Ordered Ramsey conjecture for monotone cycles and alternating paths

Let $C_a^\mathrm{mon}$ be a monotone cycle of order $a$ and $P_b^\mathrm{alt}$ an alternating path of order $b$. Monotone-cycle–alternating-path conjecture. For any $a \ge 3$ and $b \ge 2$, we have

$$R_\mathrm{ord}(C_a^\mathrm{mon}, P_b^\mathrm{alt}) = \left\lceil \left(a - \frac{1}{2}\right)(b - 1) \right\rceil.$$

The conjecture is based on the limited computational data reported for monotone cycles versus alternating paths. No general proof is given, so the formula remains open.