Real and complex analysis·OpenAI Math·Result 073·Lean formalisation listed
The Falconer distance conjecture
One of the 372 results in OpenAI's public mathematics catalogue, filed under real and complex analysis: 1 preprint, the latest dated 23 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.
Latest paper
The Falconer distance conjecture in all dimensions
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What OpenAI claims
Resolves the Falconer distance conjecture in every dimension d ≥ 2: every compact set E ⊂ ℝd with Hausdorff dimension greater than d/2 determines a set of Euclidean distances of positive Lebesgue measure. (Lean)
Paper
The Falconer distance conjecture in all dimensions
We resolve the Falconer distance conjecture in every dimension. For every integer d ≥ 2, a compact subset of ℝd with Hausdorff dimension greater than d/2 determines a set of Euclidean distances of positive Lebesgue measure.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
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