The Bridge, Proved: H(M) for M Lorentzian

This paper proves what was assumed. 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 (B1)-(B3): that a Lorentzian CTC gives a unital map T(H(M)) → E. 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, not just A1. Here we construct H(M) for M Lorentzian, and prove (B1)-(B3). H(M) is the simplicial set of causal histories: n-simplices are n+1 causally ordered points p0 ≤ p1 ≤ ... ≤ pn in M, with face maps deleting points, degeneracy maps repeating points. A CTC γ: S^1 → M gives a 1-cycle in H(M), hence a class [γ] in H^1(H(M)) ≠ 0 if γ is not causal-homotopic to a point. A CTC gives a unital evaluation map T(H(M)) → E by evaluating cochains on γ. By Unifier (2026e/k), no such map preserves [x,y]. Hence no CTC without an eraser. This is the Bridge, proved. This does not prove chronology protection in full GR. It proves it in the model T_A(H(M)) defined here, assuming H(M) as defined. The remaining open step is: does H(M) as defined capture the full Lorentzian geometry of M? We give the construction and the proof, and state the limitation precisely. Tseglin 2026l = Ch. 147. 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.