{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:VIVPQ2XZSF3QG3TMFUGYA55KKN","short_pith_number":"pith:VIVPQ2XZ","schema_version":"1.0","canonical_sha256":"aa2af86af99177036e6c2d0d8077aa537c6e0bb4f5610072f18e680014c81bae","source":{"kind":"arxiv","id":"0803.3766","version":2},"attestation_state":"computed","paper":{"title":"The Quantum McKay Correspondence for polyhedral singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Amin Gholampour, Jim Bryan","submitted_at":"2008-03-26T16:31:04Z","abstract_excerpt":"Let G be a polyhedral group, namely a finite subgroup of SO(3). Nakamura's G-Hilbert scheme provides a preferred Calabi-Yau resolution Y of the polyhedral singularity C^3/G. The classical McKay correspondence describes the classical geometry of Y in terms of the representation theory of G. In this paper we describe the quantum geometry of Y in terms of R, an ADE root system associated to G. Namely, we give an explicit formula for the Gromov-Witten partition function of Y as a product over the positive roots of R. In terms of counts of BPS states (Gopakumar-Vafa invariants), our result can be s"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0803.3766","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-03-26T16:31:04Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"2ee31576a85ca9cd7c78e5ccfb0a4bb33db7991053c2a129c480e14967f088c6","abstract_canon_sha256":"a654388d8dd1fbfb6e35772472efda0d23144365fb2df838e44b33b73e956b70"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:59.809179Z","signature_b64":"FFx1yzq/8cNfNxdMJgaGqToa2a7mQmifRj4VLpCLIYg+QJvOcP3O6P+AzXpdCxaY1WwAZkB769WOuCMJ/G2pAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa2af86af99177036e6c2d0d8077aa537c6e0bb4f5610072f18e680014c81bae","last_reissued_at":"2026-05-18T02:15:59.808629Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:59.808629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Quantum McKay Correspondence for polyhedral singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Amin Gholampour, Jim Bryan","submitted_at":"2008-03-26T16:31:04Z","abstract_excerpt":"Let G be a polyhedral group, namely a finite subgroup of SO(3). Nakamura's G-Hilbert scheme provides a preferred Calabi-Yau resolution Y of the polyhedral singularity C^3/G. The classical McKay correspondence describes the classical geometry of Y in terms of the representation theory of G. In this paper we describe the quantum geometry of Y in terms of R, an ADE root system associated to G. Namely, we give an explicit formula for the Gromov-Witten partition function of Y as a product over the positive roots of R. In terms of counts of BPS states (Gopakumar-Vafa invariants), our result can be s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.3766","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0803.3766","created_at":"2026-05-18T02:15:59.808698+00:00"},{"alias_kind":"arxiv_version","alias_value":"0803.3766v2","created_at":"2026-05-18T02:15:59.808698+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.3766","created_at":"2026-05-18T02:15:59.808698+00:00"},{"alias_kind":"pith_short_12","alias_value":"VIVPQ2XZSF3Q","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"VIVPQ2XZSF3QG3TM","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"VIVPQ2XZ","created_at":"2026-05-18T12:25:58.018023+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VIVPQ2XZSF3QG3TMFUGYA55KKN","json":"https://pith.science/pith/VIVPQ2XZSF3QG3TMFUGYA55KKN.json","graph_json":"https://pith.science/api/pith-number/VIVPQ2XZSF3QG3TMFUGYA55KKN/graph.json","events_json":"https://pith.science/api/pith-number/VIVPQ2XZSF3QG3TMFUGYA55KKN/events.json","paper":"https://pith.science/paper/VIVPQ2XZ"},"agent_actions":{"view_html":"https://pith.science/pith/VIVPQ2XZSF3QG3TMFUGYA55KKN","download_json":"https://pith.science/pith/VIVPQ2XZSF3QG3TMFUGYA55KKN.json","view_paper":"https://pith.science/paper/VIVPQ2XZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0803.3766&json=true","fetch_graph":"https://pith.science/api/pith-number/VIVPQ2XZSF3QG3TMFUGYA55KKN/graph.json","fetch_events":"https://pith.science/api/pith-number/VIVPQ2XZSF3QG3TMFUGYA55KKN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VIVPQ2XZSF3QG3TMFUGYA55KKN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VIVPQ2XZSF3QG3TMFUGYA55KKN/action/storage_attestation","attest_author":"https://pith.science/pith/VIVPQ2XZSF3QG3TMFUGYA55KKN/action/author_attestation","sign_citation":"https://pith.science/pith/VIVPQ2XZSF3QG3TMFUGYA55KKN/action/citation_signature","submit_replication":"https://pith.science/pith/VIVPQ2XZSF3QG3TMFUGYA55KKN/action/replication_record"}},"created_at":"2026-05-18T02:15:59.808698+00:00","updated_at":"2026-05-18T02:15:59.808698+00:00"}