Improved lower bound for the complex Grothendieck constant
The complex Grothendieck constant is shown to exceed 1.35584631827168, closing more than a quarter of the gap between the long-standing Davie lower bound and the Haagerup upper bound.
- Lab
- Independent
- Model
- Odin Automatic AI Research Agent
- Field
- Mathematics
- Date
- 2026-09-07
- Human collaborators
- Shengtao Guo, Ethan X. Fang, Junwei Lu
What was found
The classical complex Grothendieck constant is bracketed between Davie's lower bound and Haagerup's upper bound, and the interval has been stubborn. This paper reports a new lower bound of 1.35584631827168 and states that it closes more than one quarter of that gap. The abstract records two separate facts about how it was produced: the numerical part of the proof is rigorously verified by interval arithmetic, and the lower bound and the proof were discovered by the Odin Automatic AI Research Agent.
Novelty check
The abstract fixes the prior state of the art by name, Davie below and Haagerup above, and states the improvement as a fraction of that gap rather than as an unqualified advance, which is the form that makes the claim checkable. No competing improvement was found in the four registries the watch reads. The AI attribution was read from the arXiv abstract directly rather than from an aggregator tag.
Caveats and known objections
Odin is the same undocumented system credited on this registry's 2026-08-16-talagrand-convolution entry, by an overlapping author set, and the caveat recorded there applies here without change: Odin is not a publicly documented system, no vendor is named, no transcript or artifact is published, and there is no way to separate discovery from human reorganization. Read the model field as the authors' attribution rather than as a verified fact. Two further gaps are worth stating. The interval-arithmetic verification is asserted in the abstract but no code or certificate is linked from it, so the computational half of the proof is not reproducible from the sources here; editorial rule 4 caps verification at claimed on that basis. Separately, the sibling Talagrand entry is graded author-verified while this one is graded claimed, and the difference rests only on that missing artifact; a maintainer may reasonably want the two aligned in one direction or the other.
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Entry history (1 event)
- AddedEntered the registry graded Claimed and AI-led.
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Graded claimed for verification and ai-led for autonomy. What these mean.
Cite this entry
whataifound.org. (2026). Improved lower bound for the complex Grothendieck constant. whataifound.org: A Registry of AI Scientific and Mathematical Discoveries. https://whataifound.org/finding/2026-09-07-complex-grothendieck-constantBibTeX
@misc{whataifound-independent-2026-constant,
title = {Improved lower bound for the complex Grothendieck constant},
author = {{whataifound.org}},
year = {2026},
howpublished = {whataifound.org: A Registry of AI Scientific and Mathematical Discoveries},
note = {Result by Independent. Verification: Claimed. Autonomy: AI-led.},
url = {https://whataifound.org/finding/2026-09-07-complex-grothendieck-constant}
}