Metric ergodicity versus essential bounded chaining

Construct a measure-class preserving action of a countable group that is metrically ergodic but not essentially boundedly chaining.

Background

The paper proves that essential bounded chaining implies metric ergodicity, while also showing that metric ergodicity does not imply bounded chaining. The unresolved issue is whether metric ergodicity may nevertheless imply the weaker property of essential bounded chaining, or whether a counterexample exists.

References

Is there an mcp action of a countable group \Gamma that is metrically ergodic but not essentially boundedly chaining?

— Bounded chaining in measurable dynamics  (2609.18061 - Tserunyan et al., 16 Sep 2026) in Question q:ME_implies_ess-bdd-C, Section 1, subsection “Open problems”