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.
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In Metric Markov Cotype Two of ℓ1, 5 October 2026
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The real space \ell_1 satisfies
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Theorem 1.2
In Metric Markov Cotype Two of ℓ1, 5 October 2026