What Would a Mathematically Precise Definition of Unified Field Theory even Look Like if We Tried to Axiomatize It?

The term unified field theory is widely used but rarely given a precise, model-independent definition. In this letter I propose a minimal axiomatic framework for what should count as a unified field theory in the sense of relativistic quantum field theory with gravity. The axioms package spacetime, internal gauge structure, matter content, dynamics, and low-energy limits into a single geometric datum, and they are designed to be compatible with existing no-go theorems such as Coleman--Mandula and Haag–Łopuszański–Sohnius. I briefly discuss how such an axiomatization could support genuine classification or uniqueness theorems for unified models.