Finitary factor-of-iid perfect matching

Construct a finitary factor-of-iid perfect matching on the Δ-regular tree T_Δ, or establish that no such finitary factor exists.

Background

The paper explains that a factor-of-iid perfect matching exists on T_Δ, but the finitary-factor complexity of this matching is unresolved. Existing results rule out subexponential tail decay, leaving open whether any almost surely finite coding radius is possible.

References

Is there a finitary factor of iid perfect matching on the $\Delta$-regular tree $T_\Delta$?

— From descriptive to distributed  (2502.15347 - Grebík et al., 21 Feb 2025) in Problem immediately following the discussion of finitary factors of iid, Section 6 (Edge colorings)