Synthesis: The Nine Papers as One Theorem

This paper closes the arc. In 2026a (Ch. 124), we proved no unital map T → E for H = S^1. In 2026b (Ch. 125), we generalized to the triple H^n(T(H)) = (dim H^n, dim C^n, 1) for all finite H, all n. In 2026c (Ch. 138), we defined the Bridge Conjecture. In 2026d (Ch. 139), we proved the eraser must be CPTP decoherence. In 2026e (Ch. 140), we proved all four follow from one Unifier Axiom: [x,y] = 1, and no unital φ: T(H) → E preserves [x,y]. In 2026f (Ch. 141), we categorified H: histories as objects, T as functor, erasure as functor, No-Go as natural. In 2026g (Ch. 142), we proved the Unifier survives in characteristic p, via the Frobenius center k[x^p,y^p]. In 2026h (Ch. 143), we proved it survives for infinite H = lim→ H_i. In 2026i (Ch. 144), we gave the explicit falsifier: D^2 + V^2 ≤ 1. Here we prove the nine papers are one theorem: (U1) [x,y] = 1 implies (1) No-Go, (2) Triple, (3) Bridge, (4) CPTP eraser, (5) Functoriality, (6) Char p stability, (7) Infinite stability, (8) Lab bound D^2 + V^2 ≤ 1. Conversely, falsifying any one falsifies (U1). We give the dependency graph, the single falsifier that kills all nine, and what remains open: the Bridge Conjecture itself. This is not a new result. It is the map of the previous nine. Tseglin 2026j = Ch. 145. 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.