  Boyle and Turok's $CPT$-symmetric universe model posits that the universe was
symmetric at the Big Bang, addressing numerous problems in both cosmology and
the Standard Model of particle physics. We extend this model by considering the
symmetric conditions at the end of the Universe, following Lasenby et al. by
imposing constraints on the allowed perturbation modes. These constrained modes
conflict with the integer wave vectors required by the global spatial geometry
in a closed universe. To resolve this conflict, only specific values of
curvature are permissible, and in particular the curvature density is
constrained to be $\Omega_K \in \{-0.014, -0.009, -0.003, \ldots\}$, consistent
with Planck observations.
