Schäffer's girth duality conjecture for normed spaces

Let $X$ be a finite-dimensional normed space, with unit sphere consisting of the points of norm one, and let $X^*$ be its dual normed space. The girth of $X$ is the infimum of the lengths of all closed, rectifiable, centrally symmetric curves on its unit sphere.

Schäffer's girth duality conjecture. The girth of $X$ equals the girth of $X^*$.

The conjecture concerns the systolic geometry of the projectivized unit sphere and its invariance under duality. The paper's abstract says that symplectic and Finsler geometry settle it, so the conjecture is solved in this source.