The instanton L-space surgery conjecture for knots

Let $K\subset S^3$ be a knot, let $p/q\in\mathbb{Q}\setminus\{0\}$, and suppose that $I^\sharp(S^3_{p/q}(K);\mathbb{Z})$ has no $2$-torsion. An instanton L-space is a rational homology sphere $Y$ satisfying

$$\dim I^\sharp(Y;\mathbb{C})=|H_1(Y;\mathbb{Z})|.$$

Instanton L-space surgery conjecture. Under these assumptions, $S^3_{p/q}(K)$ must be an instanton L-space, meaning

$$\dim I^\sharp(S^3_{p/q}(K);\mathbb{C})=|H_1(S^3_{p/q}(K);\mathbb{Z})|=|p|,$$

and $K$ must be an instanton L-space knot. Consequently, $K$ is fibered and strongly quasi-positive, and $|p/q|>2g(K)-1$. This conjecture extends the paper's integral-torsion criterion from nonzero integral surgeries to arbitrary nonzero rational surgeries; the stated consequences are supported by the cited results, while the conjectural implication itself remains open.