Eq. (\[genform\]) the only terms that could be modified by Kähler corrections are the $(2,1)$, $(3,1)$ and $(3,2)$ terms. For instance, for $Y_{3,1}<Y_{2,1}$ the Kähler correction can dominate the $(3,1)$ element. However in this case, from the structure in Eq. ([genform]{}) and with $N_{i<j} \leq \epsilon$, $Y_{3,1}^{t}\leq \epsilon ^{4}$. Clearly this is too small to affect masses or $LH$ mixing angles at leading order. It can be easily checked that the same is true in the case of the $(2,1)$ and $(3,2)$ elements. As we have discussed, for the hierarchical textures of interest here, the leading correction to a given Yukawa element is suppressed by at least ${\mathcal{O}}(\epsilon ^{2})$.

One might worry that the condition $Y_{kj}<Y_{ij}$ for $i>k$ and $\ j\geq i$ is too strong and that what are constrained are the elements after Kähler mixing, i.e. $Y_{kj}^{t}<Y_{ij}^{t}$ for $i>k$ and $\ j\geq i$ and the condition on $Y_{kj}$ is not satisfied. However this is inconsistent. To see this note that the phenomenological structure of $Y_{kj}^{t}$ in Eq. ([genform]{}) would correspond both to the basis of canonical Kähler with upper triangular transformations or to the basis of “standard” canonical transformations. This is due to the fact that both basis are 