Canonical Ramsey property versus Ramsey property

Determine whether every Ramsey set is canonically Ramsey and whether every canonically Ramsey set is Ramsey.

Background

Canonical Euclidean Ramsey theory asks whether every colouring yields either a monochromatic or a rainbow copy, whereas classical Euclidean Ramsey theory seeks monochromatic copies under a fixed finite colour bound. The paper reports a conjecture that all Ramsey sets are canonically Ramsey, while explicitly stating that both this conjecture and the converse implication remain unresolved.

References

Fang, Ge, Shu, Xu, Xu, and Yang have conjectured that all Ramsey sets should be canonically Ramsey, but both this conjecture and its converse remain open.

— The regular pentagon is canonically Ramsey  (2608.19183 - Shaw, 19 Aug 2026) in Section 1, Introduction