Sawhney: Astra proved the asymptotic linear programming bound for sphere packing
Mehtaab Sawhney · Inside OpenAI’s Breakthroughs in Mathematical Reasoning · Sep 8, 2026 · at 27:09
OpenAI researcher Mehtaab Sawhney explains to a16z partner Lisha Li how OpenAI's reasoning initiative, Astra, resolved an open problem regarding high-dimensional sphere packing.
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“And what the model shows is that Actually the linear programming bound in large dimensions has this extremely nice asymptotic behavior, and the proof kind of explains where this is coming from, and because you understand this LP bound perfectly, this actually just gives a better bound on delta D. It turns out that this old bound can be kind of reinterpreted in this framework, and what the model does is it shows you the best possible bound you can get by this framework.”
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