Axis Completeness and Boundary Duality under Descent on Qₙ

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.