In recent work. we presented the construction of a family of difference equations associated with the Stieltjes continued fraction expansion of a certain function on a hyperelliptic curve of genus $g$. As well as proving that each such discrete system is an integrable map in the Liouville sense. we also showed it to be an algebraic completely integrable system. https://macorners.shop/product-category/snow-globe-shaped-acrylic-ornament/