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Whether the number of distinct low-energy universes is finite is unknown.","posed_since":"","precise":"Determine whether the set of string compactifications to 4D with a bounded number of light fields and effective theories valid below a fixed cutoff is finite, including whether the number of topologically distinct Calabi-Yau threefolds is finite.","problem_ref":null,"references":"","settled_by":"A finiteness theorem for all compactifications below a fixed cutoff, or an infinite family of distinct consistent vacua.","status_note":"Finiteness of tadpole-bounded flux vacua on a fixed Calabi-Yau orientifold was proven with tame geometry (Bakker, Grimm, Schnell, Tsimerman 2021); finiteness of Calabi-Yau threefold topologies remains open.","title":"Is the number of string vacua 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