::::::::::::AFAIK, general relativity says you can always define things in such a way that the local speed of light is c, so do you mean "any evidence that GR is broken"? BTW, the CIPM in 2002 explicitly stated that "in the context of general relativity, the metre is considered a unit of proper length. Its definition, therefore, applies only within a spatial extent sufficiently small that the effects of the non-uniformity of the gravitational field can be ignored (note that, at the surface of the Earth, this effect in the vertical direction is about 1 part in 1016 per metre). In this case, the effects to be taken into account are those of special relativity only."