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This has never been proved for general solutions.","posed_since":"1970","precise":"For generic 3+1 vacuum solutions with a spacelike singularity, prove that spatial derivatives become negligible near the singularity, so that each spatial point evolves as an independent homogeneous Bianchi IX (mixmaster) cosmology with infinitely many Kasner epochs. An answer is a proof of these asymptotics for an open set of data, or a counterexample.","problem_ref":null,"references":"","settled_by":"A rigorous description of the asymptotics near a generic spacelike singularity in vacuum, confirming or refuting local mixmaster oscillations.","status_note":"Stable Kasner-like big bang formation is proved in non-oscillatory regimes such as stiff matter or high dimensions (Fournodavlos, Rodnianski, Speck 2020); the oscillatory vacuum case is open as of 2026.","title":"Are generic spacelike singularities locally oscillatory, as the BKL picture 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