Ex -identification and scientific discovery

Consider the empirical laws established in the History of Science. The process of scientific discovery can be roughly explained by (Popper-Kuhn's) cycle which starts with collecting evidence, introducing a model to explain observations, predicting further observations, and confronting them with experimentation, reinforcing or disproving the model. We attempt to prove that the empirical evidence modeled by arithmetical operations can be automatically discovered with a small amount of information, i.e. with very short Blums' locking sequences, due to the suitable enumerations of arithmetical functions.