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An inaccuracy of composite fermion model is identified for Landau levelfillings out of 1/p, p odd. The corrected version of hierarchy for fractionalquantum Hall effect is proposed by mapping onto integer effect within thecyclotron braid approach. Flux-tubes and vortices for composite fermionconstructions are explained in terms of cyclotron braids. The even denominatorfractional lowest Landau level fillings, including Hall metal, are alsodiscussed in cyclotron braid terms.

On auxiliary flux tubes associated to composite fermions in 2D Hall systems