{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XUUDSGA4NHVF4FBNOLDUFTN25D","short_pith_number":"pith:XUUDSGA4","canonical_record":{"source":{"id":"1611.04137","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-13T13:46:15Z","cross_cats_sorted":["math.AC","math.AG","math.RA"],"title_canon_sha256":"feecfc6214f2253d9141bd6923d3eb76c8bb8bb6732291ed45284c6cd674e020","abstract_canon_sha256":"f9d130c0bb4f415da21797ff3bcf1398a81e4c25a052b4375c669c10eeb4f569"},"schema_version":"1.0"},"canonical_sha256":"bd2839181c69ea5e142d72c742cdbae8da019eb460c8cf027c3319934a96fe85","source":{"kind":"arxiv","id":"1611.04137","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04137","created_at":"2026-05-18T00:59:17Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04137v1","created_at":"2026-05-18T00:59:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04137","created_at":"2026-05-18T00:59:17Z"},{"alias_kind":"pith_short_12","alias_value":"XUUDSGA4NHVF","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XUUDSGA4NHVF4FBN","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XUUDSGA4","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XUUDSGA4NHVF4FBNOLDUFTN25D","target":"record","payload":{"canonical_record":{"source":{"id":"1611.04137","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-13T13:46:15Z","cross_cats_sorted":["math.AC","math.AG","math.RA"],"title_canon_sha256":"feecfc6214f2253d9141bd6923d3eb76c8bb8bb6732291ed45284c6cd674e020","abstract_canon_sha256":"f9d130c0bb4f415da21797ff3bcf1398a81e4c25a052b4375c669c10eeb4f569"},"schema_version":"1.0"},"canonical_sha256":"bd2839181c69ea5e142d72c742cdbae8da019eb460c8cf027c3319934a96fe85","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:17.411312Z","signature_b64":"W4+0Cu3iv5PmBdA1fuArV7DbEZ9RW5ZHBkrZMuwLhNDaLZI915fONqO9CNqa0hfmg6M5s6Xs34b4tV1vPKnsAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd2839181c69ea5e142d72c742cdbae8da019eb460c8cf027c3319934a96fe85","last_reissued_at":"2026-05-18T00:59:17.410635Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:17.410635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.04137","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:59:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+fq+kx+uxTipHy2RjFdabUIiTfNDgJw58xD62xBZkcQ8ksgnMblLCiqsRYYzVb3pocwwghNTolM5PqNRBMSVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T00:32:46.046025Z"},"content_sha256":"51fd0b161d5f6801d1fb0fd847c23429813fe7c876aca13f520c12bd7d6d1b24","schema_version":"1.0","event_id":"sha256:51fd0b161d5f6801d1fb0fd847c23429813fe7c876aca13f520c12bd7d6d1b24"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XUUDSGA4NHVF4FBNOLDUFTN25D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gorenstein modifications and $\\mathbb{Q}$-Gorenstein rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG","math.RA"],"primary_cat":"math.RT","authors_text":"Hailong Dao, Michael Wemyss, Osamu Iyama, Ryo Takahashi","submitted_at":"2016-11-13T13:46:15Z","abstract_excerpt":"Let $R$ be a Cohen--Macaulay normal domain with a canonical module $\\omega_R$. It is proved that if $R$ admits a noncommutative crepant resolution (NCCR), then necessarily it is $\\mathbb{Q}$-Gorenstein. Writing $S$ for a Zariski local canonical cover of $R$, then a tight relationship between the existence of noncommutative (crepant) resolutions on $R$ and $S$ is given. A weaker notion of Gorenstein modification is developed, and a similar tight relationship is given. There are three applications: non-Gorenstein quotient singularities by connected reductive groups cannot admit an NCCR, the cent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04137","kind":"arxiv","version":1},"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":"2026-05-18T00:59:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T6KKfqIbsFyGW9YNa+rqPYJixgqH6M8bW9Wdi/H16B2diWV1oAhnt2lULhEzDOLMedFgwEZ+t/zhs8zT+c1eBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T00:32:46.046398Z"},"content_sha256":"2524a6a32e56feb2b1abffa9a42a7476db344566bab509a552552eae46ce8749","schema_version":"1.0","event_id":"sha256:2524a6a32e56feb2b1abffa9a42a7476db344566bab509a552552eae46ce8749"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XUUDSGA4NHVF4FBNOLDUFTN25D/bundle.json","state_url":"https://pith.science/pith/XUUDSGA4NHVF4FBNOLDUFTN25D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XUUDSGA4NHVF4FBNOLDUFTN25D/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":"2026-06-22T00:32:46Z","links":{"resolver":"https://pith.science/pith/XUUDSGA4NHVF4FBNOLDUFTN25D","bundle":"https://pith.science/pith/XUUDSGA4NHVF4FBNOLDUFTN25D/bundle.json","state":"https://pith.science/pith/XUUDSGA4NHVF4FBNOLDUFTN25D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XUUDSGA4NHVF4FBNOLDUFTN25D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XUUDSGA4NHVF4FBNOLDUFTN25D","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":"f9d130c0bb4f415da21797ff3bcf1398a81e4c25a052b4375c669c10eeb4f569","cross_cats_sorted":["math.AC","math.AG","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-13T13:46:15Z","title_canon_sha256":"feecfc6214f2253d9141bd6923d3eb76c8bb8bb6732291ed45284c6cd674e020"},"schema_version":"1.0","source":{"id":"1611.04137","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04137","created_at":"2026-05-18T00:59:17Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04137v1","created_at":"2026-05-18T00:59:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04137","created_at":"2026-05-18T00:59:17Z"},{"alias_kind":"pith_short_12","alias_value":"XUUDSGA4NHVF","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XUUDSGA4NHVF4FBN","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XUUDSGA4","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:2524a6a32e56feb2b1abffa9a42a7476db344566bab509a552552eae46ce8749","target":"graph","created_at":"2026-05-18T00:59:17Z","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":"Let $R$ be a Cohen--Macaulay normal domain with a canonical module $\\omega_R$. It is proved that if $R$ admits a noncommutative crepant resolution (NCCR), then necessarily it is $\\mathbb{Q}$-Gorenstein. Writing $S$ for a Zariski local canonical cover of $R$, then a tight relationship between the existence of noncommutative (crepant) resolutions on $R$ and $S$ is given. A weaker notion of Gorenstein modification is developed, and a similar tight relationship is given. There are three applications: non-Gorenstein quotient singularities by connected reductive groups cannot admit an NCCR, the cent","authors_text":"Hailong Dao, Michael Wemyss, Osamu Iyama, Ryo Takahashi","cross_cats":["math.AC","math.AG","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-13T13:46:15Z","title":"Gorenstein modifications and $\\mathbb{Q}$-Gorenstein rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04137","kind":"arxiv","version":1},"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":"sha256:51fd0b161d5f6801d1fb0fd847c23429813fe7c876aca13f520c12bd7d6d1b24","target":"record","created_at":"2026-05-18T00:59:17Z","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":"f9d130c0bb4f415da21797ff3bcf1398a81e4c25a052b4375c669c10eeb4f569","cross_cats_sorted":["math.AC","math.AG","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-11-13T13:46:15Z","title_canon_sha256":"feecfc6214f2253d9141bd6923d3eb76c8bb8bb6732291ed45284c6cd674e020"},"schema_version":"1.0","source":{"id":"1611.04137","kind":"arxiv","version":1}},"canonical_sha256":"bd2839181c69ea5e142d72c742cdbae8da019eb460c8cf027c3319934a96fe85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd2839181c69ea5e142d72c742cdbae8da019eb460c8cf027c3319934a96fe85","first_computed_at":"2026-05-18T00:59:17.410635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:17.410635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W4+0Cu3iv5PmBdA1fuArV7DbEZ9RW5ZHBkrZMuwLhNDaLZI915fONqO9CNqa0hfmg6M5s6Xs34b4tV1vPKnsAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:17.411312Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04137","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51fd0b161d5f6801d1fb0fd847c23429813fe7c876aca13f520c12bd7d6d1b24","sha256:2524a6a32e56feb2b1abffa9a42a7476db344566bab509a552552eae46ce8749"],"state_sha256":"97c629f63e9194bac5c0694333bfd2f751cdfe5ba4120d4a0104e64a8be97615"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xJxxV6BMpzdfuw5QMVTcQOxzz8ygLdb+aJHuZdIrV1YTS2Twq5k6ktbGTnEbBqHbVFO/LWP4tpa/++tPW9OtCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T00:32:46.048494Z","bundle_sha256":"78f95661a4f56dc92c7b94216ac842bf9ee1675ce54b60c403798171e1233637"}}