{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VNKHTBUFKYMYXXC2TD32S3MYL6","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":"1c659732c80025ae084eb373df523e276ab17aefe9ad8cd6f92f81e73ddf8657","cross_cats_sorted":["hep-th","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-21T04:55:23Z","title_canon_sha256":"22b02a5ba76350ff47559ea18b4110f8ea47850b2c7661e7637821593e70ab41"},"schema_version":"1.0","source":{"id":"1106.4088","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4088","created_at":"2026-05-18T04:18:44Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4088v3","created_at":"2026-05-18T04:18:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4088","created_at":"2026-05-18T04:18:44Z"},{"alias_kind":"pith_short_12","alias_value":"VNKHTBUFKYMY","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VNKHTBUFKYMYXXC2","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VNKHTBUF","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:294fed246ec318635227f1c2514e6469acc95ba8c2be23ead00a59a1392b518f","target":"graph","created_at":"2026-05-18T04:18:44Z","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 study the representation theory of the Ding-Iohara algebra $\\calU$ to find $q$-analogues of the Alday-Gaiotto-Tachikawa (AGT) relations. We introduce the endomorphism $T(u,v)$ of the Ding-Iohara algebra, having two parameters $u$ and $v$. We define the vertex operator $\\Phi(w)$ by specifying the permutation relations with the Ding-Iohara generators $x^\\pm(z)$ and $\\psi^\\pm(z)$ in terms of $T(u,v)$. For the level one representation, all the matrix elements of the vertex operators with respect to the Macdonald polynomials are factorized and written in terms of the Nekrasov factors for the $K$","authors_text":"A. Hoshino, B. Feigin, H. Awata, J. Shiraishi, M. Kanai, S. Yanagida","cross_cats":["hep-th","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-21T04:55:23Z","title":"Notes on Ding-Iohara algebra and AGT conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4088","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":"sha256:006407039289aa3e9d3cf95ed2e97bf85ef9b4616dffbadfb6656033c8d48496","target":"record","created_at":"2026-05-18T04:18:44Z","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":"1c659732c80025ae084eb373df523e276ab17aefe9ad8cd6f92f81e73ddf8657","cross_cats_sorted":["hep-th","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-21T04:55:23Z","title_canon_sha256":"22b02a5ba76350ff47559ea18b4110f8ea47850b2c7661e7637821593e70ab41"},"schema_version":"1.0","source":{"id":"1106.4088","kind":"arxiv","version":3}},"canonical_sha256":"ab5479868556198bdc5a98f7a96d985fb7187a4ce828322435f7f3e93bba7b85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab5479868556198bdc5a98f7a96d985fb7187a4ce828322435f7f3e93bba7b85","first_computed_at":"2026-05-18T04:18:44.338838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:44.338838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bt2g/AZJ5NrHn7nukE335hGv+k4DW1XhNZFdaIwoWlfr3BhcRgmym0wU20q5L5pIQ6hOwoKjVxy4qkUZZF29Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:44.339408Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.4088","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:006407039289aa3e9d3cf95ed2e97bf85ef9b4616dffbadfb6656033c8d48496","sha256:294fed246ec318635227f1c2514e6469acc95ba8c2be23ead00a59a1392b518f"],"state_sha256":"7fb77c41b2092937e29b998cfcf6873ccb50bf8579df517b283d048d2e176fe6"}