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If the UV completion of the Standard Model (SM) is unitary, local, and causal, then a rigid structure emerges in the IR description of the physics provided by the SMEFT. In this talk I will outline how these restrictions emerge, describe how they apply to the SMEFT, and mention the experimental implications, including for existing collider searches. The constraints require the positivity of various SMEFT Wilson coefficients, but also require a deep connection between effects that conserve and violate flavor and CP in the theory. I will present the sharp statements that can be made at dimension eight, but also detail what additional assumptions are required to extend the results to dimension six.