Leaving aside that it is off by one...

Remember I said earlier that it will be very handy to use the difference magnifier?

So let's use it.

Here I set up, in parallel, both the ordinary Diffuse node, and my fake pure-math version of it.

I then run those into my difference magnifier. Initially I use a factor of 1.

I render.

Look - the back side shows a difference, but not the front.

Why is that?

Because I lied. When a back-facing polygon is used in the dot product, we get a negative number. Now it turns out that when we rendered that, we saw black, but there was actually a negative color generated. We just could not see it.

But now we can see it because we're using the difference magnifier, and it will show us positive or negative differences.

Neat huh?

We've come full circle.

The back-facing polygons are actually in shadow. Remember I said the equation was correct, as long as we ignore shadows. But we can't ignore shadows.

For back-facing polygons, the effective illumination is zero, not a negative number.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)