Boolean functions violate the square-root degree bound by arbitrary factors

Disproves the proposed square-root bound relating a Boolean function's linear Fourier coefficients to its polynomial degree. For every C > 0, there is a sign-valued Boolean function f with $\sum_i\widehat f(\{i\})\gt C\sqrt{\deg(f)}$. Thus its total signed correlation with individual input bits can exceed the proposed bound by an arbitrary factor.