Conjecture on connected sums of torus knots concordant to L-space knots

A torus knot is a knot of the form $T(p,q)$ on the standard torus in the three-sphere, and a connected sum is the knot operation denoted by $\#$. An $L$-space knot is a knot admitting a positive Dehn surgery yielding an $L$-space, and two knots are concordant if they cobound a smoothly embedded annulus in $S^3\times[0,1]$. A positive torus knot is a torus knot $T(p,q)$ with positive parameters, with the orientation convention used for positive torus knots.

Concordance conjecture for sums of torus knots. If a connected sum of possibly several torus knots is concordant to an $L$-space knot, then it is concordant to a positive torus knot.

This conjecture generalizes the paper's result for differences of multiples of pairs of positive torus knots and the theorem stated immediately before it. It asks whether concordances from arbitrary connected sums of torus knots to $L$-space knots can occur only through positive torus knots; the source does not state a resolution.