The quarter-bias conjecture for bit-commitment coin-flipping protocols

Let a strong coin-flipping protocol based on bit-commitment be any protocol in the family formally defined in Section~, and let its bias be the maximum excess of either party's cheating probability over $1/2$. Quarter-bias conjecture. Every such protocol has bias at least

$$\frac{1}{4}.$$

The conjecture is based on computational searches over the parameterized protocol family, including zoning-in tests around protocols with bias $1/4$; resolving whether all protocols in the family satisfy this bound remains an open problem.