  We discuss possible phase factors for the S-matrix of planar N=4 gauge
theory, leading to modifications at four-loop order as compared to an earlier
proposal. While these result in a four-loop breakdown of perturbative
BMN-scaling, Kotikov-Lipatov transcendentality in the universal scaling
function for large-spin twist operators may be preserved. One particularly
natural choice, unique up to one constant, modifies the overall contribution of
all terms containing odd zeta functions in the earlier proposed scaling
function based on a trivial phase. Excitingly, we present evidence that this
choice is non-perturbatively related to a recently conjectured
crossing-symmetric phase factor for perturbative string theory on AdS_5xS^5
once the constant is fixed to a particular value. Our proposal, if true, might
therefore resolve the long-standing AdS/CFT discrepancies between gauge and
string theory.
