The unique minimal point conjecture for torus knots

Let $K$ be a torus knot, let $\gamma_4(K)$ denote its smooth nonorientable 4-genus, and let $(e,h)$ denote the normal Euler number and nonorientable genus of a surface bounded by $K$. A pair of the form $(e,\gamma_4(K))$ is called a minimal point when it is realizable. The unique minimal point conjecture. All torus knots have a single realizable minimal point. In other words, for a torus knot $K$, there is exactly one realizable pair of the form $(e,\gamma_4(K))$. This conjecture asserts uniqueness of the normal Euler number among realizable surfaces attaining the nonorientable 4-genus, a question concerning the geography of nonorientable surfaces bounded by knots.