The predicted virtual chi_y-genus blowup formula

Let $\Phi$ be the multiplicative class specified in Examples 3 and 3, and let $Z_a$ be the power series defined by the virtual $\chi_y$-genus blowup relation. For the generating series $Y_a(z,w)$ associated with rank-two fixed-determinant moduli spaces, with coefficients regarded as polynomials in $y$, Virtual $\chi_y$-genus conjecture. One has

$$Y_a(z,w)=Y_a(z,0)=Z_a(y,z^4).$$

This predicts that $Y_a$ is independent of $w$ and is obtained from $Z_a$ by substituting $z^4$ for its second variable. The surrounding discussion presents this as a natural prediction rather than a proved theorem; the precise definitions of the referenced examples and of $Z_a$ occur elsewhere in the paper.