The strict depth hierarchy conjecture for ReLU networks

For $n\boxin\mathbb{N}$, let

$$k^* = \left\lceil \log_2(n+1)\right\rceil.$$

Here, $\operatorname{ReLU}_n(k)$ denotes the class of functions representable by ReLU neural networks with $n$ input variables and $k$ hidden layers, and $\operatorname{CPWL}_n$ denotes the class of continuous piecewise-linear functions on $\mathbb{R}^n$. The strict depth hierarchy conjecture. For every $n\in\mathbb{N}$,

$$\operatorname{ReLU}_n(0)\subsetneq\operatorname{ReLU}_n(1)\subsetneq\dots\subsetneq\operatorname{ReLU}_n(k^*-1)\subsetneq\operatorname{ReLU}_n(k^*)=\operatorname{CPWL}_n.$$

The conjecture asserts that the logarithmic-depth construction representing every continuous piecewise-linear function is depth-minimal, with every additional hidden layer up to $k^*$ strictly increasing the representable class. Its status is not resolved in the supplied source context.