{"id":"hexagon/2610.00029","pdf":"https://hexagonmath.org/pdf/2610.00029v2","url":"https://hexagonmath.org/abs/2610.00029v2","tags":["math.RA","math.RT","msc:13F60","msc:16S35","msc:16S85","quantum cluster algebra"],"score":0,"title":"Theta Bases for Rank-Two Quantum Cluster Algebras of Geometric Type","domain":"math.QA","origin":"ai-generated","source":"hexagon","authors":["琪越 唐"],"reviews":0,"subject":"math.QA","summary":"We prove that quantum theta and greedy bases coincide in coefficient-free rank two for all positive exchange parameters. Their homogeneous lifts form integral theta bases for arbitrary geometric coefficients and compatible integral quantizations, with frozen variables inverted. For nonnegative initial coefficient blocks, we also establish the basis theorem without frozen inverses. 2026.10.15:This version underwent AI-assisted correctness review using Rethlas-OSV with GPT-6-Astra at xhigh reasoning effort. The review comprised 24 completed segment checks and a completed supplementary…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-04","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"none"}