  A finite non-classical framework for physical theory is described which
challenges the conclusion that the Bell Inequality has been shown to have been
violated experimentally, even approximately. This framework postulates the
universe as a deterministic locally causal system evolving on a measure-zero
fractal-like geometry $I_U$ in cosmological state space. Consistent with the
assumed primacy of $I_U$, and $p$-adic number theory, a non-Euclidean (and
hence non-classical) metric $g_p$ is defined on cosmological state space, where
$p$ is a large but finite Pythagorean prime. Using number-theoretic properties
of spherical triangles, the inequalities violated experimentally are shown to
be $g_p$-distant from the CHSH inequality, whose violation would rule out local
realism. This result fails in the singular limit $p=\infty$, at which $g_p$ is
Euclidean. Broader implications are discussed.
