  The dynamical commutators of the light-front Poincar\'e algebra yield first
order differential equations in the $p^+$ momenta for the interaction vertex
operators. The homogeneous solution to the equation for the quartic vertex is
studied. Consequences as regards the constructibility assumption of quartic
higher spin amplitudes from cubic amplitudes are discussed. The existence of
quartic contact interactions unrelated to cubic interactions by Poincar\'e
symmetry indicates that the higher spin S-matrix is not constructible. Thus
quartic amplitude based no-go results derived by BCFW recursion for Minkowski
higher spin massless fields may be circumvented.
