Characterization of L-space knots by conjugate-slope and cofinal detection properties

Let $K$ be a nontrivial knot in $S^3$. The conjugate-slope property and the cofinal detection property are the properties defined in the paper. L-space knot characterization conjecture. $K$ is an L-space knot if and only if it has both the conjugate-slope property and the cofinal detection property. If true, this would characterize L-space knots through group-ordering properties and yield a systematic approach to obstructing left-orderability of Dehn fillings; the equivalence is open in the supplied text.