I see a problem with this: There doesn't seem to be a way to tell if omega itself is in the laws of physics or some finite precision approximation to omega. Given any set of finite observable phenomena and any finite amount of time there will be some finite precision approximation to any real number which is sufficient in the equations to explain all observations, assuming the models used are otherwise correct and otherwise computable. How would one tell if the universe uses the real value Pi or a finite precision version of Pi whose finiteness is epsilon greater then what is needed to calculate any observable value?