Bing doubles do not bound framed Whitney towers of order six

Let $K$ be a knot with non-trivial classical Arf invariant, and let its Bing double be the associated 2-component link. Framed Bing-double conjecture. The Bing double of any such knot does not bound an order $6$ framed Whitney tower. This is the Whitney-tower formulation of the degree-six framed Arf conjecture and is equivalent in the source to the non-triviality of the corresponding finite type concordance invariant. It remains open.