We present a five-reservoir open-system model for the 182Hf-182W and 146Sm-142Nd isotope evolution of the Earth to constrain early mantle-crust exchange and late accretion processes. In the presented model, core for-mation is complete within 30-100 Myr after solar system formation. The complementary bulk silicate Earth (BSE) differentiates to form a continental crust (CC), an incompatible element depleted upper mantle (UM), an initially primitive but continuously evolving lower mantle (LM), and an isolated reservoir (IR) where the recycled crust is stored before mixing into the LM. In our default model, late accretion adds bulk Earth-like material to the mantle after core formation, concurrent to progressive silicate differentiation. The 182W and 142Nd isotope evolution in each reservoir is calculated with a series of differential equations that compute the changing abundance of each isotope from the start of solar system evolution (t = 4.56 Ga) to the present (t = 0 Ga). Core formation, by far, has the greatest influence on the 182Hf-182W isotopic evolution of the bulk silicate Earth (BSE). It determines the-200 ppm offset between BSE's mu 182W (mu 182WBSE -0) and chondrites (mu 182Wchondrite --200ppm), whereas late accretion adds-10% of BSE's W which changes mu 182WBSE by only-several 10s ppm. Most compatible with the modeled 182W evolution and W content of the silicate Earth are core formation processes lasting until-45-60 Myr after solar system initial and subsequent addition of about 1.0-0.5% late accreted material to Earth's mantle. However, both the pre-late accretion mu 182W and W content of the BSE depend strongly on the rate and duration of core formation and ultimately determine the amount and type of late accreted material necessary to evolve to the present mu 182WBSE - 0, or any other value slightly higher or lower. Because tight constraints on the timing and rate of core formation during accretion are still lacking, the trade-off between core formation processes and the effects of late accretion on BSE's 182W evolution remains grossly under-constrained, making the mu 182W evolution of Earth's mantle-crust system similarly under-determined. Nevertheless, robust constraints are that heterogeneous distribution of the late accreted material to Earth's mantle in combination with Hadean crust formation and recycling is required to form a mantle reservoir with a small range of 182W excesses between 10 and 15 ppm throughout the Archean, as observed in most Archean rocks. Reproducing the observed 142Nd and 182W signatures in Hadean-Eoarchean mantle-derived rocks with our model further requires that continental crust formation starts within the first-50 Myr after core formation. Continuous exchange between the crust and the different mantle reservoirs in our model leads to post-Archean homogenization of early-formed 182W and 142Nd heterogeneities and makes it difficult to preserve ancient mu 182W and mu 142Nd deviations from BSE values. Nevertheless, mu 182W < 0 inherited from the combined effects of early crust-mantle differentiation and late accretion may under certain conditions be preserved in parts of Earth's mantle throughout the Archean, and perhaps even until today. The mu 182W < 0 observed in recent oceanic basalts may therefore be inherited from early silicate differentiation or originate from potential core-mantle interaction at any time during Earth's history.
