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Singular-λ case for asymmetric Σ_n–CBFA consistency

Determine whether the consistency of the asymmetric bounded Σ_n-correct forcing axiom Σ_n–CBFA_{<κ}^{<λ}(Γ) follows from the existence of a Σ_n‑correctly H_λ‑reflecting cardinal when λ is singular.

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Background

The consistency of Σn–CBFA{<κ}{<λ}(Γ) is proved under regular λ using correctly reflecting Laver functions and a Baumgartner-style iteration. The construction relies essentially on λ being regular; the singular case is left unresolved.

References

The construction of $Y$ in the above proof makes essential use of the regularity of $\lambda$; it is unclear whether the consistency of $\Sigma_n\mhyphen CBFA_{<\kappa}{<\lambda}(\Gamma)$ follows from the existence of a $\Sigma_n$-correct $H_\lambda$-reflecting cardinal when $\lambda$ is singular.

— $Σ_n$-correct Forcing Axioms (2405.09674 - Goodman, 15 May 2024) in Section 4.2 (Consistency Proofs), after Theorem 4.2