This paper introduces the SUI/LUI framework: a discrete, thresholded update law for any system that learns, adapts, or reorganizes. A Smallest Unit of Intelligence (SUI) is defined as a minimal, irreversible update event triggered when an accumulated tension functional of prediction error crosses a critical threshold. Largest Units of Intelligence (LUIs) are the attractor structures carved by long histories of SUIs. From three axioms we derive concrete, falsifiable predictions: learning curves must be piecewise rather than smooth, chaotic physical systems should emit activity in discrete bursts, and high-entropy neural states (such as psychedelics) should show metastable attractor hopping instead of continuous drift. We then run preregistered stress-tests across four independent domains: human and artificial learning curves, asteroid Bennu’s particle ejections, psychedelic dynamic functional connectivity, and cosmic-web topology. In three domains, discrete change-point and state-switching models decisively outperform smooth nulls; in cosmology, current data provide a boundary where no excess discreteness is detected. The result is an empirically grounded unification: the same drift—tension—threshold—jump pattern explains learning, surface chaos, and neural reconfiguration, with explicit fail conditions rather than universal claims.