{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:DIXZQCCNAFWHEOKTBVDUHXESRD","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":"a5f48d0a270c033040bac78f660c781e829d0c1d8f8b99a24dc69f891043fe4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-03-20T12:56:50Z","title_canon_sha256":"2a429e5afccb7ccdd0c80835538274b596e92006baf6d3045c46b6a893a7ae9e"},"schema_version":"1.0","source":{"id":"0803.2990","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.2990","created_at":"2026-05-18T03:55:37Z"},{"alias_kind":"arxiv_version","alias_value":"0803.2990v2","created_at":"2026-05-18T03:55:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.2990","created_at":"2026-05-18T03:55:37Z"},{"alias_kind":"pith_short_12","alias_value":"DIXZQCCNAFWH","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"DIXZQCCNAFWHEOKT","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"DIXZQCCN","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:e393cab022f3f0b798fdeb1d0af28d876169b4914f4110c01ae6d82004ed40f3","target":"graph","created_at":"2026-05-18T03:55:37Z","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":"We propose a three dimensional generalization of the geometric McKay correspondence described by Gonzales-Sprinberg and Verdier in dimension two. We work it out in detail when G is abelian and C^3/G has a single isolated singularity. More precisely, we show that the Bridgeland-King-Reid derived category equivalence induces a natural geometric correspondence between irreducible representations of G and subschemes of the exceptional set of G-Hilb (C^3). This correspondence appears to be related to Reid's recipe.","authors_text":"Sabin Cautis, Timothy Logvinenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-03-20T12:56:50Z","title":"A derived approach to geometric McKay correspondence in dimension three"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.2990","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:b2d64de4cd0125e3efd46a8ca32a2a2ceda1bddd25c43782c99be01bfec8f1b4","target":"record","created_at":"2026-05-18T03:55:37Z","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":"a5f48d0a270c033040bac78f660c781e829d0c1d8f8b99a24dc69f891043fe4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-03-20T12:56:50Z","title_canon_sha256":"2a429e5afccb7ccdd0c80835538274b596e92006baf6d3045c46b6a893a7ae9e"},"schema_version":"1.0","source":{"id":"0803.2990","kind":"arxiv","version":2}},"canonical_sha256":"1a2f98084d016c7239530d4743dc9288f0efdf7d80700f07f6df9c3d7d5f14d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a2f98084d016c7239530d4743dc9288f0efdf7d80700f07f6df9c3d7d5f14d6","first_computed_at":"2026-05-18T03:55:37.797861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:37.797861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t6bBPB+i2XGofkmU2GrgoXlB9NXQQzLYTZU12u0dVHqBNPVEZ07BbYSOczY566rVk4h8Brk6C4OAMAg+mBTfBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:37.798575Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.2990","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2d64de4cd0125e3efd46a8ca32a2a2ceda1bddd25c43782c99be01bfec8f1b4","sha256:e393cab022f3f0b798fdeb1d0af28d876169b4914f4110c01ae6d82004ed40f3"],"state_sha256":"7bfb7915a48b4727f7646348f6fdf5b45387de9c3c7fafe26391946c742c52e2"}