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We show that certain connection coefficients for solutions of the associated linear problem coincide with the $Q$-function of the quantum sine-Gordon $(\\alpha>0)$ or sinh-Gordon $(\\alpha<-1)$ models."},"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":"1003.5333","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-03-28T01:03:31Z","cross_cats_sorted":["cond-mat.str-el","hep-th","math.MP"],"title_canon_sha256":"a289f29e2bcf415158d5b21398f1f50e08c52908b9aa342387cb429ce256d9c7","abstract_canon_sha256":"90395f22054c20223af3cb2f8b436e3c8b1227bbc0b292b992b1965c98889b66"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:26.442168Z","signature_b64":"MbVuwOTmpV9L0WXyYIrtEK9rlD93n4CzEmc711D4Nx6NOy63Bc4UGmmYFUIOKb2CAvqLNTg1a7eNb++jkR6/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e06e79d272d216838c350cccacefe2d06797ff6f848ca84326766023fa1535d0","last_reissued_at":"2026-05-18T02:24:26.441587Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:26.441587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum Sine(h)-Gordon Model and Classical Integrable Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"A.B. 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