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For every $\\ell,m\\ge2$, we have \\[ \\mathcal R_{\\ell,m}=\\mathcal U(\\Sigma_{\\ell,m}), \\] with polynomial frozen coefficients, and $\\Sigma_{\\ell,m}$ admits a reddening sequence. The theta basis extends across the frozen boundary exactly for para"},"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":"2608.00963","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-08-02T03:22:24Z","cross_cats_sorted":["math.AC","math.CO"],"title_canon_sha256":"9cbe3a9ea1a736412e5ab743dd1d74f08c1836dfbec5e7575adcc9b2cd9f7c63","abstract_canon_sha256":"092b4e23d86d31728753ef36d9c18a7e7f412da14b764116fcedd2264d72d27f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T01:55:57.822660Z","signature_b64":"v7j7y/BMJmfIO2WxaUnLGUoQvyDy5HgKedB/39eT5e42RPOH+F1RIF7o7wGgMxemaQNxcAxWnsQnWrrsVjm/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"242b72b305973a8f013fcc0b329cb91b96be93729fefd848dd9d46dc317fd0fc","last_reissued_at":"2026-08-04T01:55:57.821115Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T01:55:57.821115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cluster Algebras for Bosonic Plethysm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CO"],"primary_cat":"math.RT","authors_text":"Jiarui Fei, Yelin Fan","submitted_at":"2026-08-02T03:22:24Z","abstract_excerpt":"Let $\\Bbbk$ be an algebraically closed field of characteristic zero, let $V=\\Bbbk^\\ell$ and $W=\\Bbbk^m$, and set \\[ \\mathcal R_{\\ell,m}=\\operatorname{Sym}(\\operatorname{Sym}^2V\\otimes W)^{U_V}. \\] We construct an explicit skew-symmetrizable seed $\\Sigma_{\\ell,m}$ by restricting and folding the determinantal seed for the flagged $m$-arrow Kronecker quiver. For every $\\ell,m\\ge2$, we have \\[ \\mathcal R_{\\ell,m}=\\mathcal U(\\Sigma_{\\ell,m}), \\] with polynomial frozen coefficients, and $\\Sigma_{\\ell,m}$ admits a reddening sequence. 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