Hyperbolic spherical space form surgery conjecture

Let $K$ be a hyperbolic knot in $S^3$, and let $p>0$ be an integer such that the $p$-surgery on $K$ is a spherical space form of $\mathbf{T}$-, $\mathbf{O}$-, or $\mathbf{I}$-type. Hyperbolic spherical space form surgery conjecture. Then $K$ is one of the knots in the table of hyperbolic knots. This conjecture proposes that the hyperbolic knots admitting these integral spherical space form surgeries are exactly those listed in the paper.