Muffin problem one-third lower-bound conjecture

Let $f(m,s)$ be the largest possible size of the smallest assigned muffin piece, where $m$ is the number of muffins and $s$ the number of students.

One-third lower-bound conjecture. For all $m>s\geq 2$,

$$f(m,s)\geq 1/3.$$

The conjecture is solved: the paper states that Cui et al. (2018) proved it, and gives a simpler proof.