The para--Racah Hamiltonian as an exactly solvable discretization of the Pöschl--Teller box

The para--Racah Hamiltonian is the Jacobi matrix $J$ of the para--Racah polynomials, taken at the persymmetric value of their isospectral deformation parameter: a mirror--symmetric tridiagonal matrix whose spectrum is a \emph{quadratic} bi--lattice, the squares $(s+a)^2$ and $(s+c)^2$ of two interla