Universal identity between refined Mochizuki and Vafa–Witten formulas

For integers $(\beta_1,\beta_2,\beta_3,\beta_4)$ and $v\geq0$, let $F_v(\beta_1,\beta_2,\beta_3,\beta_4,y)$ and $G_v(\beta_1,\beta_2,\beta_3,\beta_4,y)$ be the universal functions defined in the source from the conjectural rank-three Vafa–Witten formula and the strong form of Mochizuki's formula. Universal identity conjecture. If $\beta_1\equiv\beta_2\pmod 2$, $0\leq v\leq\beta_1-3\beta_2+4\beta_4$, $\beta_3\geq\beta_4-3$, and $\beta_3\geq-1$, then

$$F_v(\beta_1,\beta_2,\beta_3,\beta_4,y)=G_v(\beta_1,\beta_2,\beta_3,\beta_4,y).$$

This conjecture asserts agreement of the two universal constructions beyond the range directly supplied by geometric examples. The source gives no resolution.