Composite fermions in the neighborhood of $\nu =1\mathrm{/}3$

We present extensive comparisons of the composite fermion theory with exact results in the filling factor range $2\mathrm{/}5>\nu >1\mathrm{/}3$, which affirm that the composite fermion theory correctly describes the qualitative reorganization of the low energy Hilbert space of the strongly correlated electrons, and predicts eigenenergies with an accuracy of $\sim 0.1$ %. These facts establish the basic validity of the composite fermion description in this filling factor region.