Soundness and completeness of UCF simplicial models for K45+NU

Let a UCF simplicial model be a simplicial model in the class called UCF in the paper, and let $d53f$ be the logic consisting of propositional logic together with the $d53945+d40dd448$ axioms, modus ponens, and necessitation for each belief modality. UCF soundness and completeness conjecture. The class of UCF simplicial models is sound and complete with respect to propositional logic plus $d53945+d40dd448$, modus ponens, and necessitation for each belief modality. This conjecture asserts an exact proof-theoretic characterization of the formulas valid in UCF simplicial models; the supplied text does not state whether it has been resolved.