2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108448We study the composite fermion construction at and below the single vortex ($L=N$) state of weakly interacting rotating Bose gases, presenting a new method for handling the large number of derivatives typically occurring via the Slater determinant. Remarkably, the CF wave function at $L=N$ becomes {\em exact} in the large $N$ limit, even though this construction is not, {\em a priori}, expected to work in the low angular momentum regime. This implies an interesting mathematical identity which may be useful in other contexts.7 pages (RevTeX), 1 figure. Slightly revised version (accepted for publication in Phys Rev A)Mesoscale and Nanoscale Physicstext