Is that inclined cut on the side of Liberty Cap, between Vernal Falls and Nevada Falls, an abandoned trail, or is that just a natural geological formation?

I don't remember seeing anything that looked like a trail there. Do you have a picture?

That is a joint with foliage growing along it. It can be hiked too as it is an approach trail to the climb.
http://supertopo.com/rockclimbing/route.html?r=yblisout

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Old Dude