Allen's unique minimal-point conjecture for torus knots

Let $K$ be a torus knot, and let $\gamma_4(K)$ denote its smooth 4-genus. A realizable pair $(e,h)$ records the normal Euler number and first Betti number of a smooth surface in $B^4$ bounded by $K$. Allen's unique minimal-point conjecture. Every torus knot has exactly one realizable pair of the form

$$(e,\gamma_4(K)).$$

Equivalently, all torus knots have a single realizable minimal point. The paper's abstract says that $T(2,5)$ and $T(2,9)$ bound smooth Möbius bands whose double branched covers are negative definite, giving counterexamples to Allen's Conjectures 1.6 and 1.8; this conjecture is identified in the source as Allen's Conjecture 1.8 and is therefore refuted.