The $9_{46}$ odd-index transformed $F$-factor conjecture

Let $9_{46}$ be the pretzel knot $(3,3,-3)$, and let $F_i$ denote its $i$th $F$-factor. Define $F_i^*$ by applying the transformation $A\mapsto Aq^2$ to $F_i$ and then multiplying by $A^2/q^4$; equivalently,

$$F_i^*=\frac{A^2}{q^4}F_i(Aq^2,q).$$

For odd positive integers $i>1$, the quotient $F_i/(1+A^2q^{2(i-1)})$ is therefore defined by the preceding divisibility conjecture.

The $9_{46}$ transformed-factor conjecture.

$$q^2(q^{2(i-1)}-1)\mid \frac{F_i}{1+A^2q^{2(i-1)}}-F^*_{i-1}.$$

This has been verified in the paper for odd integers $3\leq i\leq 7$ and is proposed as a general pattern that may help derive arbitrary $F$-factor formulas.