3 problems

Almost-everywhere entry conjecture. For Lebesgue-almost every point in $\triangle$, the region $U$ can be reached after finitely many iterations of the $\mathbb{R}^3(e,13,e)$ TRIP…

Full-measure conjecture. There is a subset of $\triangle$ of full Lebesgue measure on which condition (I') or condition (II') is satisfied.

Finite-family Hermite matrix conjecture. There is a family of multidimensional continued fractions spanned by finitely many multidimensional continued fraction algorithms such that