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The elemental composition of a sediment is set by the composition of its protolith and modified by weathering, sorting, and diagenesis. An important problem is deconvolving these contributions to a sediment's composition to arrive at information about processes that operate on the Earth's surface. We approach this problem by developing a predictive and invertible model of sedimentary major element composition. We compile a data set of sedimentary rock, river sediment, soil, and igneous rock compositions. Principal component analysis of the data set shows that most variation can be simplified to a small number of variables. We thus show that any sediment's composition can be described with just two vectors of igneous evolution and weathering. We hence define a model for sedimentary composition as a combination of these processes. A 1:1 correspondence is observed between predictions and independent data. The log ratios urn:x-wiley:ggge:media:ggge22195:ggge22195-math-0001 and urn:x-wiley:ggge:media:ggge22195:ggge22195-math-0002 are found to be simple proxies for, respectively, the model's protolith and weathering indices. Significant deviations from the model can be explained by sodium‐calcium exchange. Using this approach, we show that the major element composition of the upper continental crust has been modified by weathering, and we calculate the amount of each element that it must have lost to modify it to its present composition. By extrapolating modern weathering rates over the age of the crust, we conclude that it has not retained a significant amount of the necessarily produced weathering restite. This restite has likely been subducted into the mantle, indicating a crust‐to‐mantle recycling rate of 1.33 ± 0.89 ×1013 kg·year−1.