Embedding all knots in a finite iteration of the Sierpinski Tetrahedron

Determine whether every knot can be embedded into some finite iteration of the Sierpinski Tetrahedron, i.e., whether for each knot there exists an n such that it occurs as a closed path in the one-skeleton of t_n.

Background

While pretzel knots are shown to embed in finite iterations of the Sierpinski Tetrahedron via a combinatorial representation, the authors explicitly state that it is unknown whether all knots can be embedded in some finite iteration. This strengthens the practical, constructive aspect of the broader conjecture by asking about occurrence at finite stages rather than only in the limit fractal.

Resolving this would compare the tetrahedron’s knot-generating complexity against the Menger Sponge, where every knot appears in some finite iteration.