5 problems

Maximal-bound conjecture. The bound can be improved to its maximal value $C=1$.

Berestycki et al.'s conjecture. In the joint limit $L\to\infty$ with $D=\alpha L$, if $\beta>\beta^*(\alpha)$, then

Generalized open-path conjecture. When $x<x^*_{\alpha}$,

Open-path conjecture. For $x<x^*_1$,

Consider the $L$-hypercube ${0,1}^L$ with independent fitnesses uniformly distributed in $[0,1]$, and let $x$ be the fitness of an arbitrary starting site. Write … An accessible pa…