Monotonicity conjecture for the length of real projective spaces

Let $\operatorname{\mathbb{R}P}^n$ denote real projective $n$-space, and let its length mean the invariant defined in the paper. Length monotonicity conjecture. The length of

$$\operatorname{\mathbb{R}P}^n$$

is an increasing function of $n$. The statement is presented as a conjecture in the paper, but the author notes that it has since been proved.