OpenAI · 177-01 · 2026-09-24 · Combinatorics
Bounded-degree coboundary expanders in every dimension
preprints/Bounded-degree-coboundary-expanders-in-every-dimension-September-24-2026
Family 177. Bounded-degree coboundary expanders in every dimension.
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
Constructs arbitrarily large finite -dimensional simplicial complexes, for every , with uniformly bounded vertex degrees and uniform coboundary expansion in every degree below . Together with the known graph and two-dimensional cases, this establishes the existence of such expanders in every positive dimension.
For every integer d ≥ 3, we construct arbitrarily large finite d-dimensional simplicial complexes with uniformly bounded vertex degrees and uniform 𝔽2 coboundary expansion in every degree below d. Together with the known graph and two-dimensional cases, this establishes the existence of bounded-degree 𝔽2 coboundary expanders in every positive dimension.
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 177: Bounded-degree coboundary expanders. 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.