This work presents a first-principles geometric derivation of the Born rule ( \(\rho = |\psi |^2\) ) within a quaternionic Einstein–Cartan–Kibble–Sciama (ECKS) framework. We represent the Dirac field as a biquaternionic (complexified-quaternionic) spinor—equivalently, as an internal \(\textrm{SU}(2)\) doublet of ordinary complex Dirac spinors—and treat spacetime geometry as composite, built from spinor bilinears. Probability is formulated covariantly through a conserved current \(J^\mu [\Psi ]\) whose hypersurface flux defines \(\mathbb {P}(\Sigma )\) . Imposing locality, internal gauge invariance, observer-independent positivity, on-shell conservation, dimensional consistency, and universality (coupling-independence) selects \(J^\mu \propto \bar{\Psi }\gamma ^\mu \Psi \) , yielding the induced density \(\rho _{(n)}=-J^\mu n_\mu \) and hence \(\rho =\Psi ^\dagger \Psi \) in the local rest frame. Harrison-style amplitude rescalings generate deformed measures that violate these requirements and are incompatible with the constrained variational principle that enforces the composite geometry map. The Born rule thus appears as a rigidity property of the spinor–geometry correspondence rather than a phenomenological postulate.
