{"id":"openai-math/Metric-Markov-Cotype-Two-of-l1","pdf":"https://github.com/openai/math/blob/main/preprints/Metric-Markov-Cotype-Two-of-l1-October-5-2026/l1-markov-cotype.pdf","url":"https://github.com/openai/math/tree/main/preprints/Metric-Markov-Cotype-Two-of-l1-October-5-2026","tags":["metric-geometry","banach-spaces","lipschitz-extension","cotype"],"score":0,"title":"Metric Markov Cotype Two of ℓ 1","domain":"Functional analysis","family":"332","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.FA","summary":"We prove that the real Banach space ℓ 1 has metric Markov cotype two, answering a question of Mendel and Naor. As a consequence, every Lipschitz map from an arbitrary subset of a real Hilbert space into ℓ 1 extends to the whole Hilbert space with a universal multiplicative loss in its Lipschitz constant, resolving Ball's extension problem for this target.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Metric Markov cotype of ℓ 1 and Hilbert-space Lipschitz extension"}