"6c453b8e4f3addddf5417252ab196702ce72c871c449f38425608726b5c4235a","schema_version":"1.0","event_id":"sha256:6c453b8e4f3addddf5417252ab196702ce72c871c449f38425608726b5c4235a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6IKM37MKXJ52ZHLUF7O3VMLLXJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noncommutative quasi-resolutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"J.J. Zhang, X.-S. Qin, Y.-H. Wang","submitted_at":"2018-02-25T21:52:38Z","abstract_excerpt":"The notion of a noncommutative quasi-resolution is introduced for a noncommutative noetherian algebra with singularities, even for a non-Cohen-Macaulay algebra. If A is a commutative normal Gorenstein domain, then anoncommutative quasi-resolution of A naturally produces a noncommutative crepant resolution (NCCR) of A in the sense of Van den Bergh, and vice versa. Under some mild hypotheses, we prove that (i) in dimension two, all noncommutative quasi-resolutions of a given non-commutative algebra are Morita equivalent, and (ii) in dimension three, all noncommutative quasi-resolutions of a give"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09092","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":"2026-05-17T23:41:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e/CbzE15PUFowrFaYZpH8SxQRlEK8qoGhHo8b7sNBASRgnXBvANNV/he15FQrPrjP5IS44qVdRrt7Vpr1WeVAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T12:05:38.361639Z"},"content_sha256":"95c9c29df5acba10dcf26b9f4e13407a1d12d8a0c5e6ba1498613f9753d96535","schema_version":"1.0","event_id":"sha256:95c9c29df5acba10dcf26b9f4e13407a1d12d8a0c5e6ba1498613f9753d96535"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6IKM37MKXJ52ZHLUF7O3VMLLXJ/bundle.json","state_url":"https://pith.science/pith/6IKM37MKXJ52ZHLUF7O3VMLLXJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6IKM37MKXJ52ZHLUF7O3VMLLXJ/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":"2026-06-20T12:05:38Z","links":{"resolver":"https://pith.science/pith/6IKM37MKXJ52ZHLUF7O3VMLLXJ","bundle":"https://pith.science/pith/6IKM37MKXJ52ZHLUF7O3VMLLXJ/bundle.json","state":"https://pith.science/pith/6IKM37MKXJ52ZHLUF7O3VMLLXJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6IKM37MKXJ52ZHLUF7O3VMLLXJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6IKM37MKXJ52ZHLUF7O3VMLLXJ","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":"83e9f2f424ed08f464db15a12f3140a0d85093b997c450ffb5b6f1c449f5ad58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-02-25T21:52:38Z","title_canon_sha256":"bdc8a6337c8e82b65fedcc420559ff3f3d9dec9bb6b646c8b7d139a791649d29"},"schema_version":"1.0","source":{"id":"1802.09092","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.09092","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1802.09092v3","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.09092","created_at":"2026-05-17T23:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"6IKM37MKXJ52","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6IKM37MKXJ52ZHLU","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6IKM37MK","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:95c9c29df5acba10dcf26b9f4e13407a1d12d8a0c5e6ba1498613f9753d96535","target":"graph","created_at":"2026-05-17T23:41:58Z","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":"The notion of a noncommutative quasi-resolution is introduced for a noncommutative noetherian algebra with singularities, even for a non-Cohen-Macaulay algebra. If A is a commutative normal Gorenstein domain, then anoncommutative quasi-resolution of A naturally produces a noncommutative crepant resolution (NCCR) of A in the sense of Van den Bergh, and vice versa. Under some mild hypotheses, we prove that (i) in dimension two, all noncommutative quasi-resolutions of a given non-commutative algebra are Morita equivalent, and (ii) in dimension three, all noncommutative quasi-resolutions of a give","authors_text":"J.J. Zhang, X.-S. Qin, Y.-H. Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-02-25T21:52:38Z","title":"Noncommutative quasi-resolutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09092","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":"sha256:6c453b8e4f3addddf5417252ab196702ce72c871c449f38425608726b5c4235a","target":"record","created_at":"2026-05-17T23:41:58Z","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":"83e9f2f424ed08f464db15a12f3140a0d85093b997c450ffb5b6f1c449f5ad58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-02-25T21:52:38Z","title_canon_sha256":"bdc8a6337c8e82b65fedcc420559ff3f3d9dec9bb6b646c8b7d139a791649d29"},"schema_version":"1.0","source":{"id":"1802.09092","kind":"arxiv","version":3}},"canonical_sha256":"f214cdfd8aba7bac9d742fddbab16bba78eb7644c4f7e69b51ac63d405ba9db4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f214cdfd8aba7bac9d742fddbab16bba78eb7644c4f7e69b51ac63d405ba9db4","first_computed_at":"2026-05-17T23:41:58.284736Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:58.284736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jXNb59PMnfzdpepoPtIqgAA+o4pkJOcDutFPQbS10z/orXDvV0/wUmRjjNSHqRGPjOPfwSsd139WqWnhbG0aCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:58.285232Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.09092","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c453b8e4f3addddf5417252ab196702ce72c871c449f38425608726b5c4235a","sha256:95c9c29df5acba10dcf26b9f4e13407a1d12d8a0c5e6ba1498613f9753d96535"],"state_sha256":"897ecc6d71b878167066725b72f03028a603451cbc7af3c9262f34e13c7d1d6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HqSMTLqgenfwHhma1tcCvDVYgndJlK3vZfX9pQjqWnUk2I82ZgbZmIJO7RU4y/3AigHl5qUf37Vd+P7GzuesBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T12:05:38.363551Z","bundle_sha256":"4a64c1f32f22ce0015b5ad4e81f38470fd89b38a021a69ac558b8880add7ea93"}}