We propose a novel mathematical framework, rooted in fiber bundle theory, to quantify the phenomenon of quantum contextuality—a fundamental aspect of quantum entanglement. To demonstrate its utility, we first apply the formalism to quantum models in the foundations of quantum physics that both capture and differentiate varying strengths of contextuality. By revealing the intrinsic geometric structure of contextuality, the framework establishes a direct link to its computational foundations, facilitating the formulation of a topology-based model of computation that encapsulates the semantics inherent to contextuality. The framework delivers a rigorous and potentially more profound mathematical characterization of quantum contextuality, while offering new modeling methodologies for quantum cognition.