Walsh's conjecture on weakly regular bent functions and weighted partial difference sets

Let $p>2$ and let $f:GF(p)^n\to GF(p)$ be a weakly regular bent function corresponding to a weighted strongly regular graph via the stated analogy. Let $\mu_{ii}$ denote the diagonal intersection number for the associated weighted partial difference set, for $1\leq i\leq s$. Walsh's conjecture. One has

$$\mu_{ii}=0,\qquad 1\leq i\leq s.$$

This predicts a structural restriction on the weighted partial difference set associated with a weakly regular bent function and its weighted strongly regular graph. The supplied text gives no resolution, so the conjecture remains open.