Perfect play in a binary-scoring nonlocal game requires infinite dimension

We construct a finite rational two-player nonlocal game with ten Alice questions, eleven Bob questions, at most six answers per question and 52 equally likely supported pairs. It has a perfect spatial strategy and no perfect finite-dimensional strategy. For arbitrary finite-dimensional local POVMs and mixed states, its dimension profile is D_Gamma(epsilon) = 10 log2(1/epsilon) + O(log log(1/epsilon)). The lower bound is 10 log2(1/epsilon) - 10 log2 log2(1/epsilon) - O(1). A direct square-root magic-square extraction, robust flagged sector law and approximate gluing force twenty Schmidt coefficients per appreciable halving level. The explicit strategy compressed to 20K dimensions has loss exactly 1/[624(4^K-1)], yielding the matching leading upper coefficient 10.