Matrix multiplication: the barrier of the 9/4 method
- upper bound ≈ 2.3712by Dupont et al.arxiv.org
- upper bound 2.2500by OpenAIgithub.com
- Last checked
Cite this frontier
DiscoverIA. Matrix multiplication: the barrier of the 9/4 method [Frontier, checked on Oct 12, 2026]. DiscoverIA registry. https://discoveria.ai/frontiers/multiplication-matricielle-barriere
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Only the upper bound is tracked. The upper bound has moved once since 2026, on Oct 2, 2026.
ω, the exponent of matrix multiplication over ℂ (infimum of τ such that two n×n matrices multiply in O_ε(n^(τ+ε)) operations). The tracked repository does not bound ω: it shows that the abstract profile constraints of OpenAI's 9/4 manuscript cannot push below 9/4.
A limit of a proof method, not a faster algorithm, not a lower bound on the true ω, not a proof that 9/4 is optimal. Plotted points come from the literature cited by OpenAI and from its preprint (an unreviewed claim). The repository adds no point to the staircase: the 9/4 barrier is an annotation (plafond-methode), never a bound. Repository results (an abstract profile, not claimed realizable by a tensor character): see notes.
Every step, as a table : Upper bound (2 points)
Best published upper bound on ω (literature cited by OpenAI, then the OpenAI 9/4 preprint).
| Date | Exact value | Nature | Authors | Source |
|---|---|---|---|---|
| Oct 2, 2026 | 9/4 Current record | published | OpenAI | github.com |
| Aug 2026 | 2.371177 Current record | published | Dupont et al. | arxiv.org |
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