Catalan correction-factor formula for the enumerative Euler class

Let $n\geq 2$, let $V$ be the vector bundle and let $\sigma=\alpha\wedge\beta$ be the section considered in the paper. Write

$$e(V,\sigma)=\frac{c(n-1)-i(n)}{2}(\langle 1\rangle+\langle -1\rangle)+i(n)\langle 1\rangle,$$

where

$$c(n-1)=\frac{(2n-2)!}{n!(n-1)!}$$

is the $(n-1)$st Catalan number and $i(n)$ is a correction factor depending only on $n$. Catalan correction-factor conjecture. For every $n\geq 2$, the displayed formula holds. The formula generalizes the paper's enumerative Euler-class computation and is motivated by the signed degrees of real Wronski maps; the correction factor is not determined here.