6 problems

Matúš's conjecture. There exists a distribution $p$ in the zero set of $J_{\mathcal C}$ such that all joint probabilities of $p$ are rational.

Asymptotic counting conjecture. The number of compositional graphoids which are representable by $n$ discrete random variables is asymptotically

Gaussoid-axioms sufficiency conjecture. If $a \perp\!\!\!\perp b \mid C$ holds for every covariance matrix $\Sigma \in \mathcal{M}_{\mathcal{G}, i \perp\!\!\!\perp j\mid K}$, then…

Matúš's rational-point conjecture. For any discrete conditional independence model $\mathcal{C}$, there exists a distribution

Two-global-statement realizability conjecture. All minimal gaussoid extensions of at most two global conditional-independence statements are realizable.

Conditional-expectation Markov category conjecture. Such a Markov category exists, with conditionals in the sense of the paper's definition, and these conditionals are given by con…