This thread is about the process of theory completion in the practice of theoretical physics, and therefore mostly directed towards practicing theoretical and mathematical physicists, but others can chime in as well. a) What exactly constitutes a natural completion of a physical theory? b) Is the process of completing a theory more aligned with the 'job description' of a mathematical physicist or of a theoretical physicist? c) Are there any specific criteria for what it means to complete a theory? d) What is meant by a completion as opposed to a natural completion? e) Is completion merely equivalent to extension? Or is completion more akin to some kind of particular unique extension of a theory? You don't necessarily need to answer all the questions, but for the sake of clarity please specify which question(s) you are answering. It seems quite obvious that theory completion is used in a much wider context than in purely the effective field theory sense a la UV completion, obviously because theories have been completed far before effective field theory (EFT) was invented, eg. Einstein already spoke about completing quantum theory decades before anyone had even heard of EFT. Opposed to theory completion, theory extension on the other hand seems to be pretty straightforward: any modification of a theory's original equations, axioms or unspecified numerical parameters. With regard to natural completion, I should also clarify by 'natural' I am not necessarily talking about 'naturalness' as is used to refer to dimensionless ratios being close to 1. That is a specific use of the term natural which doesn't seem at all to really capture all the forms in which the term can be and is used in the context of physics, which is why I see no good reason for an a priori insistence upon that particular usage of the term. By analogy, the term 'uncertainty' does not necessarily refer to (an effect of) stochasticity, stochasticity instead merely being a specific form of uncertainty, pretty similar to how kinetic energy is a form of energy; perhaps something similar applies to UV completion and completion? Is there some existing hierarchical listing of all forms of theory completion?