Order-condition characterization of affine interval exchange codings

Let $W$ be a set of words, let $F(W)$ denote the associated object, and let $(<_A,<_D)$ be the pair of orders used in the order condition. Order-condition characterization conjecture. $F(W)$) satisfies the order condition for $(<_A,<_D)$ if and only if $W$ is produced, through the natural coding, by an affine interval exchange transformation with the same orders. The statement is presented as an unresolved question about the optimality and characterization of the interval-exchange construction; no resolution is supplied in the source.