We study quotients of the hypercube group Q_n under a descent condition. Descent forces translation invariance and yields a linear quotient structure V/H. A two-face forcing argument shows that admissibility implies a Two-Type restriction (dim(V/H) ≤ 1). In the nontrivial case, the induced binary label is linear. The existence of a compositional tracking operation reduces to a consistency condition, and undecidability appears as a boundary phenomenon. Invertibility is not forced by the structural axioms, producing a branch-type boundary instance. We further prove axis completeness: under a fixed base signature, no new independent structural directions arise. Any additional demand requires signature extension and is classified as a scope-type boundary.