Proposition: Exact-count structure

At frozen weights and consistent tie breaking,

Fixed parameter masks commute:

A real fraction mapped to an integer retention count gives a piecewise-constant hard intervention with possible jumps. It need not define a continuous accuracy surface.

Proof. The first $j$ positions are a subset of the first $k$. Mask projections multiply coordinates by zeros and ones. A count changes at an integer threshold; deletion of a nonzero decision-relevant weight can change the logits and the predicted class abruptly.