The Hopf-invariant formulas for fibered knots

Let $K$ be a knot, let $\genusK$ denote its genus, let $\hopfK$ denote its Hopf invariant, let $\el(K)$ denote the integer-valued exponent invariant in the leading term of $F_K$, let $\Delta_K(y)$ denote its Alexander polynomial, and let $\an{n}{K}$ denote its Habiro coefficients. Hopf-invariant formulas conjecture. The formulas

$$\el(K)=\genusK-\hopfK$$

and

$$\hopfK = \genusK-\sum_{i=0}^{2\genusK-1} \frac{1}{i!}\frac{\partial^i\Delta_K^3(y)}{\partial y^i}\biggr|_{y=0} \frac{\partial \an{2\genusK-i}{K}}{\partial q}\biggr|_{q=1}$$

hold for all fibered knots. These formulas relate the leading behavior of $F_K$ to the Hopf invariant and to Habiro coefficients. The paper proves them for homogeneous braid knots and fibered knots of at most 12 crossings, leaving the assertion for all fibered knots open.