Hyperdeterminism? Spacetime 'Analyzed'

When modelling spacetime and classical physical fields, one typically assumes smoothness (infinite differentiability). But this assumption and its philosophical implications have not been sufficiently scrutinized. For example, we can appeal to analytic functions instead, which are also often used by physicists. Doing so leads to very different philosophical interpretations of a theory. For instance, our world would be 'hyperdeterministic' with analytic functions, in the sense that every field configuration is uniquely determined by its restriction to an arbitrarily small region. Relatedly, the hole argument of general relativity does not get off the ground. We argue that such an appeal to analytic functions is technically feasible and, conceptually, not obviously objectionable. The moral is to warn against rushing to draw philosophical conclusions from physical theories, given their drastic sensitivity to mathematical formalisms.