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Although the notion of superdeterminism can, in principle, account for theviolation of the Bell inequalities, this potential explanation has been roundlyrejected by the quantum foundations community. The arguments for rejection, oneof the most substantive coming from Bell himself, are critically reviewed. Inparticular, analysis of Bell's argument reveals an implicit unwarrantedassumption: that the Euclidean metric is the appropriate yardstick formeasuring distances in state space. Bell's argument is largely negated if thisyardstick is instead based on the alternative $p$-adic metric. Such a metric,common in number theory, arises naturally when describing chaotic systems whichevolve precisely on self-similar invariant sets in their state space. Alocally-causal realistic model of quantum entanglement is developed, based onthe premise that the laws of physics ultimately derive from an invariant-setgeometry in the state space of a deterministic quasi-cyclic mono-universe.Based on this, the notion of a complex Hilbert vector is reinterpreted in termsof an uncertain selection from a finite sample space of states, leading to anovel form of `consistent histories' based on number-theoretic properties ofthe transcendental cosine function. This leads to novel realisticinterpretations of position/momentum non-commutativity, EPR, the Bell Theoremand the Tsirelson bound. In this inherently holistic theory - neitherconspiratorial, retrocausal, fine tuned nor nonlocal - superdeterminism is notinvoked by fiat but is emergent from these `consistent histories'number-theoretic constraints. Invariant set theory provides new perspectives onmany of the contemporary problems at the interface of quantum and gravitationalphysics, and, if correct, may signal the end of particle physics beyond theStandard Model.

$p$-adic Distance, Finite Precision and Emergent Superdeterminism: A Number-Theoretic Consistent-Histories Approach to Local Quantum Realism