Solution-count conjecture for Vinogradov systems modulo $N$

Let $\gamma(t)=(t,t^2,\ldots,t^n)$ and define $\Phi(\vec t)=\sum_{i=1}^n\gamma(t_i)$. For $\vec t\in[\mathbb Z/N\mathbb Z]^n$, let $\mathbf N(\vec t;N)$ be the number of $\vec s\in[\mathbb Z/N\mathbb Z]^n$ satisfying $\Phi(\vec s)=\Phi(\vec t)$. Use $|t_j-t_k|$ for the least nonnegative representative of the difference's absolute value in the source's ring metric. Solution-count conjecture for Vinogradov systems modulo $N$. For all $\varepsilon>0$ there exists a constant $C_{\varepsilon,n}>0$ such that

$$\mathbf N(\vec t;N)\leq\min\left\{C_{\varepsilon,n}N^{\varepsilon+n(n-1)/2}\prod_{1\leq j<k\leq n}|t_j-t_k|^{-1},\,N^n\right\}.$$

This conjecture is suggested by comparison with the Euclidean Jacobian estimate and would control the multiplicities in the discrete convolution argument; the source does not establish it.