Theorem: F: potential coarsening and one-shot activation

For every legal run,

at the level of endpoint pairs. Each latent identifier activates at most once. If initially ${\sigma }_{X\mid Y}=0$, no crossing active edge or latent link is ever reachable.

Proof. Retiring capacity changes no reachability generator. Deleting structure removes generators. Activation replaces the two potential orientations of its latent link by one of those orientations. Thus its generator set only shrinks, and so does its reachability closure.

An activated identifier never returns to the latent component. The final assertion follows either from Theorem thm:E or directly from the absence of crossing generators.