Projected-limit conjecture for twisted q-characters

Fix i\frac{in I}, a\frac{inmathbb{C}^*, a Weyl group element w\frac{in W, and a monomial $m$ independent of $k$. Let $M_k$ be the Kirillov–Reshetikhin monomial specified in the source, and let $\chi_q^w(L(M_km))$ be the $w$-normalized $q$-character. Define projected $w$-normalized $q$-characters by applying the projection that replaces $A_{i,aq^n}^{1}{}^{1}$ by $e^{17falpha_i}$ for $n<R$ and leaves it unchanged for n\frac{ge R. Projected-limit conjecture. The projected $w$-normalized $q$-characters converge as $k\to+\infty$, and their limits converge as $R\to-\infty$.