4 problems

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

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.