strength of the same electronic state in all gap patches. Clearly, if the large-gap patches even at optimal doping correspond to a competing electronic state, a very different approach is necessary. The naïve proposal that these gap patches correspond to pseudogap regions does not, however, suffice to explain the absence of impurity resonances, since most models of the pseudogap state allow for such resonances,[@kruis; @wang; @morr; @andersen032] and in addition, by heating the sample through $T_c$, they have now been observed to survive well in to the pseudogap state.[@chatterjee] The Gaussian distribution of gap sizes observed by STS also suggests that there is no qualitative difference between, e.g. large-gap regions and intermediate-gap regions.

Third, we note that all our calculations (and those of others) have been performed for models of a single impurity in some realization of a $d$-wave superconductor. In the real many-impurity problem, interference between different impurity resonances leads to distortions of fourfold symmetry and shifts of resonance energies.[@stavropoulos; @zah; @andersen03] These effects are particularly strong for near-unitary scatterers like Zn.[@ahz03] Direct comparison of a single experimental spectrum with a 1-impurity theoretical prediction are therefore generally problematic. It is likely that these effects are responsible for the fact 