Nonreducibility conjectures for cohesive and stable Ramsey principles

Let $\mathsf{COH}$ denote the cohesive principle, let $\operatorname{\mathsf{Ind}}\mathscr{E}_k$ denote the indicated indivisibility problem for $k$-colorings, and let $\leq_{\mathrm{c}}$ denote the relevant computable reducibility. Write $\mathbb{N}$ for the set of natural numbers. Nonreducibility conjecture.

$$\mathsf{COH} \not\leq_{\mathrm{c}} \operatorname{\mathsf{Ind}}\mathscr{E}_{\mathbb{N}}$$

and

$$\operatorname{\mathsf{Ind}}\mathscr{E}_2 \not\leq_{\mathrm{c}} \mathsf{SRT}^2_{\mathbb{N}},$$

or, at least,

$$\operatorname{\mathsf{Ind}}\mathscr{E}_k \not\leq_{\mathrm{c}} \mathsf{SRT}^2_k.$$

The conjecture concerns the open separation of the indivisibility principles from cohesive and stable Ramsey principles under computable reducibility; the source presents these nonreducibilities as conjectural after noting that the corresponding reducibility questions are open.