R. V. Gurjar and M. Miyanishi [Affine surfaces with $\bar {\kappa}\leq 1$, Algebraic geometry and commutative algebra, in Honor of Masayoshi Nagata, Vol. I, 99-124 (1988) ZBL0707.14015] gave a classification of smooth affine surfaces of logarithmic Kodaira dimension zero, whose coordinate ring is factorial and has trivial units. G. Freudenburg et al. [``Smooth factorial affine surfaces of logarithmic Kodaira dimension zero with trivial units'', https://arxiv.org/abs/1910.03494] identified a gap in this classification, which was closed in Tomasz Pełka and Paweł Raźny, Classification of smooth factorial affine surfaces of Kodaira dimension zero with trivial units, ZBL07383176 who classified an additional infinite series of such surfaces.