Answer by Jesse for Labeling node values on the axes

An quick method is to modify this line by adding shift={(0.3cm,-0.3cm)} to fine tune the location.

    \draw[dotted,name intersections={of=ucurve and uintersect, by=I}] let \p1 = (I) in (I) -- (\x1,0) node[shift={(0.3cm,-0.3cm)},blue]{$E(w)-\pi$};

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