The Gaussian vs. MZ derivatives conjecture

Let $D_{\mathcal{A}}$ be an $n$-th generalized Riemann differentiation at a point $x$. An MZ differentiation is one for which, for every function $f$ that is $n-1$ times Peano differentiable at $x$, $f$ is $n$ times Peano differentiable at $x$ if and only if $f$ is $\mathcal{A}$-differentiable at $x$. An $n$-th Gaussian differentiation is the $n$-th generalized Riemann differentiation whose nodes are either $0,1,q,q^2,\ldots,q^{n-1}$ or $1,q,q^2,\ldots,q^n$, where $q\neq 0,\pm1$. The Gaussian vs. MZ derivatives conjecture. Each MZ differentiation is a Gaussian differentiation. This conjecture was proved for $n=1,2$ and remains open for $n\geq3$; the paper under consideration presents counterexamples to it.