Alternative general global maximum conjecture for the rank-two likelihood model

Let $n\ge2$ and let $s,t$ satisfy $0<s\le t$. Let $L(P)$ be the likelihood function defined in the source by equation (newLP). Alternative likelihood conjecture. The matrix

$$P=\begin{pmatrix}\frac{2s}{n^2(s+t)}&\frac1{n^2}&\cdots&\frac1{n^2}&\frac{2t}{n^2(s+t)}\\frac1{n^2}&\frac1{n^2}&\cdots&\frac1{n^2}&\frac1{n^2}\\vdots&\vdots&\vdots&\vdots&\vdots\\frac1{n^2}&\frac1{n^2}&\cdots&\frac1{n^2}&\frac1{n^2}\\frac{2t}{n^2(s+t)}&\frac1{n^2}&\cdots&\frac1{n^2}&\frac{2s}{n^2(s+t)}\end{pmatrix}$$

is a global maximum for $L(P)$.

This is another proposed extension of the likelihood maximization result to arbitrary $n$. The supplied context does not define $L(P)$ or establish the claim, so its resolution is unclear.