  We prove that the validity of the recently proposed dressed, asymptotic Bethe
ansatz for the planar AdS/CFT system is indeed limited at weak coupling by
operator wrapping effects. This is done by comparing the Bethe ansatz
predictions for the four-loop anomalous dimension of finite-spin twist-two
operators to BFKL constraints from high-energy scattering amplitudes in N=4
gauge theory. We find disagreement, which means that the ansatz breaks down for
length-two operators at four-loop order. Our method supplies precision tools
for multiple all-loop tests of the veracity of any yet-to-be constructed set of
exact spectral equations. Finally we present a conjecture for the exact
four-loop anomalous dimension of the family of twist-two operators, which
includes the Konishi field.
