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The single-molecule magnet {Mn84} is a challenge to theory because of its high nuclearity. We directly compute two experimentally accessible observables, the field-dependent magnetization up to 75 T and the temperature-dependent heat capacity, using parameter-free theory. In particular, we use first-principles calculations to derive short- and long-range exchange interactions and compute the exact partition function of the resulting classical Potts and Ising spin models for all 84 Mn S = 2 spins to obtain observables. The latter computation is made possible by using hyperoptimized tensor network contractions, a technique developed to simulate quantum supremacy circuits. We also synthesize the magnet and measure its heat capacity and magnetization, observing qualitative agreement between theory and experiment and identifying an unusual bump in the heat capacity and a plateau in the magnetization. Our work also identifies some limitations of current theoretical modeling in large magnets, such as sensitivity to small, long-range exchange couplings.