Generic Whitehead minimality conjecture

Let $F_r$ be a free group of rank $r\geq 2$, and interpret “almost all” using asymptotic density on the set of elements of $F_r$ ordered by word length. An element is Whitehead minimal if no Whitehead automorphism reduces its length. Generic Whitehead minimality conjecture. Almost all elements of $F_r$ are Whitehead minimal. The conjecture is motivated by the efficiency of Whitehead descent algorithms; the source notes a theoretical justification relative to asymptotic density, but does not state that the conjecture is fully resolved.