Brown–Schwartz conjecture on the 3‑half‑twist Möbius band

Establish whether the infimal aspect ratio of an embedded paper Möbius band of width 1 with three half‑twists equals 3.

Background

The introduction summarizes known exact results for small twist numbers and cites a specific conjecture by Brown and Schwartz for the case of a 3‑half‑twist embedded paper Möbius band. This conjecture proposes a precise optimal aspect ratio value of 3, extending the pattern observed in previously solved cases.

Confirming or refuting this conjecture would provide a definitive benchmark for the 3‑twist case and inform the broader understanding of how minimal aspect ratios behave with increasing twist count.