OpenAI research collection Ā· 1 manuscript Ā· Source checked 2026-10-19
OpenAI's result summary
Constructs arbitrarily large finite d-dimensional simplicial complexes, for every d ā„ 3, with uniformly bounded vertex degrees and uniform š½_(2) coboundary expansion in every degree below d. Together with the known graph and two-dimensional cases, this establishes the existence of such expanders in every positive dimension.
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MANUSCRIPT 01
Bounded-degree coboundary expanders in every dimension
For every integer d ā„ 3, we construct arbitrarily large finite d-dimensional simplicial complexes with uniformly bounded vertex degrees and uniform š½_(2) coboundary expansion in every degree below d. Together with the known graph and two-dimensional cases, this establishes the existence of bounded-degree š½_(2) coboundaryā¦
Full source abstract
For every integer d ā„ 3, we construct arbitrarily large finite d-dimensional simplicial complexes with uniformly bounded vertex degrees and uniform š½_(2) coboundary expansion in every degree below d. Together with the known graph and two-dimensional cases, this establishes the existence of bounded-degree š½_(2) coboundary expanders in every positive dimension.
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New mathematical reasoning could help AI tackle harder scientific and computational problems. How reliably these skills transfer beyond mathematics will determine how much they contribute to general intelligence.