The sloshing eigenvalue counting asymptotic conjecture for a triangular prism

Let $N(c3)$ be the eigenvalue counting function of the sloshing problem, and let $N^e(c3)$ and $N^s(c3)$ denote respectively the counting functions for edge-wave and surface-wave quasi-eigenvalues. Counting asymptotic conjecture.

$$N(c3)=N^e(c3)+N^s(c3)+o(c3).$$

The previously established lower bound gives $N(c3)\geq N^e(c3)+N^s(c3)+o(c3)$. Equality is proved in the special cases $b1=b2=\frac{\pi}{2}$ and $b1=b2=\frac{\pi}{4}$, while numerical evidence supports the conjecture for other angles; the missing ingredient is a quasi-eigenvalue close to every real sloshing eigenvalue.