Quote -  Interesting.

And I agree, if you're using procedural textures/shaders, NO uvmap can often produce better results than a wrong UVmap (wrong considering the shape of the model)

I'm baffled that a planar map would be the best option here, but apparently, it is :)

Since my own Poser is tied up with a large render.. perhaps someone could try applying a checkered PROCEDURAL map to that cylinder? I'd like to see how the ends are looking.

Here ya go:

Using the "Tile" generator, rectangular shape, .1 tile width plugged into the diffuse color.  Weird huh?

The thing is that what I'm trying to target, the shadowy "ripping" artifacts seen in the other cylinders, is (so far) not produced when using a Planar map.  Moreover, the quality of the Planar map doesn't matter at all.  As you can see, the quality of this UVMap leaves much to be desired.  But, as long as it's not a measured pattern, it doesn't really matter, apparently.  (I wonder if that is because of the way the units for a procedural pattern are calculated?  Otherwise, the uvmap shouldn't matter, should it?)

Anyway, no artifacts yet with Planar projections but lots with other projection modes.  Since this is  problem I see posted on time and time again with lots of frustrated creators trying to get their objects to look appropriate, it definitely insists on further inquiry.  I'd love this to solve some people's problems and save them the headache of splitting verts, adding corrective geometry (bevels), when trying to solve this particular type of issue.

*Just a Note on "smoothing" : I believe this is entirely different from "smoothing" issues where split verts and beveled edges are normally used.  Vertex normals are the determiner there.  Unless a UVMap is somehow interacting with the generation of vertex normals and that interaction is only dependent upon the initial Projection mode, then it's a somewhat unrelated issue.  So, this won't keep edges sharp when the object is smooth shaded. (At least, I don't think it will.)  But, it appears it will help to remove the ripping artifact that plagues many.  More tests still to be done before it can be called "verified" though.  I really need others to reproduce the effects to discount any application specific effects I may be experiencing before being more confident of the results.