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Too bad when you posted again, you didn't notice that your previous post had suggestions. Might have fixed this already instead of you spinning your wheels.

Yes, it is too bad. However, you said "Increase your ray bias (shadow min bias) on the light" and that had no effect on the stitches. You also said "You're using displacement and the ray-tracer part of Poser isn't aware of displacement. Thus, the displaced copies of those polygons cast a shadow on their own un-displaced copies." No joy there. 

However, your suggestion to turn off the Smooth Polygons on the Cyc seems to work! With the Render Settings at "Final" again but the Smooth Polygons box unchecked on the Cyc the render exhibits no artifacts - hurray! I'm sorry if you feel like you're dealing with the village idiot; I'm used to POV-Ray and have little experience with Poser. The two have little in common.

I will keep my fingers crossed that the Smooth Polygons uncheck trick will continue to work as I try some of the older scenes I have had problems with.

Thanks to all of you who responded!