H^n for Quantum Spacetime: The Triple (dim H^n, dim C^n, 1) Cannot Be Erased

This paper generalizes Tseglin 2026a to all degrees n and all finite history spaces H. In Tseglin 2026a, we proved for H=S^1 that T = A1 ⊗ C*(S^1;k) has two witnesses, pi_1 ≠ 0 and [x,y]=1, and no unital map T → E=k exists. Here we prove the same obstruction in every degree. Let A1 = k<x,y>/(xy-yx-1), T(H) = A1 ⊗ C*(H;k) for H finite simplicial, E=k. Define H^n(T(H)) = (dim H^n(H;k), dim C^n(H;k), c), c = 1 iff [x,y] ≠ 0. Claim: For all finite H and all n ≥ 0, H^n(T(H)) = (dim H^n(H), dim C^n(H), 1). Hence T(H) is never E in the triple, even when H={*}. Falsifier: If an interferometer run finds c=0 with T(H) ≠ E, i.e. D ≈ 1 and V ≈ 1 with no eraser, this model is false. Tseglin 2026b = Ch. 125. Cites Tseglin 2026a, DOI 10.5281/zenodo.23977165.