Metric Markov cotype of \ell_{1} and Hilbert-space Lipschitz extension

Proves that real ℓ₁ has metric Markov cotype two, answering Mendel and Naor's question. Consequently, every Lipschitz map from an arbitrary subset of a real Hilbert space into ℓ₁ extends to the whole space with a universal multiplicative loss in its Lipschitz constant, resolving Ball's extension problem for this target.

Manuscript

Metric Markov Cotype Two of ℓ₁

October 5, 2026 · source · cite as \cite{OAI:Metric-Markov-Cotype-Two-of-l1-October-5-2026}

We prove that the real Banach space ℓ₁ 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 ℓ₁ extends to the whole Hilbert space with a universal multiplicative loss in its Lipschitz constant, resolving Ball's extension problem for this target.

Result 332 · Functional analysis. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.