The symmetric Riemann vs. MZ derivatives conjecture

Let $D_n^s$ be the $n$-th symmetric Riemann differentiation, and let a symmetric MZ differentiation be an $n$-th symmetric generalized Riemann differentiation satisfying the symmetric Peano equivalence condition. The symmetric Riemann vs. MZ derivatives conjecture. For $n\geq5$, the $n$-th symmetric Riemann differentiation $D_n^s$ is not a symmetric MZ differentiation. The conjecture was disproved for $n=3,4$ and proved for $n=5,6,7,8$; it remains open for $n\geq9$.