The conjecture that the BCZ map is an adic transformation

Let the BCZ map denote the Boca–Cobeli–Zaharescu map arising as a Poincaré return map for horocycle flow on the space of lattices. An adic transformation is a measurable transformation represented by an adding-machine action on a Bratteli–Vershik diagram. BCZ adic-transformation conjecture. The BCZ map is an adic transformation. This would give an adic model for the relevant horocycle-flow dynamics and connect the BCZ map with the known adic realizations of horocycle flows on quotients by lattices. The paper presents this as a natural conjecture; no resolution is supplied here.