The Born Rule as a Consistency Condition of Realized Context

Why does quantum theory assign outcome probabilities by squared amplitudes rather than by some other function of the wave function? Existing results show that the Born rule is singled out by the structure of Hilbert space together with consistency requirements on probability measures, yet the physical role of measurement context is often treated as a mere choice of observable. Here we make the context interface explicit by introducing contextons, a unit of outcome capacity: the smallest increment in a context’s ability to produce one additional stable, externally accessible outcome record (within a fixed reliability threshold). We model the measurement interface as a realization condition that instantiates an orthogonal decomposition of possibilities into distinguishable outcomes. Under three basic requirements – normalization, additivity under coarse-graining of orthogonal outcomes, and representation invariance – outcome weights must take the quadratic form induced by the inner product, yielding and, for rank-one outcomes, . The Born weights are thus read as a context-conditioned “fit” measure: not an extra postulate, but the consistent outcome weight associated with realized distinguishability. The main contribution is conceptual: contextons operationalize measurement context as finite outcome capacity and make explicit the record-level structure on which standard uniqueness results act.