Remark: Family 094. Subpolynomial dimension reduction in L p

For every fixed $1<p<\infty$ and distortion $D>1$, every $n$-point subset of real $L_p$ embeds into ${{\ell }_p}^d$ with distortion at most $D$ and dimension $d=n^{o(1)}$, answering Naor's sublinear-dimension question for $p\ne 2$. In contrast, exact embeddings require worst-case dimension $\Theta (n^2)$ when $p\ne 2$.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.