From Lorentzian CTC to Toy Obstruction: The Bridge Conjecture for Chronology Protection

This paper is the bridge between Tseglin 2026a/2026b and general relativity. It does not claim the bridge is proved. In 2026a, we proved: for T = A1 ⊗ C*(S^1;k), there is no unital algebra map T → E=k. In 2026b, we generalized to T(H) = A1 ⊗ C*(H;k) for all finite H, all n: H^n(T(H)) = (dim H^n, dim C^n, 1), c=1 always. Here we define what a bridge must be: a functor B from Lorentzian spacetimes with a closed timelike curve to toy models T(H) such that a CTC in M implies a unital map T(H) → E preserving c. We prove a conditional theorem: if such a bridge exists and is faithful on c, then no CTC can form without an eraser. We state the three obstructions that must be overcome to prove the bridge exists, and the falsifier that would kill the program. This is a program paper, not a proof paper. Its value is that it makes the gap precise. Tseglin 2026c = Ch. 138. Cites Tseglin 2026a DOI 10.5281/zenodo.23977165 and Tseglin 2026b DOI 10.5281/zenodo.23980498.