Causal Cohomology: H^n_causal(H(M))

This paper defines causal cohomology. 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 as causal histories. In 2026m (Ch. 148), we defined causal homotopy, π1^causal, and H1^causal. Here we define H^n_causal(H(M)) for all n. A causal n-cochain is a function f on causal n-simplices (p0 ≤ ... ≤ pn) that is invariant under causal homotopy. We prove: (1) d^2 = 0 on causal cochains, so H^n_causal is defined, (2) H^0_causal = locally constant causal functions, (3) H^1_causal ≠ 0 iff there is a non-trivial CTC, (4) the causal Triple (dim H^n_causal, dim C^n_causal, 1) holds, with 1 = [x,y] = 1, (5) causal cohomology is functorial under causal maps, and erasure is a functor on causal cochains, (6) if M is globally hyperbolic, H^n_causal = H^n_ordinary for the causal nerve, and H^1_causal = 0. This completes the causal version of 2026b for H(M). The Bridge now has a full causal cohomology theory behind it. Tseglin 2026n = Ch. 149. 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.