Nontrivial delta move finite type invariants detect unknotting number

Let $U_n(K^\Delta)$ be the finite type group associated with delta moves, and let $A_{n,1}\subseteq A_{n,2}\subseteq\cdots\subseteq A_{n,n}=U_n(K^\Delta)$ be the filtration arising in its finite generation. A knot has unknotting number $1$ if it can be transformed into the unknot by one crossing change.

Delta move finite type invariant conjecture. For some $n$, we have

$$A_{n,1}\neq U_n(K^\Delta).$$

Therefore, there exists a nontrivial delta move finite type invariant that vanishes on knots of unknotting number $1$. Thus, delta move finite type invariants yield nontrivial lower bounds for unknotting number.

Explicitly computing these groups and determining whether the filtration is nontrivial are active problems; the conjecture would provide finite type lower bounds for unknotting number.