  Although the notion of superdeterminism can, in principle, account for the
violation of the Bell inequalities, this potential explanation has been roundly
rejected by the quantum foundations community. The arguments for rejection, one
of the most substantive coming from Bell himself, are critically reviewed. In
particular, analysis of Bell's argument reveals an implicit unwarranted
assumption: that the Euclidean metric is the appropriate yardstick for
measuring distances in state space. Bell's argument is largely negated if this
yardstick is instead based on the alternative $p$-adic metric. Such a metric,
common in number theory, arises naturally when describing chaotic systems which
evolve precisely on self-similar invariant sets in their state space. A
locally-causal realistic model of quantum entanglement is developed, based on
the premise that the laws of physics ultimately derive from an invariant-set
geometry in the state space of a deterministic quasi-cyclic mono-universe.
Based on this, the notion of a complex Hilbert vector is reinterpreted in terms
of an uncertain selection from a finite sample space of states, leading to a
novel form of `consistent histories' based on number-theoretic properties of
the transcendental cosine function. This leads to novel realistic
interpretations of position/momentum non-commutativity, EPR, the Bell Theorem
and the Tsirelson bound. In this inherently holistic theory - neither
conspiratorial, retrocausal, fine tuned nor nonlocal - superdeterminism is not
invoked by fiat but is emergent from these `consistent histories'
number-theoretic constraints. Invariant set theory provides new perspectives on
many of the contemporary problems at the interface of quantum and gravitational
physics, and, if correct, may signal the end of particle physics beyond the
Standard Model.
