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Consistency of the two remaining non(M) < cov(M) constellations of Cichoń’s Maximum

Determine whether the two remaining constellations of Cichoń’s Maximum with non(M) < cov(M), depicted in Figures CMaxQ1 and CMaxQ2, are consistent with ZFC (possibly under large cardinal assumptions).

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Background

Using Boolean ultrapowers, the notes establish two constellations of Cichoń’s Maximum with non(M) < cov(M). However, among the four possible constellations with non(M) < cov(M), two remain unsettled.

The question asks for consistency results—ideally from ZFC alone, or with large cardinals—showing that the outstanding constellations can occur in a forcing extension.

References

There are four possible constellations of Cicho n's maximum with $\non(M)<\cov(M)$. We have proved two of them, but the consistency of each of the other two is not known. Is each of the constellations in \autoref{fig:CMaxQ1} and \autoref{fig:CMaxQ2} consistent with $ZFC$ (even under large cardinals)?

— Forcing techniques for Cichoń's Maximum: Lecture notes for the mini-course at the University of Vienna (2402.11852 - Mejía, 19 Feb 2024) in Section on Boolean ultrapowers, after Theorem mainBUP2 and Figures CMaxQ1 and CMaxQ2