The upper-bound conjecture for the density of zero Möbius values

Let $d_n$ be the probability that the principal Möbius function value $\mu[\pi]$ is zero for a uniformly random permutation $\pi$ of size $n$.

Upper-bound conjecture. The values $d_n$ are bounded from above by $0.6040$.

This conjecture proposes a uniform numerical upper bound for the density of zeros of the Möbius function on permutations. The paper presents it on the basis of computational data through size $12$; no resolution is supplied here.