{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BBPA7IAEZEOR3NXYTPPH6WEFFI","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":"34c4022d638eacd75cdc899baa131f3b15a980e53d4422c929f817df6ff59cb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-10-25T19:56:30Z","title_canon_sha256":"72233152cf0da01144f0a434ff4f925707bff8ef489dc0047d5da13cc5129c4c"},"schema_version":"1.0","source":{"id":"1110.5628","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5628","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5628v3","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5628","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"pith_short_12","alias_value":"BBPA7IAEZEOR","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BBPA7IAEZEOR3NXY","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BBPA7IAE","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:9d3f3d2bd95f0a2adba93f809d2fe4c594475f0ba6e7cbf027544c1023125c56","target":"graph","created_at":"2026-05-18T03:29:14Z","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":"In this paper we study the correspondence between the $\\hat{\\textrm{su}}(n)_{k}\\oplus \\hat{\\textrm{su}}(n)_{p}/\\hat{\\textrm{su}}(n)_{k+p}$ coset conformal field theories and $\\mathcal{N}=2$ SU(n) gauge theories on $\\mathbb{R}^{4}/\\mathbb{Z}_{p}$. Namely we check the correspondence between the SU(2) Nekrasov partition function on $\\mathbb{R}^{4}/\\mathbb{Z}_{4}$ and the conformal blocks of the $S_{3}$ parafermion algebra (in $S$ and $D$ modules). We find that they are equal up to the U(1)-factor as it was in all cases of AGT-like relations. Studying the structure of the instanton partition funct","authors_text":"G. M. Tarnopolsky, M. N. Alfimov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-10-25T19:56:30Z","title":"Parafermionic Liouville field theory and instantons on ALE spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5628","kind":"arxiv","version":3},"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":"sha256:25a06bf0149a48b36bc624eb90bc87829cf3ddedd1a2362577dbaaa0f00129e6","target":"record","created_at":"2026-05-18T03:29:14Z","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":"34c4022d638eacd75cdc899baa131f3b15a980e53d4422c929f817df6ff59cb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2011-10-25T19:56:30Z","title_canon_sha256":"72233152cf0da01144f0a434ff4f925707bff8ef489dc0047d5da13cc5129c4c"},"schema_version":"1.0","source":{"id":"1110.5628","kind":"arxiv","version":3}},"canonical_sha256":"085e0fa004c91d1db6f89bde7f58852a2fa8744d6266e548bfe23b8d7c724339","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"085e0fa004c91d1db6f89bde7f58852a2fa8744d6266e548bfe23b8d7c724339","first_computed_at":"2026-05-18T03:29:14.064122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:14.064122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SjKxgKykCOZWHh42pLavvM1vdzaeurMhQlA83DeqHtiJxwkVCvMz5lCiciiVM/3tN8rtoXNy8U2CG7Yh7GLiCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:14.064768Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.5628","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25a06bf0149a48b36bc624eb90bc87829cf3ddedd1a2362577dbaaa0f00129e6","sha256:9d3f3d2bd95f0a2adba93f809d2fe4c594475f0ba6e7cbf027544c1023125c56"],"state_sha256":"ed5dea1a41b4512ed592ba89ca306e94ce07f47b7127d53f15c18b49f0e89fee"}