Torus Chambers and Class Frames for Pratt's Tripartition Tensor: R(P₃) ≤ 212 and R(T₂,₂,₃) ≤ 53

We prove R̲(P₃) ≤ 212 and R̲(T₂,₂,₃) ≤ 53 for Pratt's balanced tripartition tensor P₃ (84 × 84 × 84) and the tripartition tensor T₂,₂,₃ (21 × 21 × 35). The previous bounds were 216 and 54, from the torus ladder (10.5281/zenodo.23339636), where the bound 212 was reached only numerically: the 53-block solution there resisted rationalisation, because after fixing 473 to 540 of its 823 nonlinear coordinates to small rationals the rest were algebraic of high degree. Two ideas make it exact. Class frames impose the symmetry S{C₁} × ⋯ × S{C_c} of a partition of the ground set into classes and reduce the 53-block problem from 1281 to 383 unknowns. Torus chambers replace the uniform torus weights by weights that are constant on classes but different between them: the relaxed system depends only on the chamber of the weight vector in a hyperplane arrangement, and the uniform weights lie on a wall of it. In the class frame {2,3,4} | {5} | {6,7,8} with weights −1, −3/4, 0 the 53-block system has exact solutions from random starts, and one of them is completely rational: all 239 coordinates of the forms ℓ and p are rationals, 161 of them integers and the largest denominator 1344, and the remaining coordinates follow from linear systems. The identity is verified on all 24 010 coefficients in rational arithmetic by two independent checkers and by an exact evaluation of the torus limit. The bound lies 44 below Pratt's 256 and 35 below the partial-Fourier bound 247. Paper, LaTeX source, certificate in two formats and verification scripts are included.