{"id":"openai-math/The-dyadic-case-of-the-Erdos-similarity-conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/The-dyadic-case-of-the-Erdos-similarity-conjecture-September-25-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-dyadic-case-of-the-Erdos-similarity-conjecture-September-25-2026","tags":["measure-theory","erdos-similarity","fractals","real-analysis"],"score":0,"title":"The dyadic case of the Erdős similarity conjecture","domain":"Real and complex analysis","family":"084","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CA","summary":"We construct a compact subset of the unit interval, of measure arbitrarily close to one, that contains no affine copy of the dyadic sequence $`\\{2^{-n}:n\\ge1\\}`$. The conclusion holds for every translation and every nonzero real dilation, of either sign, proving the dyadic case of the Erdős similarity conjecture.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"The geometric case of the Erdős similarity conjecture"}