Kravchuk–Mazáč–Pal conjecture on the bass note spectrum

For a cocompact lattice $\Gamma$ in $G=\operatorname{PSL}_2(\mathbf{R})$, let $\lambda_1(\Gamma\backslash\mathbf{H})$ be the first Laplace eigenvalue of the compact hyperbolic $2$-orbifold $\Gamma\backslash\mathbf{H}$. The bass note spectrum is the set of all such positive eigenvalues. Kravchuk–Mazáč–Pal conjecture. The bass note spectrum is

$$(0,15.7902...]\cup\{23.0785...\}\cup\{28.0798...\}\cup\{44.8883...\},$$

where the four isolated values are the first eigenvalues of specific triangle orbifolds. The source states that almost all of this conjecture was proved in the cited work, but does not specify that every part has been resolved, so the database status remains open.