Constant Steps Are s-Composable: An Exact Interpolation Certificate for Gradient Descent

Grimmer, Shu, and Wang asked whether a balanced constant schedule is $s$-composable at every horizon. More precisely, for an integer $n\geq 1$, let $\bar{h}=1+r$, where $r\in(0,1)$ is the unique solution of $$r^n\bigl(1+n(1+r)\bigr)=1,$$ and run gradient descent for $n$ steps with normalized stepsiz