Several other properties of the chiral bag are notable: It provides a better fit to the low energy nucleon properties, to within 5–10%, and these are almost completely independent of the chiral bag radius (as long as the radius is less than the nucleon radius). This independence of radius is referred to as the "Cheshire Cat principle", after the fading of Lewis Carroll's Cheshire Cat to just its smile. It is expected that a first-principles solution of the equations of QCD will demonstrate a similar duality of quark-pion descriptions.