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**Not as big as a barn: Upper bounds on dark matter-nucleus cross sections**

Critical probes of dark matter come from tests of its elastic scattering with nuclei. The results are typically assumed to be model independent, meaning that the form of the potential need not be specified and that the cross sections on different nuclear targets can be simply related to the cross section on nucleons. For pointlike spin-independent scattering, the assumed scaling relation is σχA∝A2μ2AσχN∝A4σχN, where the A2 comes from coherence and the μ2A≃A2m2N from kinematics for mχ≫mA. Here we calculate where model independence ends, i.e., where the cross section becomes so large that it violates its defining assumptions. We show that the assumed scaling relations generically fail for dark matter-nucleus cross sections σχA∼10−32–10−27 cm2, significantly below the geometric sizes of nuclei and well within the regime probed by underground detectors. Last, we show on theoretical grounds, and in light of existing limits on light mediators, that pointlike dark matter cannot have σχN≳10−25 cm2, above which many claimed constraints originate from cosmology and astrophysics. The most viable way to have such large cross sections is composite dark matter, which introduces significant additional model dependence through the choice of form factor. All prior limits on dark matter with cross sections σχN>10−32 cm2 with mχ≳1 GeV must therefore be reevaluated and reinterpreted.