Define a knot shadow as a projection of a knot that does not indicate over- and under-crossings. So, if there are $c$ crossings, there are $2^c$ possible over/under assignments, and so that many conventional knot diagrams are consistent with the shadow.
Is it always the case that, if the knot shadow is the shadow of a true knot, that one of the knot diagrams consistent with that shadow is the trivial knot, i.e., the unknot?
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I just want to add a piece of very concrete intuition on this, something you can try easily with pencil and paper.
Given a knot shadow, imagine tracing it with a pencil. Start by putting your pencil down anywhere other than a crossing and following the curves, going straight through any intersections. Each time you come to a crossing with a previous pencil mark you've made, indicate you're going "under" that previous mark. When you're done tracing, you'll have a diagram of the unknot!
To see why, think about this as a 3D situation, and your pencil moving away from you in space as you trace. At the end, when you reconnect with your starting point, imagine you're connecting back up to the starting plane. Rotating your viewpoint 90 degrees, you can see that you've actually drawn a simple loop.
Yes. Every knot has a finite unknotting number.