Theorem: Tensor-free one-layer support

For the layer (eq:layercomposition),

Its restriction to $\mathfrak{A}(Y)$ depends only on the specified global devices in the blocks meeting $Y$.

Proof. Let ${\mathcal{P}}_s(Y)$ be the meeting blocks. By commutation, compose them first. Repeated use of (eq:enlargement) places the result in $\mathfrak{A}(U_s(Y))$. Every remaining block is disjoint from $U_s(Y)$, so its device fixes that entire algebra by (eq:exteriorfix). It makes no contribution.