Szemberg's Pell-equation lower bound for Seshadri constants

Let $X$ be a smooth projective surface with $\rho(X)=1$, let $L$ be the ample generator of $N^1(X)$, and write $(L^2)=N$. Assume that $N$ is not a square. Let $(p_0,q_0)$ be the primitive solution of the Pell equation

$$y^2-dx^2=1.$$

Szemberg's conjecture. For a very general point $x\in X$,

$$\epsilon(L;x)\geqslant \frac{p_0N}{q_0}.$$

This is a proposed lower bound for Seshadri constants on surfaces of Picard number one. The source attributes it to Szemberg but supplies no evidence of resolution.