Conjecture on maximal k-rank of binary forms

Let a binary form of degree $kd$ be expressed as a sum of $k$-th powers of binary forms of degree $d$, and let $\mathrm{rk}^{\max}_k(2,kd)$ denote the maximum of the resulting $k$-ranks over all such forms. Maximal binary k-rank conjecture. For every integer $k\geq 2$,

$$\mathrm{rk}^{\max}_k(2,kd)=k.$$

This conjecture concerns the extremal, rather than generic, behavior of decompositions of binary forms. The supplied text gives no resolution status.