Synthesis III: The Eighteen Papers as One Theorem

This is Synthesis III. It proves the eighteen papers 2026a–2026r are one theorem. In 2026a (Ch. 124), we proved no unital map T → E for H = S^1. 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. In 2026k (Ch. 146), we proved the Unifier survives for any A with [x,y] = 1. In 2026l (Ch. 147), we constructed H(M) for M Lorentzian. In 2026m (Ch. 148), we defined causal homotopy, π1^causal, and H1^causal. In 2026n (Ch. 149), we defined H^n_causal(H(M)) for all n. In 2026o (Ch. 150), we proved the fourteen papers are one theorem. In 2026p (Ch. 151), we proved Einstein + NEC + Bridge ⇒ no CTC, and NEC violation still forces erasure. In 2026q (Ch. 152), we proved quantum M still forces erasure, branch + interference. In 2026r (Ch. 153), we gave the concrete lab protocol: Mach-Zehnder, W, E, D^2+V^2 ≤ 1, delayed-choice without retro-causation. We prove: (1) all eighteen are equivalent to the One Theorem: [x,y] = 1 + H^1_causal ≠ 0 ⇒ no unital Φ: T → E preserving [x,y], eraser must be CPTP, (2) 2026p/q/r add no new axiom: Einstein, quantum M, and lab are all consequences of the same One Theorem, (3) the whole arc has one falsifier: a repeatable D ≈ 1, V ≈ 1, no eraser, at >3σ, or a CTC with H^1_causal ≠ 0 and a unital Φ preserving [x,y], falsifies all eighteen, (4) the arc is closed: Synthesis III + 2026a–2026r is self-contained, no paper outside the arc is needed except Hawking 1992 and Englert 1996 as classical inputs. This does not prove the One Theorem is true in nature. It proves: the eighteen papers stand or fall together. Tseglin 2026s = Ch. 154. 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, 2026k DOI 10.5281/zenodo.23991603, 2026l DOI 10.5281/zenodo.23991665, 2026m DOI 10.5281/zenodo.23991998, 2026n DOI 10.5281/zenodo.23992083, 2026o DOI 10.5281/zenodo.23992187, 2026p DOI 10.5281/zenodo.23992267, 2026q DOI 10.5281/zenodo.23992317, 2026r DOI 10.5281/zenodo.23992397.