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Determine whether $N_{e}$ lenses distributed around a ring raise the tolerable intensity by a factor above 1.5 at fixed loss, accounting for breaking of lattice periodicity by finite $N_{e}$, coherent electron-proton instabilities, and lens current noise, with proton tests at the Fermilab IOTA ring as the reference case.","problem_ref":"fb6f4553695fff0c193bb5aa790c54f1cd4abad56252dd717aa728e7e9702300","references":"","settled_by":"A ring experiment showing increased intensity at fixed loss with lenses on versus off, consistent with simulation.","status_note":"","title":"Can electron lenses compensate space charge in hadron 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