Reciprocity and self-tuning relations without wrapping

We consider scalar Wilson operators of N = 4 SYM at high spin, , and generic twist in the multicolor limit. We show that the corresponding (non)linear integral equations (originating from the asymptotic Bethe Ansatz equations) respect certain “reciprocity” and functional “self-tuning” relations up to all terms 1/(ln)^ (inclusive) at any fixed ’t Hooft coupling . Of course, this relation entails straightforwardly the well-known (homonymous) relations for the anomalous dimension at the same order in . On this basis we give some evidence that wrapping corrections should enter the nonlinear integral equation and anomalous dimension expansions at the next order(ln)^2 /^2 , at fixed ’t Hooft coupling, in such a way to reestablish the aforementioned relation (which fails otherwise).