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The fused transfer matrices are associated with nodes of the infinite dominant integral weight lattice of $s\\ell(3)$. For generic values of the crossing parameter $\\lambda$, the $T$- and $Y$-systems do not truncate. For the case $\\frac{\\lambda}{\\pi}=\\frac{(2p'-p)}{4p'}$ rational so that $x=\\mathrm{e}^{\\mathrm{i}\\lambda}$ is a root of unity, we find explicit closure relations and derive closed finite"},"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":"1905.07973","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-05-20T10:21:19Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.MP"],"title_canon_sha256":"13fd3b4302aaca6307cd5dc7916075bdb0f2eab9427d98ec43595450e7708ca5","abstract_canon_sha256":"872e37a81ec35055fa3320e532b78de8cdbb23ce39d89a5687a9d6ab75054aa0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:36:23.596725Z","signature_b64":"M2JuT4sS8abG7CxwsYAM+o1euj8bHlHQRjLmH4RvnIegFSBJO6XQE5qJWQ3fBa2aTR8NRmpL2qMnzYG+Xy47Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38a8a021d8bb9b1fd34da065ea1b0613ec9d2a39d7ccc50f2de2bdbaa862bceb","last_reissued_at":"2026-07-05T00:36:23.596299Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:36:23.596299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fusion hierarchies, $T$-systems and $Y$-systems for the dilute $A_2^{(2)}$ loop models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Alexi Morin-Duchesne, Paul A. 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