Homomorphism to compact subshifts

Determine whether Marks’ example Borel-homomorphs to every compact subshift of the free part of 2^{Γ_Δ} that lacks a Borel Δ-coloring, and determine the projective complexity of such subshifts.

Background

The paper suggests that compact or continuous settings might avoid the noncompactness used in known complexity constructions.

References

Does Marks' example Borel homomorph to ${G}$? What is the projective complexity of such subshifts?

— From descriptive to distributed  (2502.15347 - Grebík et al., 21 Feb 2025) in Problem 14, Section 7 (Complexity)

Assume that ${G}$ is a compact subshift of the free part of $2{\Gamma_\Delta}$ that does not admit a Borel $\Delta$-coloring, for $\Delta \geq 3$. Does Marks' example Borel homomorph to ${G}$? What is the projective complexity of such subshifts?

— From descriptive to distributed  (2502.15347 - Grebík et al., 21 Feb 2025) in Problem 14, Section 11 (Open problems), Complexity