Tightness conjecture for gradient descent with variable mid-range stepsizes

Let $f\in\mathcal{F}_{\mu,L}$ with $\mu\in(-\infty,0)$, and consider $N$ gradient-descent iterations from $x_0$ with stepsizes satisfying $\gamma_iL\in[1,\gbari[1]]$ for $i=0,\dots,N-1$. Variable-mid-range-stepsize tightness conjecture. The convergence-rate bound from the preceding theorem is tight:

$$\max_{f\in\mathcal{F}_{\mu,L};\,x_0}\frac{1}{2L}\min_{0\leq i\leq N}\{\|\nabla f(x_i)\|^2\} = \frac{f(x_0)-f_*}{1+\sum_{i=0}^{N-1}\gamma_iL\frac{(2-\gamma_iL)(2-\gamma_i\mu)}{2-\gamma_iL-\gamma_i\mu}}.$$

This claim would establish exact worst-case convergence rates in the nonconstant mid-range stepsize regime. The paper says it is supported by numerical verification of the interpolation conditions, but gives no proof, so it remains open.