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The systems I-IV can be used to compute minimal affinizations with weights of the form $\\lambda_1 \\omega_1 + \\lambda_2 \\omega_2 + \\lambda_3 \\omega_3$, where at least one of $\\lambda_1$, $\\lambda_2$, $\\lambda_3$ are zero. Using the systems I-IV, we compute the characters of the restr"},"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":"1305.2098","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-05-09T14:05:17Z","cross_cats_sorted":[],"title_canon_sha256":"a4b90a0113da9405dd55e12e00184f5a50339fae19682d48afa46d215539cc23","abstract_canon_sha256":"a38c13e595dd376dd6fdbc42c46bd8b390b82a648446bf230008aa2d1eff41c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:42.225597Z","signature_b64":"3ZMZEgKqVq6p1ZHdiPGdfHmgP8Ul8bhRrMduDd8rPTKaKcvs6t0JL0ufF0THnxQWWwnQ2GrnZqNVHCSYyQNEAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05b94cba45fd9fa57b36b34e5ae1fb93f7c668acded99bc5aebd807eb846561b","last_reissued_at":"2026-05-18T00:40:42.224830Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:42.224830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the extended T-system of type $C_3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Jian-Rong Li","submitted_at":"2013-05-09T14:05:17Z","abstract_excerpt":"We continue the study of extended T-systems of quantum affine algebras. We find a sub-system of the extended T-system of the quantum affine algebra $U_q \\hat{\\mathfrak{g}}$ of type $C_3$. The sub-system consisting of four systems which are denoted by I, II, III, and IV. Each of the systems I, II, III, IV is closed. The systems I-IV can be used to compute minimal affinizations with weights of the form $\\lambda_1 \\omega_1 + \\lambda_2 \\omega_2 + \\lambda_3 \\omega_3$, where at least one of $\\lambda_1$, $\\lambda_2$, $\\lambda_3$ are zero. 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