= Weierstrass excess function
{c}
{title2=$E(x,y,p,q)=f(x,y,q)-f(x,y,p)-f_v(x,y,p)(q-p)$}
This excess measures the height of the slope-dependent integrand above its tangent line at the reference slope $p$, evaluated at a trial slope $q$. A <convex function> of slope has nonnegative excess. At a smooth strong local minimizer, localized needle variations force nonnegative excess along the minimizing curve for every trial slope. It detects fast-gradient competitors that the <second variation> around a fixed derivative can miss.
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