Equality conjecture for Welschinger invariants of real projective three-space

Let $d$ be a positive integer, and let $W_{\mathbb{R}P^3}(d,l)$ denote the Welschinger invariant of degree $d$ with the parameter $l$ specifying the real-point constraint. Equality conjecture. For every positive integer $d$, one has

$$W_{\mathbb{R}P^3}(d,d-1)=W_{\mathbb{R}P^3}(d,d).$$

The computed values in the paper support the equality for the displayed degrees; the conjecture asks whether it holds for all positive degrees.