Ordered Ramsey conjecture for complete graphs and alternating paths

Let $K_a$ be a complete graph of order $a$ and $P_b^\mathrm{alt}$ an alternating path of order $b$. Complete-graph–alternating-path conjecture. For any $a \ge 2$ and $b \ge 3$, we have

$$R_\mathrm{ord}(K_a, P_b^\mathrm{alt}) = \left\lceil \frac{3ab - 5a}{2} \right\rceil - 2b + 5.$$

The formula is inferred from the computational comparison of ordered Ramsey numbers for complete graphs and alternating paths. The general ordered result remains open.