Lecuona's topological sliceness conjecture for 3-stranded pretzel knots

For an odd integer $a\geq 3$, let $P(a,-a-2,-\frac{(a+1)^2}{2})$ denote the corresponding $3$-stranded pretzel knot. A knot is topologically slice if it bounds a locally flat, embedded disk in $D^4$.

Lecuona's conjecture. For every odd integer $a\geq 3$, the $3$-stranded pretzel knot

$$P(a,-a-2,-\frac{(a+1)^2}{2})$$

is not topologically slice.

This concerns the infinite family left unresolved by earlier slice-ribbon results. The paper states the conjecture as an open question, while proving that four-fifths of the remaining knots in the family are not slice.