Artificial intelligent assistant

Is a knot shadow always compatible with the trivial knot? 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? !TrefoilNot

Yes. Every knot has a finite unknotting number.

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