The Blaschke-Lebesgue problem asks for the least volume of a convex solid of constant width 
in three-dimensional Euclidean space and for the
bodies attaining it. The conjectured minimizers are the two Meissner
tetrahedra.
Jiang (2026) proved that every such body 
satisfies
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The Meissner tetrahedra provide the upper bound
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The lower bound does not identify a minimizing body, so the three-dimensional problem remains open.
Jiang (2026) reports assistance from GPT-6 Astra in exploratory derivations, calculations, and checks and takes responsibility for the final proof.
