The study of the classical instantons on the spacetime has led to many interesting mathematics. In a series of papers, Nekrasov introduced and studied the generalised ADHM equations, whose solutions are instantons on the “origami spacetime”. In this talk, I will explain how to interpret Nekrasov’s gauge origami via DT4 theory. Our main result computes the orientation in the Oh-Thomas localisation formula and matches it with the definition from physics. If time permits, I will discuss some applications and a conjectural sheaf-theoretic description of the gauge origami theory. This is joint work in progress with N. Arbesfeld and M. Kool.