Equality of the minimal and maximal travelling-wave speeds

Let $\underline{c}\leq\overline{c}$ be the speed bounds defined by Theorem. Speed-threshold conjecture.

$$\underline{c}=\overline{c}.$$

The conjecture asserts that the interval of admissible speed thresholds collapses to a single value, consistent with the numerical observations for KPP, monostable, and bistable nonlinearities in the favourable area. The provided text does not establish this equality analytically.