Existence of correctly reflecting Laver functions

Determine whether correctly reflecting Laver functions exist in ZFC for every Σ_n‑correctly H_λ‑reflecting cardinal κ<λ, without additional forcing (i.e., whether one can construct a function g:κ→V_κ that anticipates parameters in H_λ in the correctly reflecting sense).

Background

The paper defines ‘correctly reflecting Laver functions’ tailored to Σn‑correctly Hλ‑reflecting cardinals and shows they can always be added via fast function forcing. Whether such functions exist outright in ZFC, analogous to classical Laver functions for supercompactness, is not settled.