The classification conjecture for five-dimensional 2-isospectral lens orbifolds

A $5$-dimensional lens orbifold is a lens orbifold of dimension $5$, and two such orbifolds are $\{2\}$-isospectral when their spectra on $2$-forms agree. They are non-isometric if no isometry relates them.

The five-dimensional $\{2\}$-isospectrality conjecture. The families of non-isometric $\{2\}$-isospectral $5$-dimensional lens orbifolds are precisely given by pairs

$$\begin{cases} L(8t;4,t,3t)\\ L(8t;8,t,3t) \end{cases}$$

for $t\geq1$ odd.

The claim is supported by computational data. The paper sketches how the displayed families can be checked for $2$-isospectrality and notes that proving they exhaust all such examples is more difficult; it also observes that they are not $0$- or $1$-isospectral.