{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5HOF6WMSD6RSP6JDOH7ST77ZFR","short_pith_number":"pith:5HOF6WMS","canonical_record":{"source":{"id":"1609.04143","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-14T06:06:30Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"f3a38893289708e2e0f79b67931e6cd9de6cf83a08425d013148e4e5b7fab03f","abstract_canon_sha256":"0c31bb02285f57fbc9156ee48a1523c64f6cb00782dc9ebfee255a21fdedec97"},"schema_version":"1.0"},"canonical_sha256":"e9dc5f59921fa327f92371ff29fff92c64841ca48c5c4f16fd0c0cc41fc6bbdd","source":{"kind":"arxiv","id":"1609.04143","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04143","created_at":"2026-05-18T01:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04143v1","created_at":"2026-05-18T01:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04143","created_at":"2026-05-18T01:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"5HOF6WMSD6RS","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5HOF6WMSD6RSP6JD","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5HOF6WMS","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5HOF6WMSD6RSP6JDOH7ST77ZFR","target":"record","payload":{"canonical_record":{"source":{"id":"1609.04143","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-14T06:06:30Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"f3a38893289708e2e0f79b67931e6cd9de6cf83a08425d013148e4e5b7fab03f","abstract_canon_sha256":"0c31bb02285f57fbc9156ee48a1523c64f6cb00782dc9ebfee255a21fdedec97"},"schema_version":"1.0"},"canonical_sha256":"e9dc5f59921fa327f92371ff29fff92c64841ca48c5c4f16fd0c0cc41fc6bbdd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:38.888366Z","signature_b64":"OxJ0L/+28v0+bZCPVunogJs11sL+/mcsVq+l99L+VuoRU5sy6ocFYCFprkgsx2ypkfI7+qUPWaISDjLZQn8jCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9dc5f59921fa327f92371ff29fff92c64841ca48c5c4f16fd0c0cc41fc6bbdd","last_reissued_at":"2026-05-18T01:04:38.887678Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:38.887678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.04143","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":"2026-05-18T01:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d5xlcPqYrOW1LJLblCcnSIjHQMvyZu3LfACwc30NCe2VXIeVqUSHFkMsTcrGlUZHTbVNGoSLKq9Rm9PiEqPXDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:02:25.884630Z"},"content_sha256":"18688c85cd645c0e1d6f8c5e4ea4a5251756d8c44094fe08c164f64ebf5bb9d8","schema_version":"1.0","event_id":"sha256:18688c85cd645c0e1d6f8c5e4ea4a5251756d8c44094fe08c164f64ebf5bb9d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5HOF6WMSD6RSP6JDOH7ST77ZFR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extended McKay correspondence for quotient surface singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Akira Ishii, Iku Nakamura","submitted_at":"2016-09-14T06:06:30Z","abstract_excerpt":"Let $G$ be a finite subgroup of $\\mbox{GL}(2)$ acting on $\\mathbf{A}^2\\setminus\\{0\\}$ freely. The $G$-orbit Hilbert scheme $G\\mbox{-Hilb}(\\mathbf{A}^2)$ is a minimal resolution of the quotient $\\mathbf{A}^2/G$. We determine the generator sheaf of the ideal defining the universal $G$-cluster over $G\\mbox{-Hilb}(\\mathbf{A}^2)$, which somewhat strengthens the well-known McKay correspondence for a finite subgroup of $\\mbox{SL}(2)$. We also study the quiver structure of $G\\mbox{-Hilb}(\\mathbf{A}^2)$ at every $G$-cluster $O_{Z_y}=O_{\\mathbf{A}^2}/I_y$ in terms of a collection of sort of minimal $G$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04143","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":"2026-05-18T01:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gMfwHVhLS9pHTm9F0iCWtUPxC3CPLYw/CQhbw8YvMD+4EmycTXDh0Qa5HAyOahdvPRjfpEMSxUnA84g8R7UkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:02:25.885010Z"},"content_sha256":"188e602938f7de4633db15ba90cbf002838827f7e8657aba1cddcec8d3ced471","schema_version":"1.0","event_id":"sha256:188e602938f7de4633db15ba90cbf002838827f7e8657aba1cddcec8d3ced471"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5HOF6WMSD6RSP6JDOH7ST77ZFR/bundle.json","state_url":"https://pith.science/pith/5HOF6WMSD6RSP6JDOH7ST77ZFR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5HOF6WMSD6RSP6JDOH7ST77ZFR/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":"2026-05-28T20:02:25Z","links":{"resolver":"https://pith.science/pith/5HOF6WMSD6RSP6JDOH7ST77ZFR","bundle":"https://pith.science/pith/5HOF6WMSD6RSP6JDOH7ST77ZFR/bundle.json","state":"https://pith.science/pith/5HOF6WMSD6RSP6JDOH7ST77ZFR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5HOF6WMSD6RSP6JDOH7ST77ZFR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5HOF6WMSD6RSP6JDOH7ST77ZFR","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":"0c31bb02285f57fbc9156ee48a1523c64f6cb00782dc9ebfee255a21fdedec97","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-14T06:06:30Z","title_canon_sha256":"f3a38893289708e2e0f79b67931e6cd9de6cf83a08425d013148e4e5b7fab03f"},"schema_version":"1.0","source":{"id":"1609.04143","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04143","created_at":"2026-05-18T01:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04143v1","created_at":"2026-05-18T01:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04143","created_at":"2026-05-18T01:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"5HOF6WMSD6RS","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5HOF6WMSD6RSP6JD","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5HOF6WMS","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:188e602938f7de4633db15ba90cbf002838827f7e8657aba1cddcec8d3ced471","target":"graph","created_at":"2026-05-18T01:04:38Z","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 $G$ be a finite subgroup of $\\mbox{GL}(2)$ acting on $\\mathbf{A}^2\\setminus\\{0\\}$ freely. The $G$-orbit Hilbert scheme $G\\mbox{-Hilb}(\\mathbf{A}^2)$ is a minimal resolution of the quotient $\\mathbf{A}^2/G$. We determine the generator sheaf of the ideal defining the universal $G$-cluster over $G\\mbox{-Hilb}(\\mathbf{A}^2)$, which somewhat strengthens the well-known McKay correspondence for a finite subgroup of $\\mbox{SL}(2)$. We also study the quiver structure of $G\\mbox{-Hilb}(\\mathbf{A}^2)$ at every $G$-cluster $O_{Z_y}=O_{\\mathbf{A}^2}/I_y$ in terms of a collection of sort of minimal $G$-","authors_text":"Akira Ishii, Iku Nakamura","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-14T06:06:30Z","title":"Extended McKay correspondence for quotient surface singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04143","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":"sha256:18688c85cd645c0e1d6f8c5e4ea4a5251756d8c44094fe08c164f64ebf5bb9d8","target":"record","created_at":"2026-05-18T01:04:38Z","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":"0c31bb02285f57fbc9156ee48a1523c64f6cb00782dc9ebfee255a21fdedec97","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-14T06:06:30Z","title_canon_sha256":"f3a38893289708e2e0f79b67931e6cd9de6cf83a08425d013148e4e5b7fab03f"},"schema_version":"1.0","source":{"id":"1609.04143","kind":"arxiv","version":1}},"canonical_sha256":"e9dc5f59921fa327f92371ff29fff92c64841ca48c5c4f16fd0c0cc41fc6bbdd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9dc5f59921fa327f92371ff29fff92c64841ca48c5c4f16fd0c0cc41fc6bbdd","first_computed_at":"2026-05-18T01:04:38.887678Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:38.887678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OxJ0L/+28v0+bZCPVunogJs11sL+/mcsVq+l99L+VuoRU5sy6ocFYCFprkgsx2ypkfI7+qUPWaISDjLZQn8jCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:38.888366Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.04143","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18688c85cd645c0e1d6f8c5e4ea4a5251756d8c44094fe08c164f64ebf5bb9d8","sha256:188e602938f7de4633db15ba90cbf002838827f7e8657aba1cddcec8d3ced471"],"state_sha256":"2d0b931cb17ab0794e818762106653b4c7d0c92b4bddba38d1b6562552982071"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dXkhI9KOOY0M8Mpzz54kD/xpkpDZ2xXw7zy0N2IZzS27QeiQ4lPSOonbgVPVdP1aYVesFKqSpokqzYuZCaiZBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:02:25.888835Z","bundle_sha256":"cabb7c37f774bdc212a1d7318a07aeac723bc8f2cd6a4642b9deadb789f18272"}}