Beyond A1: The Unifier in Full QFT

This paper removes the toy algebra. In 2026a (Ch. 124), we proved no unital map T → E for H = S^1 with T = A1 ⊗ C*(H). In 2026b (Ch. 125), we generalized to the triple (dim H^n, dim C^n, 1). In 2026c (Ch. 138), we defined the Bridge Conjecture. In 2026d (Ch. 139), we proved the eraser must be CPTP. In 2026e (Ch. 140), we proved all four follow from one Unifier Axiom: [x,y] = 1. In 2026f (Ch. 141), we categorified H. In 2026g (Ch. 142), we proved the Unifier survives in characteristic p. In 2026h (Ch. 143), we proved it survives for infinite H. In 2026i (Ch. 144), we gave the lab falsifier D^2 + V^2 ≤ 1. In 2026j (Ch. 145), we proved the nine papers are one theorem. Here we ask: does the Unifier survive when A1 is replaced by a full QFT algebra A? We define T_A(H) = A ⊗ C*(H;k), where A is any algebra with a pair x,y satisfying [x,y] = 1, e.g. Weyl algebra, CCR algebra, free field algebra, or a type III von Neumann factor with a Heisenberg pair. We prove the No-Go, Triple, CPTP, Functoriality, Char p, Infinite, and Lab results all survive, with the same proof, because the proof never used that A = A1, only that [x,y] = 1 ≠ 0 in A. We prove the only new obstruction is: if A is commutative, the Unifier dies. Hence the Unifier is exactly noncommutativity. This does not prove QFT. It proves the toy was not essential. Tseglin 2026k = Ch. 146. 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, 2026e DOI 10.5281/zenodo.23982063, 2026f DOI 10.5281/zenodo.23982359, 2026g DOI 10.5281/zenodo.23985216, 2026h DOI 10.5281/zenodo.23991367, 2026i DOI 10.5281/zenodo.23991442, 2026j DOI 10.5281/zenodo.23991535.