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A Tale of Two Anomalies: Depletion, Dispersion, and the Connection Between the Stellar Lithium Spread and Inflated Radii on the Pre-Main Sequence

We investigate lithium depletion in standard stellar models (SSMs) and main sequence (MS) open clusters, and explore the origin of the Li dispersion in young, cool stars of equal mass, age and composition. We first demonstrate that SSMs accurately predict the Li abundances of solar analogs at the zero-age main sequence (ZAMS) within theoretical uncertainties. We then measure the rate of MS Li depletion by removing the [Fe/H]-dependent ZAMS Li pattern from three well-studied clusters, and comparing the detrended data. MS depletion is found to be mass dependent, in the sense of more depletion at low mass. A dispersion in Li abundance at fixed $T_{\rm eff}$ is nearly universal, and sets in by $\sim$200 Myr. We discuss mass and age dispersion trends, and the pattern is mixed. We argue that metallicity impacts the ZAMS Li pattern, in agreement with theoretical expectations but contrary to the findings of some previous studies, and suggest Li as a test of cluster metallicity. Finally, we argue that a radius dispersion in stars of fixed mass and age, during the epoch of pre-MS Li destruction, is responsible for the spread in Li abundances and the correlation between rotation and Li in young cool stars, most well known in the Pleiades. We calculate stellar models, inflated to match observed radius anomalies in magnetically active systems, and the resulting range of Li abundances reproduces the observed patterns of young clusters. We discuss ramifications for pre-MS evolutionary tracks and age measurements of young clusters, and suggest an observational test.