The fractional BP upper-bound conjecture for the permanent at gamma equals minus one-half

Let $p$ be a non-negative matrix, and let $Z_{o\text{-}f}^{(\gamma)}(p)$ denote the fractional BP partition-function estimate at parameter $\gamma$. In particular, write $Z_{o\text{-}f}^{\gamma=-1/2}(p)$ for its value at $\gamma=-1/2$. Fractional BP upper-bound conjecture. For any non-negative $p$,

$$\operatorname{perm}(p)\leq Z_{o\text{-}f}^{\gamma=-1/2}(p).$$

This is presented as a reformulation of the preceding exponential BP-bound conjecture, motivated by the doubly degenerate block example where the bound is attained. The source gives no resolution of this inequality.