The largest sample ever recorded of $\numub$ charged-current quasi-elastic (CCQE, $\numub + p \to \mup + n$) candidate events is used to produce the minimally model-dependent, flux-integrated double-differential cross section $\frac{d^{2}\sigma}{dT_\mu d\uz}$ for $\numub$ incident on mineral oil. This measurement exploits the unprecedented statistics of the MiniBooNE anti-neutrino mode sample and provides the most complete information of this process to date. Also given to facilitate historical comparisons are the flux-unfolded total cross section $\sigma(E_\nu)$ and single-differential cross section $\frac{d\sigma}{d\qsq}$ on both mineral oil and on carbon by subtracting the $\numub$ CCQE events on hydrogen. The observed cross section is somewhat higher than the predicted cross section from a model assuming independently-acting nucleons in carbon with canonical form factor values. The shape of the data are also discrepant with this model. These results have implications for intra-nuclear processes and can help constrain signal and background processes for future neutrino oscillation measurements.
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