The Unifier: One Axiom from Which Erasure, Triple, Bridge, and CPTP Follow

This paper unifies Tseglin 2026a/b/c/d. In 2026a, we proved no unital map T → E. In 2026b, we generalized to the triple H^n(T(H)) = (dim H^n, dim C^n, 1) for all H, all n. In 2026c, we defined the Bridge Conjecture. In 2026d, we proved the eraser, if physical, must be a CPTP decoherence map. Here we prove: all four follow from one axiom. We call it the Unifier Axiom: quantum does not commute, and erasing quantum is not an algebra map. Formally: [x,y] = 1 in T(H), and there is no unital φ: T(H) → E preserving [x,y]. We prove 2026a is the case H = S^1, 2026b is the case all H, all n, 2026c is the conditional bridge from this axiom to M, and 2026d is the physical form of the eraser forced by this axiom. This paper does not add a new experiment. It adds the roof. If you accept the Unifier, you accept a/b/c/d. If you reject the Unifier, you must say which part fails. Tseglin 2026e = Ch. 140. Cites Tseglin 2026a DOI 10.5281/zenodo.23977165, 2026b DOI 10.5281/zenodo.23980498, 2026c DOI 10.5281/zenodo.23980738, 2026d DOI 10.5281/zenodo.23981860.