The Azumaya-positive knot conjecture for L-space knots

Let $K$ be a fibered hyperbolic knot whose canonical component is Azumaya positive, meaning that the canonical component satisfies the paper's Azumaya-positivity condition. An $L$-space knot is a knot in $S^3$ admitting a positive Dehn surgery yielding an $L$-space, where an $L$-space is a rational homology $3$-sphere whose Heegaard--Floer homology has rank $|H_1(M;\mathbb{Z})|$.

Azumaya-positive knot conjecture. $K$ is not an $L$-space knot.

The conjecture is motivated by examples of Azumaya-positive fibered hyperbolic knots whose Alexander polynomials have coefficients other than $0$ and $\pm1$, whereas $L$-space knots have symmetrized Alexander polynomials with all nonzero coefficients equal to $\pm1$. The claim remains open in the supplied source.