Arnold's sequence conjecture for the f-transform

Let $(u_k)_{k\geq1}$ be Arnold's sequence, and let $f$ be the map on finite sequences of nonnegative integers defined in the paper. Starting from a finite sequence, repeatedly applying $f$ produces an infinite sequence called its $f$-transform.

Arnold's sequence conjecture. Arnold's sequence $(u_k)_{k\geq1}$ is the $f$-transform of the quadruple $(2,4,4,4)$.

The construction is motivated by the initial values of Arnold's sequence and is presented as a conjectural description; the paper does not prove that the resulting $f$-transform equals $(u_k)_{k\geq1}$, so the conjecture remains open.