In skeleton-based human action recognition the highest reported accuracies come almost invariably from multi-stream ensembles that average the softmax outputs of parallel joint, bone and velocity branches. The operator defined by such an ensemble, however, has never been supplied with a provable stability guarantee. This paper closes that gap with a self-contained compositional Lipschitz analysis. We model the multi-stream recogniser as a convex aggregation of parallel branches, each of which composes a hand-designed stream generator, a deep graph-temporal encoder and a softmax classifier. Our central finding is that the complete operator's Lipschitz constant equals the weight-averaged branch constant. Convex aggregation can therefore never degrade stability below that of the least stable branch, while the factor predicted by a naive parallel-composition argument is cancelled exactly by the aggregation weights. We then derive explicit constants, readable from trained weights, for the layer types that occur in practice - multi-subset graph convolution, temporal convolution, residual connections, inference-time BatchNorm, pooling, the linear head and softmax, as well as for the joint, bone and velocity stream generators.