African Astronomy and Astrophysics (Pure Science): a mixed-methods study of Pure Science mechanisms and measurable outcomes across African contexts

Pure astrophysical inquiry explains distant processes through nearby signals, yet the logic connecting mechanism to measurement often remains implicit. It formalises mechanisms as parameterised physical processes, observables as the output of a forward operator subject to noise and selection, and measurable outcomes as inferential claims whose scope is bounded by identifiability and stability. Three formal propositions characterise when distinct mechanisms generate indistinguishable data, when spectral and calibration perturbations preserve inference, and when Fisher information sets a principled limit on precision. The quantitative formalism is integrated with a prospective mixed-methods protocol that treats observing practices, calibration cultures and archival decisions as qualitative material essential to interpreting quantitative constraints. The framework proposes, rather than executes, empirical application to optical spectroscopy, radio interferometry and very-high-energy observation in African contexts, and it clarifies what pure science can legitimately claim under instrumental constraint.