  In previous publications I have proposed a geometrical framework underpinning
the local, realistic, and deterministic origins of the strong quantum
correlations observed in Nature, without resorting to superdeterminism,
retrocausality, or other conspiracy loopholes usually employed to circumvent
Bell's argument against such a possibility. The geometrical framework I have
proposed is based on a Clifford-algebraic interplay between the quaternionic
3-sphere, or $S^3$, which I have taken to model the geometry of the
three-dimensional physical space in which we are confined to perform all our
physical experiments, and an octonion-like 7-sphere, or $S^7$, which arises as
an algebraic representation space of this quaternionic 3-sphere. In this paper
I first review the above geometrical framework, then strengthen its
Clifford-algebraic foundations employing the language of geometric algebra, and
finally refute some of its critiques.
