No-divot conjecture for limiting missing-difference probabilities

Let $\ell(k)$ be the limiting probability of exactly $k$ missing differences:

$$\ell(k)=\lim_{n\to\infty}P_n^{\mathrm{M}}(k).$$

No-divot conjecture. The limiting probabilities satisfy

$$\ell(4)>\ell(2)>\ell(6)>\ell(0)>\ell(8)>\ell(10)>\ell(12)>\cdots.$$

In other words, the sequence $\ell$ has no divots.

Earlier results in the paper compare only finitely many of these limiting probabilities. The conjecture extends the observed decay pattern beyond $\ell(12)$ and asserts that no further divots occur.