{"id":"openai-math/The-higher-dimensional-Erdos-distinct-distances-conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/The-higher-dimensional-Erdos-distinct-distances-conjecture-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-higher-dimensional-Erdos-distinct-distances-conjecture-September-23-2026","tags":["discrete-geometry","distinct-distances","erdos-problems","combinatorial-geometry"],"score":0,"title":"The higher-dimensional Erdős distinct-distances conjecture","domain":"Combinatorics","family":"166","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CO","summary":"For every fixed integer d ≥ 3, we prove that every set of n ≥ 2 distinct points in ℝ d determines at least $`c_d n^{2/d}`$ distinct distances, where $`c_d\\gt 0`$ depends only on d . This resolves the higher-dimensional Erdős distinct-distances conjecture positively.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"The higher-dimensional Erdős distinct-distances conjecture"}