Asymptotic plausibility conjecture for shapes with r=2

A shape $(n,\kappa,r,s)$ is called plausible when it satisfies the paper's plausibility criterion for detecting whether sufficiently general ideals of that shape are plausibly generic. Asymptotic plausibility conjecture. Given $r=2$, $s>2$, and $\kappa\geq 2$, the shape $(n,\kappa,2,s)$ is plausible for all sufficiently large $n$. This conjecture concerns the asymptotic behavior of the plausibility criterion; the paper offers it based on an analysis of that criterion, while no general theorem establishing such genericity is known.