zero in $Y_{23}$ or $Y_{32}$ implies that $Y_{22}=\epsilon ^{2}$ and hence these zeros can be filled at most at ${\mathcal{O}}(\epsilon ^{3})$. As we will now show, these subleading terms only contribute to physical quantities at subleading order even though the texture zero may be filled in. The only exception to this is when the hierarchical structure is spoilt through an ${\mathcal{O}}(1)$ term in $Y_{23}.$ In this case, following the discussion given above, the Kähler corrections can contribute at ${\mathcal{O}}(1)$ to physical quantities.

Kähler corrections to the mass matrix eigenvalues and mixing angles
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To complete our proof we need to demonstrate that the entries of Eq. ([genform]{}) are the smallest that can affect masses and mixing angles and thus the Kähler corrections, which we have shown are smaller than those of Eq. (\[genform\]), are necessarily subdominant in determining physical quantities.

Quark and charged lepton masses and mixing angles.
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Since the Kähler corrections are wave function corrections which cannot change the rank of the mass matrix we know that they lead to multiplicative normalisations of the masses. For hierarchical Yukawa matrices the wave function normalisation has the form $N_{ik}=\delta _{ik}+{\mathcal{O}}(\leq
\varepsilon ) $ and this means the Kähler corrections to 