Joint Definability, Context–Instantiated Geometry, and the Inapplicability of Fine’s Theorem

We extend our description of the electron’s quaternion spin (Q–spin) as a geometric rotor. This follows from incorporating both the symmetric polarization and the antisymmetric coherence into the theory. Polarization is observed only through the local process we call contextual instantiation. For an EPR pair the observed correlation is reconstructed statistically from the coincidence populations and follows from the scalar invariant of the quaternion rotor, yielding the observed correlation. Numerical simulations reproduce this correlation using only local detector events, and show the same data retain complementary polarization and coherence structure producing a lemniscate rotor portrait. Because spin observables are not jointly definable on a single Kolmogorov probability space, the CHSH quadruple cannot be formed and Bell’s theorem is therefore not applicable. The results provide a unified geometric description of spin, measurement, and Bell correlations, contributing to the foundations of quantum mechanics.