The coefficient-pattern conjecture for cable knots of the figure-eight knot

Let $K_r=C_{(r,2)}(\bm{4_1})\subseteq S^3$ be the family of cable knots from the preceding conjecture, with $r>8$ odd and monic Alexander polynomial. Let $\{f_m(q)\}$ be the coefficient functions, partitioned into $\{f_t^+(q)\}_{t\in I^+}$ and $\{f_w^-(q)\}_{w\in I^-}$. Coefficient-pattern conjecture. Every nonzero $f_m(q)$ has an odd number of terms, and the exponent of $q$ changes by one between consecutive terms. Moreover, for every $v\in I^-$, the coefficients of $f_v^-(q)$ agree up to sign with those of $f_{v-2r}^+(q)$. This refines the preceding sign-classification conjecture with a precise index shift and term-spacing pattern; the source gives no resolution status.