Observables in Schrödinger CFTs: How Aliens Built the Pyramids

We discuss the algebraic structure of observables in Schr\"odinger CFTs. These operators have zero mass (or particle number) and generically transform in staggered ''pyramid representations'' built from ''alien operators,'' as we explain with the doubled state-operator correspondence. We comment on implications for the space of non-relativistic CFTs, thermal physics, and generalize the exceptional symmetry conservation laws of Bekaert, Meunier, and Moroz, and Golkar and Son. We show that alien operators are analogous to double-twist operators in Lorentzian CFT, with systematic cross-channel corrections from massless particles when they exist.