Since one can produce a converging sequencing of approximations to formula_43 from below by considering finite-dimensional states and observables, if formula_40, then this procedure can be combined with the NPA hierarchy to produce a halting algorithm to compute the Tsirelson bound, making it a computable number (note that in isolation neither procedure halts in general). Conversely, if formula_43 is not computable, then formula_39. In January 2020, Ji, Natarajan, Vidick, Wright, and Yuen claimed to have proven that formula_43 is not computable, thus solving Tsirelson's problem.