6 problems

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…

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

A LUBF-gaussoid is a gaussoid in the exceptional class denoted by LUBF; let $n$ be its dimension. Single-exponential growth conjecture. There is a single exponential upper bound fo…

Four-symbol tropical realizability conjecture. All tropical gaussoids for $n=4$ are realizable; equivalently, the square trinomials and edge trinomials are a tropical basis for…

Quadratic generation conjecture. The ideal $J_n$ is generated by its quadrics, listed explicitly in Theorem.

All-quadrics compatibility conjecture. Every gaussoid is compatible with all quadrics in $J_n$, not just trinomials.