Jones-Conway polynomial detection conjecture for cables of non-isotopic simple knots

Let $K_1$ and $K_2$ be non-isotopic simple knots. For integers $p$ and $q$, the cable-detection conjecture asserts that there exist numbers $p$ and $q$ such that the $(p,q)$-cables of $K_1$ and $K_2$ have distinct Jones–Conway polynomials.

This conjecture asks whether suitable cabling always enables the Jones–Conway polynomial to distinguish any two non-isotopic simple knots. The source's e-print correction replaces “prime” by “simple”; the claim remains open.