OpenAI · 094-01 · 2026-09-23 · Convex and metric geometry
Subpolynomial dimension reduction in Lp
preprints/Subpolynomial-dimension-reduction-in-Lp-September-23-2026
Family 094. Subpolynomial dimension reduction in .
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
For every fixed and distortion , every -point subset of real embeds into with distortion at most and dimension , answering Naor's sublinear-dimension question for . In contrast, exact embeddings require worst-case dimension when .
For every fixed and D > 1, every n-point subset of a real Lp space embeds into with distortion at most D and subpolynomial dimension . The target has the same exponent p, and the embedding need not be linear.
Preprint source and Lean scope
The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.
This preprint is named in the Lean scope note for 094: Subpolynomial dimension reduction in <i>L</i><sub><i>p</i></sub>. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.