 Degree and energetic stability of a field configuration

A nonzero topological degree obstructs smooth unwinding with fixed boundary data, but does not by itself give a stable finite size. In three dimensions a two-derivative energy scales as $R$ and can decrease as a configuration shrinks at fixed degree. The four-derivative Skyrme term scales as $R^{-1}$ and can balance this tendency. Derrick theorem addresses the energetic issue; a singular limiting configuration can evade smooth homotopy conservation.