= Degree and energetic stability of a field configuration
{title2=$E_2(R)\propto R,\quad E_4(R)\propto R^{-1}$}
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.
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