Global bound for the constructed maximal commutative system

Let $n=4k+9$ with $k\geq 2$, and define

$$K_n:=\frac{|\mathcal{C}|}{2^{n-2}},$$

where $\mathcal{C}$ is the constructed maximal commutative algebraic system. $K_n$ bound conjecture. Is $K_n<1$ for all $n=4k+9$ with $k\geq 2$? Numerical verification in the source establishes the inequality for $n<1000$. The conjecture extends that verified finite range to every $n=4k+9$ with $k\geq 2$.