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Abstract: We show that there exists a quantity, depending only on data of a Riemannian metric, that agrees with the usual ADM mass at infinity whenever the ADM mass exists, but has a well-defined limit at infinity for any continuous Riemannian metric that is asymptotically flat in the sense and has nonnegative scalar curvature in the sense of Ricci flow. Moreover, the mass at infinity is independent of choice of -asymptotically flat coordinate chart, and the local mass has controlled distortion under Ricci-DeTurck flow when coupled with a suitably evolving test function.