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Corrections explain the gap, but it is unconfirmed whether very long chains finally reach power 3.","posed_since":"","precise":"For monodisperse linear polymer melts, eta_0 ~ $M^3$.4 is observed while pure reptation gives M^3; contour-length fluctuations and constraint release account for the difference at moderate $M / M_e$. Determine whether $\\eta_0$ crosses over to $M^3$ at very high $M / M_e$, and at what $M / M_e$, in experiment and in simulation.","problem_ref":null,"references":"","settled_by":"Measurements of $\\eta_{0}$ for narrowly distributed melts extending to $M / M_{e}$ of order 1e3 or more, or equivalent simulations, showing the local exponent approaching 3 or not.","status_note":"Exponents near 3 were reported for very high M polybutadiene (Colby, Fetters and Graessley 1987) and ultrahigh-molecular-weight polyethylene (Vega et al. 2004), but polydispersity and equilibration make these claims disputed; tube theory explains the 3.4 regime quantitatively.","title":"Does melt viscosity cross over to pure reptation 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