A Four-Point Obstruction to Completeness for Three Atomic Inner Functions

For the atomic singular inner functions u_(xi,alpha)(z)=exp[-alpha(xi+z)/(xi-z)], we construct an explicit four-point functional annihilating all individual nonnegative powers at singularities 1, -1 and i with mass 3*pi, while detecting z^2. Their linear span is therefore not weak-star dense in H-infinity, not dense in H^p for any 0<p