Embedding all knots in the Sierpinski Tetrahedron (limit fractal)

Determine whether every knot can be embedded into the Sierpinski Tetrahedron, i.e., the limiting fractal obtained as the intersection of the iterative tetrahedral construction described in Section 2.1.

Background

The paper proves that any knot can be embedded in a finite iteration of the Menger Sponge and that all pretzel knots can be embedded in a finite iteration of the Sierpinski Tetrahedron. However, the authors were not able to extend the latter to all knots. In the introduction they explicitly highlight this gap and formally posit a conjecture that every knot can be embedded into the Sierpinski Tetrahedron itself (the limiting fractal).

This problem seeks to clarify whether the Sierpinski Tetrahedron has universality for knots analogous to the Menger Sponge’s universality for compact one-dimensional spaces, but with the added constraint of preserving knot type in the three-dimensional fractal limit.