5 problems

Small-cube conjecture. There is a unitary basis $L$ such that

The cyclic-quadrilateral non-Ramsey conjecture. This cyclic quadrilateral is not Ramsey. The paper proves that this quadrilateral does not embed into any finite transitive set, and…

Cyclic-quadrilateral conjecture. There exists a cyclic quadrilateral that is not subtransitive.

Product conjecture. For every positive integer $k$, there exists a positive integer $n$ such that some scaling of $X^n$ is $k$-Ramsey for $X$.

The transitive-set conjecture. A finite set $X\subset\mathbb R^n$ is Ramsey if and only if it is congruent to a subset of a finite transitive set.