O's spectral conjecture for edge-connectivity of regular graphs

Let $G$ be a $d$-regular simple graph. For integers $d$ and $t$, define

$$\rho(d,t)=\begin{cases} \frac{d-4 + \sqrt{(d+4)^2-8t}}{2}, & \text{when } t \text{ is odd}, \\ \frac{d-3 + \sqrt{(d+3)^2-8t}}{2}, & \text{when } t \text{ is even}.\end{cases}$$

O's conjecture. For $t\geq 3$, if

$$\lambda_2(G)<\rho(d,t),$$

then $\kappa'(G)\geq t+1$. This conjecture extends known spectral sufficient conditions for higher edge-connectivity of regular simple graphs; the supplied text does not state whether it has been proved or disproved.