The lower bound for the Mina-margin endpoint

Let $\lambda$ be the constant for which the set of Mina-margin values of positive ABMN solutions is $[\lambda,\lambda^{-1}]$, with the established upper bound $\lambda\leq 0.999904$. Lower-bound conjecture. The value of $\lambda$ is at least $0.999902$. This would narrow the admissible Mina-margin interval to a very small range near $1$; no resolution is supplied here.