7 problems

Critical survival-probability conjecture. Under this condition,

Let $\eta$ be an integrable random variable taking values in $\{1,2,\ldots\}$ with $m=\mathbf{E}(\eta)>1$, and define the generalized Derrida–Retaux process by … where the…

Critical generating-function asymptotics conjecture. As $n\to\infty$, for $s\in(0,m)$ with $s\ne1$,

Critical moment-asymptotics conjecture. Then

Conditional geometric-limit conjecture. Conditionally on $X_n\ne0$, the random variable $X_n$ converges weakly to a random variable $Y_\infty$ satisfying

Positive-dimensional recursive model conjecture. If some positive-dimensional model $M\models T$ is recursive, then all models of $T$ are recursively presentable.

Recursive-spectrum trichotomy conjecture.