Conjecture on Fuchsian types of three Nakayama algebras

Let $N_{14}(4)$, $N_{14}(5)$, and $N_{16}(8)$ be the indicated Nakayama algebras, and let $\langle a,b,c\rangle$ denote Fuchsian type.

Fuchsian-type conjecture. The following three statements hold:

1. $N_{14}(4)$ has Fuchsian type $\langle 2,5,7\rangle$.
2. $N_{14}(5)$ has Fuchsian type $\langle 2,6,6\rangle$.
3. $N_{16}(8)$ has Fuchsian type $\langle 2,3,11\rangle$.

These cases extend the preceding classification results, but their associated singularities are complete intersections rather than hypersurfaces. Consequently, the suspension functors lack a comparably simple description, and constructing the required tilting objects remains difficult.