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We consider four-dimensional Higher-Spin Theory at the first nontrivial ordercorresponding to the cubic action. All Higher-Spin interaction vertices areexplicitly obtained from Vasiliev's equations. In particular, we obtain thevertices that are not determined solely by the Higher-Spin algebra structureconstants. The dictionary between the Fronsdal fields and Higher-Spinconnections is found and the corrections to the Fronsdal equations are derived.These corrections turn out to involve derivatives of arbitrary order. Weobserve that the vertices not determined by the Higher-Spin algebra producenaked infinities, when decomposed into the minimal derivative vertices andimprovements. Therefore, standard methods can only be used to check a ratherlimited number of correlation functions within the HS AdS/CFT duality. Apossible resolution of the puzzle is discussed.

Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal