Problem detail · source-aware
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How dense can a sphere packing in $\mathbb{R}^n$ be as $n \to \infty$? The Kabatiansky-Levenshtein upper bound stood for almost fifty years; the new proof improves the asymptotic upper bound all the way down to the Cohn-Elkies linear-programming threshold.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
Generated by an internal version of OpenAI's Astra: per the announcement, the mathematical arguments were produced by the system (roughly 2,000 dollars of compute at Sol API rates across all ten results), humans prepared the manuscripts with the same model, and the model then formalized the argument in Lean. A narrated reasoning walkthrough is published for each result.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Kernel-checked Lean 4 certificate in OpenAI's public ten-proofs repository (Lean 4.32, mathlib, `lake build All`), with an independent Comparator checking route. Statement fidelity and community review of the day-old company announcement remain pending.
Correctness: supported · statement fidelity: audited · peer review: none
upper bounds reach the Cohn-Elkies threshold; the true asymptotic density remains open
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.