Miller–Wong conjecture on the odd invariant of smooth 2-knots

Let $F$ be a smooth $2$-knot, let $n(F)$ denote its odd Khovanov invariant, and let $\Sigma(F)$ denote the branched double-cover associated to $F$. Miller–Wong's conjecture. For every smooth $2$-knot,

$$n(F)=\lvert H_1(\Sigma(F);\mathbb{Z})\rvert.$$

The conjecture generalizes the theorem for ribbon $2$-knots stated earlier in the paper. More recently, Spyropoulos, Vidyarthi, and Zhang proved the conjecture in general, so it is solved.