{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DEPDLKJOQEDLKLM4O3ZREWNTJ4","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":"dd65ee8a063c436954b01486b2af699d8e8333c1b16a9acc11f60d9c5417155f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-12-03T14:16:55Z","title_canon_sha256":"8a4eac587c1e3a9cf13a433d91b6ac51a00be2c54ad8f96db2c806551c116f41"},"schema_version":"1.0","source":{"id":"1512.01084","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01084","created_at":"2026-05-18T01:24:23Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01084v2","created_at":"2026-05-18T01:24:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01084","created_at":"2026-05-18T01:24:23Z"},{"alias_kind":"pith_short_12","alias_value":"DEPDLKJOQEDL","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DEPDLKJOQEDLKLM4","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DEPDLKJO","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:4ecd07b748ffb9d55a528e4a487972b0c775d36b49c17aa7c0e5258957301047","target":"graph","created_at":"2026-05-18T01:24:23Z","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":"A root of unity limit of the $q$-deformed Virasoro algebra is considered. The $\\widehat{sl}(2)_k$ current algebra and the integral formulas of the solutions of the KZ equations can be realized by the $q$-deformed boson at the limit and an additional boson. We explicitly construct the integral representation of the four-point blocks with a $\\mathcal{K}$-operator insertion.","authors_text":"Reiji Yoshioka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-12-03T14:16:55Z","title":"The integral representation of solutions of KZ equation and a modification by $\\mathcal{K}$ operator insertion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01084","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":"sha256:3d8fa4c55fa8bbf3861f791eebcaa7f562511aa7b409c1bc4b2779b589977ceb","target":"record","created_at":"2026-05-18T01:24:23Z","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":"dd65ee8a063c436954b01486b2af699d8e8333c1b16a9acc11f60d9c5417155f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-12-03T14:16:55Z","title_canon_sha256":"8a4eac587c1e3a9cf13a433d91b6ac51a00be2c54ad8f96db2c806551c116f41"},"schema_version":"1.0","source":{"id":"1512.01084","kind":"arxiv","version":2}},"canonical_sha256":"191e35a92e8106b52d9c76f31259b34f14906a5a46173c737d5aaa6d148a5635","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"191e35a92e8106b52d9c76f31259b34f14906a5a46173c737d5aaa6d148a5635","first_computed_at":"2026-05-18T01:24:23.980998Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:23.980998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KYyyg5fMPANFz9HAP3PPu2W6nysZahAOQ5rcumS7n6zvnrEL4OT2GUJ1UWe5PRgn7NpEPqZxhdyVcZXLOXT8CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:23.981665Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01084","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d8fa4c55fa8bbf3861f791eebcaa7f562511aa7b409c1bc4b2779b589977ceb","sha256:4ecd07b748ffb9d55a528e4a487972b0c775d36b49c17aa7c0e5258957301047"],"state_sha256":"7952aef35598d5a3a0ef6758d94d69ecfe3e2060e8f4a361426fc9613a778241"}