Chinburg–Reid–Stover's surgery-prime conjecture for twist knots

Let $K$ be a hyperbolic knot in $S^3$ that fails condition $(\star)$. Let $S$ be the set of rational primes lying under a finite prime ramifying a specialization of the canonical-component quaternion algebra, and let $S_D\subseteq S$ be the set of rational primes $p$ for which some hyperbolic Dehn surgery specialization has quaternion algebra ramified at a prime above $p$.

Chinburg–Reid–Stover's conjecture. In the notation above,

$$S=S_D.$$

Chinburg–Reid–Stover conjectured that every rational prime arising from ramification in the specialized quaternion algebras is realized by a hyperbolic Dehn surgery when condition $(\star)$ fails. The supplied text gives no resolution status for this conjecture; the paper presents its results as evidence for it.