Chapman's conjecture on a Legendre-symbol determinant

Let $p$) be an odd prime, let $\varepsilon_p$ be the fundamental unit of $\mathbb{Q}(\sqrt{p})$, and let $h(p)$ be the class number of $\mathbb{Q}(\sqrt{p})$. Write

$$\varepsilon_p^{(2-(2/p))h(p)}=a_p'+b_p'\sqrt{p},$$

with $a_p',b_p'\in\mathbb{Q}$. Chapman's conjecture.

$$\det\left[\left(\frac{j-i}{p}\right)\right]_{1\le i,j\le (p+1)/2}=\begin{cases}-a_p'&\text{if }p\equiv1\pmod4,\\1&\text{otherwise.}\end{cases}$$

This conjecture concerns the connection between determinants of Legendre-symbol matrices and arithmetic invariants of real quadratic fields. The supplied source gives no resolution status.