No Ties conjecture for residue-class biases in indivisible partitions

Let $k,t\geq 2$ be coprime, and let $\prec_{k,t}$ be the ordering on $\mathbb{Z}/t\mathbb{Z}$ defined by the eventual comparison of the quantities $D_k^\times(r,t;n)$: namely, $r\prec_{k,t}s$ when $D_k^\times(r,t;n)<D_k^\times(s,t;n)$ for sufficiently large $n$. No Ties conjecture. The ordering $\prec_{k,t}$ is a total ordering on $\mathbb{Z}/t\mathbb{Z}$. This conjecture is solved in the current paper by the theorem proving that the relevant bias parameters are distinct for distinct residue classes.