Five-or-more-half-twist Möbius-band aspect-ratio conjecture

An embedded paper Möbius band with $5$ or more half-twists is a paper Möbius band embedded in space with at least five half-twists; its aspect ratio is the ratio of its length to its width. Five-or-more-half-twist Möbius-band conjecture. The infimal aspect ratio is

$$3\sqrt{3}.$$

Known results give lower-complexity benchmarks, including aspect ratio $\sqrt{3}$ for an embedded paper Möbius band and aspect ratio $3$ for a three-half-twist example, while the infimal value for five or more half-twists remains open.