We prove that, for each fixed genus g, the portion of semigroups belonging to infinite chains in the semigroup tree approaches 0 as the genus grows to infinite. This problem has been open since 2009.

翻译：我们证明，对于每个固定的亏格g，在半群树中属于无限链的半群比例随着亏格趋于无穷而趋于0。该问题自2009年以来一直悬而未决。