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2541 bytes, as of the version from 2026-10-29 10:15 (current). Recorded here, not run.
# T5 literature update, 29 October 2026
The live website document is the baseline. This edit preserves T5, its slug,
parameter-free entry and revision history. It replaces `[2, 2.371177]` with
`[2, 2.25]`; both endpoints are exact bounds, not a computed value of omega.
## Source scope
- [OpenAI's manuscript](https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Matrix-Multiplication-Nine-Fourths-October-2-2026/paper.pdf), Theorem 1.1, is over the complex numbers. Its manuscript date is October 2; the public release was October 6. The inspected paper has no subsequent file revision in its repository history.
- [Amanov, van den Berg and Zuiddam](https://arxiv.org/abs/2610.30054v1), Theorem 1.1, gives the all-fields bound. Their Theorem 5.4 is a restriction on the available proof ingredients, not a lower bound for the exponent itself.
- [Shpilka](https://eccc.weizmann.ac.il/report/2026/281/), Section 7, independently explains extension to every field, including finite fields. This is why T5 need not be restricted to characteristic zero.
- [Lü](https://arxiv.org/abs/2610.18914v1) gives another separation construction; [Pass](https://arxiv.org/abs/2610.28627v1) gives a constructive integer-arithmetic approach. These are supporting follow-ups, not improvements below 9/4.
- Earlier primary references remain in the table. The Coppersmith–Winograd citation now points to the paper rather than Wikipedia. The historical Alman et al. bound cites arXiv v2 because v3 incorporates the later Dupont et al. optimization.
## Checks and limits
Checked the theorem statements, field hypotheses, asymptotic-operation model,
proof route and bibliographic metadata. The definition states polynomial-identity
arithmetic complexity, not approximate arithmetic or bit complexity.
The epsilon slack is essential; neither omega = 9/4 nor practical running-time
improvements follow. No smaller established upper bound was found in this review.
OpenAI, Zuiddam and Navot provide formal proof artifacts. Their published scope
and verification records were inspected; no fresh local Lean build or new
formal certification was performed. The contemporary papers are preprints,
not claimed here to have completed journal peer review.
`check-report.json` records exact rational endpoint checks and document integrity,
not a reproof of the literature. There is no numerical generator for the unknown
exponent. This is an AI-assisted literature revision submitted for human review,
not an editorial acceptance.