F1: generated boundary is not protocol attainment

Let

Every nonzero finite conical combination is strictly inside ${\mathcal{L}}_m$: the strict triangle estimate gives

when at least one ${\lambda }_j>0$. Nevertheless,

by density of rational interior points in the closed unit ball.

This is a generator example, not a faithful quantum event representation. It shows why a closure-produced null boundary need not contain an attained generator or protocol. XXII-B gives the same scope test CheungXXIIB (Failure test F3).

Even convergence of implemented endpoints to a null target does not assert equality with that target at any finite refinement. Exact logical transmission and exact null-coordinate attainment are also different predicates.