The paper "Measuring Propagation Speed of Coulomb Fields" by R. de Sangro et al points out that:
...the Lienard-Weichert retarded potential leads to the same formula as the one obtained assuming that the electric field propagates with infinite velocity
Moreover, they conduct an experiment which purportedly measures a "rigid" (aka infinite velocity) $-\nabla \phi $ ("Coulomb Field") and further claim:
The Feynman interpretation of the L.W. formula for uniformly moving charges does not show consistency with our experimental data.
This violates special relativity because information can be transmitted at infinite speed simply by changing the position of a charge and measuring, at a large distance, the associated changes in $-\nabla \phi $.
Where did they go wrong?