{"id":"openai-math/A-doubling-Hilbert-subset-with-no-finite-dimensional-bi-Lipschitz-embedding","pdf":"https://github.com/openai/math/blob/main/preprints/A-doubling-Hilbert-subset-with-no-finite-dimensional-bi-Lipschitz-embedding-September-25-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-doubling-Hilbert-subset-with-no-finite-dimensional-bi-Lipschitz-embedding-September-25-2026","tags":["metric-geometry","banach-spaces","bi-lipschitz-embedding"],"score":0,"title":"A doubling Hilbert subset with no finite-dimensional bi-Lipschitz embedding","domain":"Convex and metric geometry","family":"098","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MG","summary":"Every infinite-dimensional real Banach space contains a compact doubling subset that admits no bi-Lipschitz embedding into any finite-dimensional real normed space. The doubling constant has a universal bound, independent of the ambient Banach space. This answers the Lang–Plaut problem negatively, even for compact subsets of Hilbert space.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":true,"family_title":"Compact counterexamples to bi-Lipschitz dimension reduction"}