As I wrote before, but here is the simple explanation.
I can only attach pictures from maxwell render V3, but I am almost sure, that nothing will be different in V5.1.
As I wrote before, this is a "classic" - caustic through dielectrics problem.
You can see in my simple pictures how it works. Every "shadow" of transparent material is considered as caustic. Caustic can be refracted or reflected. Caustic can be seen directly or indirectly (refracted through another dielectric material or reflected through a mirror). The most difficult caustic is indirectly seen caustic of almost unidirectional beam light sources as is Sun (0,5°) or any small light sources shining from a big distance. There is nothing wrong with Your HDR images as You can see, there is good enough contrast between the shadow of a lit object and another unshadowed part. If there will be a problem with HDR images (dynamic range), there will be much less contrast or the edge of the shadow will be much softer. There is also no problem with the resolution of HDR as You can see.
You can see in the attached pictures, that the caustic is there, but in much higher sampling levels. Another point is that in the physical sun and sky scenario, there is a problem just with indirect seen refracted caustic. In the pictures with HDR, there is the same bad-looking directly (my surprise too!) and indirectly seen refracted caustic. And You can predict from small preview images, that the caustic will be there, but clean in SL 40 or even above. In the Fire engine, there is all caustic disabled (correct me please if I am wrong).
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