Abstract: The study of classical instantons on spacetime has led to many interesting developments in mathematics. In a series of papers, Nekrasov introduced the generalized ADHM equations, whose solutions are instantons on the “origami spacetime.” In this talk, I will explain how to interpret gauge origami via DT4 theory. The main result shows that Nekrasov’s origami partition function, defined by local contributions, coincides with a global definition via Oh–Thomas classes in DT4 theory. This global definition is crucial for deriving the Dyson–Schwinger equation, which was one of Nekrasov’s main motivations for introducing gauge origami theory. I will also briefly discuss a conjectural sheaf-theoretic description of gauge origami. This is joint work with N. Arbesfeld and M. Kool.