Near full groups of bounded type, \rom{2}

What the math gives to ML

The paper develops a constructive method for generating large alternating permutation groups from a small set of local, fragmented generators on a hierarchical Bratteli diagram. Its transferable asset is the combination of diagonal inheritance, localized selectors, and bounded-delay propagation: one operation is replicated across many descendant substructures while another selectively activates a chosen level or connector type. This suggests a hierarchical token-mixing module in which a small generator bank produces structured permutations at multiple resolutions, reducing the cost of global mixing while preserving exact tree symmetries. The most credible application is tree-structured or multiscale data, where dense attention can be replaced or augmented by sparse generator permutations and shared local feature transforms.