There would be no hypothesis in your hypothesis-space to describe the standard model of physics, where space is continuous, indefinitely divisible, and has complex amplitude assignments over uncountable cardinalities of points.
I’m not sure this is necessarily correct. We typically model quantum configurations as functions defined over a continuous domain, but it’s yet possible that quantum configurations could be representable by a finite set of numbers (more precisely: that all possible configurations of our universe could be expressed as f(x) for some arbitrary but fixed f and some finite vector x). This would follow if the amount of information in the universe is finite, since we know that information is neither created nor destroyed over time. In this case we could represent states of the universe as a finite set of numbers and draw causal arrows between these arrows over time. Of course, such a representation might be much less convenient than thinking about continuous wavefunctions etc.
I’m not sure this is necessarily correct. We typically model quantum configurations as functions defined over a continuous domain, but it’s yet possible that quantum configurations could be representable by a finite set of numbers (more precisely: that all possible configurations of our universe could be expressed as f(x) for some arbitrary but fixed f and some finite vector x). This would follow if the amount of information in the universe is finite, since we know that information is neither created nor destroyed over time. In this case we could represent states of the universe as a finite set of numbers and draw causal arrows between these arrows over time. Of course, such a representation might be much less convenient than thinking about continuous wavefunctions etc.