The upper-bound conjecture for diameters of small resolutions of line arrangements

Let $d$ be a positive integer and let $\mathcal R$ be a real small resolution of a line arrangement of degree $d$. A diameter is a real diameter of the resolved real-algebraic curve.

Diameter upper-bound conjecture. The number of diameters of $\mathcal R$ does not exceed

$$\binom{d}{2}+2\binom{d}{2}(d-2)+4\binom{\binom{d}{2}}{2}=\frac{1}{2}d^4-3d^2+\frac{5}{2}d.$$

The claim proposes a universal upper bound for diameters obtainable from small resolutions of line arrangements. The supplied text gives no evidence that this bound has been proved or disproved.