{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:UICLOX6CFAJLSASCN4V6KYGQO3","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":"c89ff23bd0c20fe7a5a80fc5dbbaf8ed549bf17bd38b18377aed65871af3cc71","cross_cats_sorted":["math.CA","math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"1993-10-14T15:19:41Z","title_canon_sha256":"bb5d0ead8125573876a400a429f8e8fb276935116a42325f2cfcc991957e01ec"},"schema_version":"1.0","source":{"id":"hep-th/9310083","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9310083","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9310083v2","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9310083","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"pith_short_12","alias_value":"UICLOX6CFAJL","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"UICLOX6CFAJLSASC","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"UICLOX6C","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:545b4fd193a6a8809ceb212624a56324b7c9831858da73299a922e7bac4ae600","target":"graph","created_at":"2026-05-18T01:06:04Z","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 consider correlation functions for the Wess-Zumino-Witten model on the torus with the insertion of a Cartan element; mathematically this means that we consider the function of the form $F=\\Tr (\\Phi_1 (z_1)\\ldots \\Phi_n (z_n)q^{-\\d}e^{h})$ where $\\Phi_i$ are intertwiners between Verma modules and evaluation modules over an affine Lie algebra $\\ghat$, $\\d$ is the grading operator in a Verma module and $h$ is in the Cartan subalgebra of $\\g$. We derive a system of differential equations satisfied by such a function. In particular, the calculation of $q\\frac{\\d} {\\d q} F$ yields a parabolic sec","authors_text":"Alexander Kirillov Jr, Pavel Etingof","cross_cats":["math.CA","math.QA"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1993-10-14T15:19:41Z","title":"Representations of affine Lie algebras, parabolic differential equations, and Lame functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9310083","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:d665ac691bfb23f070829f0b6fa32e86e45176154f36153f4c3cbf16b71cde75","target":"record","created_at":"2026-05-18T01:06:04Z","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":"c89ff23bd0c20fe7a5a80fc5dbbaf8ed549bf17bd38b18377aed65871af3cc71","cross_cats_sorted":["math.CA","math.QA"],"license":"","primary_cat":"hep-th","submitted_at":"1993-10-14T15:19:41Z","title_canon_sha256":"bb5d0ead8125573876a400a429f8e8fb276935116a42325f2cfcc991957e01ec"},"schema_version":"1.0","source":{"id":"hep-th/9310083","kind":"arxiv","version":2}},"canonical_sha256":"a204b75fc22812b902426f2be560d076e94bf2cd86019d338a6bcbabb51f12cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a204b75fc22812b902426f2be560d076e94bf2cd86019d338a6bcbabb51f12cd","first_computed_at":"2026-05-18T01:06:04.755787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:04.755787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6tT2lUhBzk6mDRinQKO+nOXAcWyJrOIAWU6Xp605IMX+MLApX1cSaizDXaaeKHmFm2cgmOgUaa3/BMB7a/0SDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:04.756472Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9310083","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d665ac691bfb23f070829f0b6fa32e86e45176154f36153f4c3cbf16b71cde75","sha256:545b4fd193a6a8809ceb212624a56324b7c9831858da73299a922e7bac4ae600"],"state_sha256":"5a06c8a40d1206a8e58998951c474b3a88c90ca0fbc707ded68712ac220fc6bb"}