Mosaic representatives as a complete invariant of tame knots

Let $k_1$ and $k_2$ be tame knots or links, and let $K_1$ and $K_2$ be arbitrary chosen mosaic representatives of $k_1$ and $k_2$, respectively. Two mosaics have the same knot mosaic type when, after possibly applying stabilization maps, they are related by the knot mosaic ambient groups. Mosaic completeness conjecture. The knots $k_1$ and $k_2$ have the same knot type if and only if their representative mosaics $K_1$ and $K_2$ have the same knot mosaic type; equivalently, knot mosaic type is a complete invariant of tame knots. Every tame knot or link admits a mosaic representative, so this conjecture asserts that the mosaic formalism detects exactly ambient isotopy classes.