Version 5.1 clarification update.This version introduces clarifying language in the introduction and Bell-related discussion to prevent common misinterpretations.No mathematical results, derivations, or conclusions have been changed. AbstractWe present a geometric representation of bipartite quantum correlations based onglobal spinor structure rather than probabilistic hidden variables. The constructionreproduces the singlet correlation and provides an explicit mapping between mea-surement interaction and observed outcomes. The framework does not modify theempirical predictions of quantum mechanics, but supplies a non-factorisable mathe-matical representation in which outcomes arise through structural compatibility ratherthan sampling over counterfactual assignments. The analysis clarifies why Bell–CHSHfactorisations cannot be constructed within this representation and identifies the ob-struction as structural. The work addresses the representation of measurement andcorrelation structure within quantum theory.