Möbius-band trefoil folded ribbonlength conjecture

Let $K$ be a folded ribbon trefoil knot that is topologically a Möbius band, and let $\operatorname{Rib}([K]_{\mathrm{Möb}})$ denote its infimal folded ribbonlength in the Möbius-band ribbon-equivalence class. Möbius-band trefoil folded ribbonlength conjecture. The infimal folded ribbonlength is

$$\operatorname{Rib}([K]_{\mathrm{Möb}})=5\cot(\pi/5)\leq 6.89.$$

The displayed folded ribbon trefoil provides the value $5\cot(\pi/5)$, and the conjecture asserts that this value is infimal within the topological Möbius-band class.