{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:P5DT2CPXGQV3F5BXCHREHURBDQ","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":"3760a64c33740afd787522c4c60ebb4ee94efa3e2c85983b1ffa8b9cbe86a877","cross_cats_sorted":["math.AG","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-05-21T04:57:59Z","title_canon_sha256":"ed20f598cd64fb6d304d5365de7a2ca40c7902dddf5f78f4c590ea43414e11b2"},"schema_version":"1.0","source":{"id":"1205.4486","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4486","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4486v2","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4486","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"P5DT2CPXGQV3","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"P5DT2CPXGQV3F5BX","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"P5DT2CPX","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:a3e5922272cf3f7a8b2ed324f86d3a8ec7c4e7120211aec6bdaa20d524678663","target":"graph","created_at":"2026-05-18T03:12:35Z","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 noetherian normal domain. We investigate when $R$ admits a faithful module whose endomorphism ring has finite global dimension. This can be viewed as a non-commutative desingularization of $\\Spec(R)$. We show that the existence of such modules forces stringent conditions on the Grothendieck group of finitely generated modules over $R$. In some cases those conditions are enough to imply that $\\Spec(R)$ has only rational singularities.","authors_text":"Charles Vial, Hailong Dao, Osamu Iyama, Ryo Takahashi","cross_cats":["math.AG","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-05-21T04:57:59Z","title":"Non-commutative resolutions and Grothendieck groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4486","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":"sha256:89b81728cdf5d5797c39ff4f34326652c6993bbe6ca5de3800e9a9478e56195f","target":"record","created_at":"2026-05-18T03:12:35Z","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":"3760a64c33740afd787522c4c60ebb4ee94efa3e2c85983b1ffa8b9cbe86a877","cross_cats_sorted":["math.AG","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-05-21T04:57:59Z","title_canon_sha256":"ed20f598cd64fb6d304d5365de7a2ca40c7902dddf5f78f4c590ea43414e11b2"},"schema_version":"1.0","source":{"id":"1205.4486","kind":"arxiv","version":2}},"canonical_sha256":"7f473d09f7342bb2f43711e243d2211c0713b936dd590c02355762a83d87cd2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f473d09f7342bb2f43711e243d2211c0713b936dd590c02355762a83d87cd2d","first_computed_at":"2026-05-18T03:12:35.186477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:35.186477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1PfCbQaEEvJvx0cFpdSuGCDsXjYwE2s9YZmStKOzXt/i/yu22a4b5vqVROphDz8mgH4+gQYFlxKds/mJLZbXCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:35.187218Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4486","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89b81728cdf5d5797c39ff4f34326652c6993bbe6ca5de3800e9a9478e56195f","sha256:a3e5922272cf3f7a8b2ed324f86d3a8ec7c4e7120211aec6bdaa20d524678663"],"state_sha256":"a3eccc720d217f2fafef14549e9c414bf21427ea099eac5f7f6ad80782e6630f"}