Geometric Weighting of Born Statistics from Measurement Coupling

This preprint introduces a compact parametrization of protocol-dependent re-weighting of quantum measurement outcomes. The resulting “geometric weighted Born rule” (GWBR) is not a modification of quantum theory; it is exactly the conditional outcome statistics induced by acceptance/weighting in the measurement pipeline. We derive the GWBR form from Bayes conditioning under outcome-dependent acceptance probabilities and provide a first-order expansion that yields centered, testable deviations. An explicit toy model based on thresholded readout illustrates how detector/processing coupling induces predictable re-weighting, and we propose falsifiable null-tests to distinguish GWBR-type bias from decoherence and simple misclassification noise.