  Building on a strategy introduced in arXiv:1706.05364, we present exact
analytic expressions for all the singlet eigenstates and eigenvalues of the
simplest non-linear ($n=2, d=3$) gauged Gurau-Witten tensor model. This solves
the theory completely. The ground state eigenvalue is $-2\sqrt{14}$ in suitable
conventions. This matches the result obtained for the ground state energy in
the ungauged model, via brute force diagonalization on a computer. We find that
the leftover degeneracies in the gauged theory, are only partially accounted
for by its known discrete symmetries, indicating the existence of previously
unidentified "hidden" global symmetries in the system. We discuss the spectral
form factor, the beginnings of chaos, and the distinction between theories with
$SO(n)$ and $O(n)$ gaugings. Our results provide the complete analytic solution
of a non-linear gauge theory in 0+1 dimensions, albeit for a specific value of
$N$. A summary of the main results in this paper were presented in the
companion letter arXiv:1802.02502.
