“Edge stability” was coined by Roman Landes to describe a steel’s Ability to hold an acute, polished edge. Therefore it isn’t a single property, but the whole set of properties that allow that to happen. So resistance to rolling or deformation (hardness), chipping (toughness), wear, and even corrosion though I’m not sure Roman included that. When carbides are larger than the edge one is attempting to sharpen, then you can get carbide pullout making sharpening difficult, or even when obtained the edges lose initial sharpness quickly until they reach the radius required by the carbides. But on the topic of toughness, areas of chipping can occur at large carbides or other defects that would be an example of “local toughness.” Retained austenite could also lead to poor local toughness.