Conjecture on linear independence of L-space knots

An $L$-space knot is a knot admitting a nontrivial Dehn surgery yielding an $L$-space. Let the knots be regarded as elements of the knot concordance group.

L-space-knot linear-independence conjecture. The set of $L$-space knots in $S^3$ is linearly independent in the knot concordance group. In particular, if $L$-space knots $K_0$ and $K_1$ are concordant, then $K_0=K_1$.

The source presents this as a potentially more manageable conjecture than Baker's conjecture and does not provide a resolution.