Ah! If I do the same but with NO displacement...

Looking at the hole in the duodecagonal disc the gaps between the meshlines and the smoothed rendered surface seem to match the appearance of the ray-traced shadow artefacts.

• Could it be that the ray-tracing is casting shadows from the UNsmoothed mesh, but catching them on the smoothed mesh ?
  • (If so, where is displacement taken into account for both casting and catching?)
• There's also the possibility that I'm barking up the wrong tree...

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The 3Dcheapskate* occasionally posts sensible stuff. Usually by accident. And it usually uses Poser 11, with units set to inches. Except when it's using Poser 6 or PP2014, or when its units are set to PNU or something else.
*soon only to be available in two flavours -  DAZ and Renderosity