Separating e_ubd from the meager invariants without centeredness

Develop a method to overcome the need for centeredness when constructing ultrafilter names at limit stages so that one can mix closed-ultrafilter-limits with FAM-limits (e.g., via the forcing \widetilde{E}) to separate e_ubd from non(M) and pr_ubd from cov(M).

Background

The text discusses using FAM-limits to keep non(\mathcal{E}) small and notes that \widetilde{E}, unlike E, has FAM-limits and even (closed-)ultrafilter-limits. This suggests that combining all three limit methods might separate e_ubd from meager invariants.

However, the construction of ultrafilter names at limit stages in the paper relies on centeredness, which \widetilde{E} lacks. The authors explicitly state they do not know how to overcome this barrier.