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Revise lower bounds for Grothendieck's constant #66

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Revise lower bounds for Grothendieck's constant #66

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4 changes: 3 additions & 1 deletion constants/10a.md
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Expand Up @@ -37,7 +37,8 @@ $u_{i},v_{j} \in S^{d-1}$ for some sufficiently large finite dimension $d$).
| $1$ | Trivial | Follows from the definitions |
| $\dfrac{\pi}{2} \approx 1.57080$ | [G1953] | Grothendieck’s original lower bound |
| $1.67696\ldots$ | [Dav1984], [Ree1991] | (due to Davie and independently Reeds) |
| $1.67696\ldots + 10^{-26}$ | [Hei26] | Best known lower bound |
| $1.67696\ldots + 10^{-26}$ | [Hei26] | Strictly improves over Davie--Reeds |
| $1.67696\ldots + 10^{-12}$ | [JM26] | Best known lower bound, concurrent with [Hei26] |

## Additional comments and links

Expand All @@ -52,6 +53,7 @@ $u_{i},v_{j} \in S^{d-1}$ for some sufficiently large finite dimension $d$).
- [Dav1984] Davie, A. M. *Lower bound for $K_{G}$.* Unpublished note (1984).
- [G1953] Grothendieck, Alexandre. *Résumé de la théorie métrique des produits tensoriels topologiques.* Bol. Soc. Mat. São Paulo **8** (1953), 1–79.
- [Hei26] Heilman, Steven. *A lower bound for Grothendieck's constant.* (2026) [arXiv:2603.22616](https://arxiv.org/abs/2603.22616)
- [JM26] Jones, Chris; Malavolta, Giulio. *The Grothendieck constant is strictly larger than Davie-Reeds' bound.* (2026) [arXiv:2603.30039](https://arxiv.org/abs/2603.30039)
- [K1979] Krivine, Jean-Louis. *Constantes de Grothendieck et fonctions de type positif sur les sphères.* Advances in Mathematics **31** (1979), 16–30.
- [Pis2012] Pisier, Gilles. *Grothendieck’s theorem, past and present.* Bull. Amer. Math. Soc. (N.S.) **49** (2012), 237–323. [arXiv:1101.4195](https://arxiv.org/abs/1101.4195)
- [Ree1991] Reeds, James A. *A new lower bound on the real Grothendieck constant.* Unpublished manuscript (1991).
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