Subpolynomial dimension reduction in Lp

What OpenAI claims

For every fixed 1 < p < ∞ and distortion D > 1, every n-point subset of real Lp embeds into ℓ_p^d with distortion at most D and dimension d=n^o(1), answering Naor's sublinear-dimension question for p ≠ 2. In contrast, exact embeddings require worst-case dimension Θ(n²) when p ≠ 2. (Lean)

Paper

1. Subpolynomial dimension reduction in Lp

   23 September 2026 · Preprint, not peer reviewed · PDF

   For every fixed 1 < p < ∞ and D > 1, every n-point subset of a real Lp space embeds into ℓ_p^d with distortion at most D and subpolynomial dimension d=n^o(1). The target has the same exponent p, and the embedding need not be linear.

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.