Abstract: Medical image classifiers typically return predictions without a native contract for independently reconstructing their spatial decision computation. Evidence Field is a trainable spatial-program architecture that jointly produces class scores, selected covering programs and signed evidence. Its encoder combines absolute and image-relative response fields with associative spatial moments and learned characteristic sums. A typed classifier scores individual regions and parent-conditioned multiplicative groups; a covering recursion selects scale, partition and composition. We establish exact one-fold coverage, optimality within the registered grammar, a bound relating smooth training to hard inference, signed-score conservation and class-centred offset invariance. Direct contractions and their adjoint specify arithmetic and storage scaling on two- and three-dimensional grids. Native output records bind inputs, parameters, supports, types and contextual dependencies to individual and ensemble predictions. In a separately reported histopathology application, patient-separated training and evaluation across held-out centres provide empirical evidence for the architecture. Trained mechanism and corrected-loss comparisons distinguish predictive effects from implementation correctness; independent readers reconstruct descriptors, routes, scores and probability mixtures. The principal contribution is a coupled representation, decision and evidence architecture whose selected computation can be reproduced independently.