25 S$_{N}$ ≃ S$_{∞}$ + Δ S N α + . . . (24) S$_{N}$ − S$_{2}$$_{N}$ = (1 − 2 − $^{α}$) δS N α (25) δS$_{N}$ ≃ A$_{N}$ N β (26) (we are integrating out heavy modes and assuming they have no corrections to the truncated theory), and we keep N finite. Still, this is a puzzle that we can not resolve satisfactorily yet. Further study is required to understand this issue better. With our data, we can find a fit to the exponent and see what happens. We can do the following analysis. We can assume that there is a limit and a scaling exponent that describes how close we are to the limit, by the following argument Then, if we take the following differences Similarly, the standard-deviation fluctuations should have some scaling pattern we can make a fit for α and check the exponent appearing in the corrections. The data is not very illuminating. We find values as large as α ∼ 0 . 7 for low values of k up to k = 6, and then it decreases towards α ∼ 0 . 1 for k = 13. Again, we should not give too much meaning to these numbers for the large values of k if the corresponding correlators are not factorized yet. If we plot the data sample to the best fit for β we get the results in figure 8. The results are roughly consistent with β ∼ 1, which is the exponent that the planar counting would suggest, but it is unclear how this data should be used, seeing as we might not yet have converged to large N sufficiently. Again, rough consistency with β ∼ 1 is not the same as knowing that β = 1. A much larger data set from more simulations would be able to verify this hypothesis. It would also require going to much large values of N (hopefully stepping up to a factor of 100 in N might be enough). If the planar counting does not work, it could be because we ignored some degrees of freedom that contribute to the limit, and that these make the full system behave as is expected. However, we should expect that the corrections induced by integrating out heavy modes involve their masses, which are expressed as powers of the large N coupling constant λ = g $^{2}$N [5, 18]. We do not have a clear understanding on how the planar counting would