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2 changes: 1 addition & 1 deletion constants/22b.md
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Expand Up @@ -14,7 +14,7 @@ Upper bounds are typically found by constructing alternating torus knots or link
| Bound | Reference | Comments |
| ----- | --------- | -------- |
|$2\pi+2\approx 8.28$ | Trivial | Hopf chain link of stadium curves
| 8.50| [O2013] | Double helix |
| 8.50| [Olsen2013] | Double helix |
| 7.63| [Huh2018] | Four-strand superhelix |
| $1+\pi\sqrt{4+\frac{1}{\pi^2}}\approx 7.36$| [Klotz2021] | Wrapped circle |
| 7.31| [Kim2024] | Asymmetric double helix |
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4 changes: 2 additions & 2 deletions constants/46a.md
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Expand Up @@ -36,9 +36,9 @@ $$

- Many papers work with the paraboloid model surface (or a bounded subset thereof); by localization and rescaling, the best-known exponents for compact strictly convex surfaces (including $S^2$) track the paraboloid results up to standard $\varepsilon$-losses that can often be removed by "epsilon removal lemmas".

- For most of the results in the literature, the $L^\infty(S^2)$ norm on the right-hand side can be replaced with $L^q(S^2)$ for various $q$; for instance, in the Tomas-Stein theorem one can take $q=2$. There are also bilinear and multilinear variants of the conjecture. See for instance [Ta2004] for more discussion.
- For most of the results in the literature, the $L^\infty(S^2)$ norm on the right-hand side can be replaced with $L^q(S^2)$ for various $q$; for instance, in the Tomas-Stein theorem one can take $q=2$. There are also bilinear and multilinear variants of the conjecture. See for instance [Tao2004] for more discussion.

- Stein's restriction conjecture $C_{46}=3$ implies the Kakeya conjecture in ${\mathbb R}^3$ (see, e.g., [Ta2004]), which was recently proven in [WZ2025].
- Stein's restriction conjecture $C_{46}=3$ implies the Kakeya conjecture in ${\mathbb R}^3$ (see, e.g., [Tao2004]), which was recently proven in [WZ2025].

## References

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