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Improve problem 3a lower bound to 1.1835129324... (exact-count certificate) #95

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Improve problem 3a lower bound to 1.1835129324... (exact-count certificate) #95

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dfbfe4b
Improve lower bound for C_3a
463464q435q43 Jun 10, 2026
e67ae9e
Fill in PR number in C_3a reference
463464q435q43 Jun 10, 2026
b9ec963
Improve C_3a lower bound to 1.1830053419... (d=320 rung of the same c…
463464q435q43 Jun 11, 2026
1aaa0c8
Improve C_3a lower bound to 1.1835129324... (d=420 rung of the same c…
463464q435q43 Jun 11, 2026
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2 changes: 2 additions & 0 deletions constants/3a.md
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Expand Up @@ -23,6 +23,7 @@ $$ |A-B| \gg |A+B|^{C_{3a}}.$$
| $1.173050$ |[G2025] |
| $1.173077$ |[Z2025]|
| $1.1740744$ | [G2026] | Base-$21$ digit construction with exact counting certificate. |
| $1.1835129324$ | [MI2026] | Base-$33$ digit construction with exact counting certificate. |


## Additional comments and links
Expand All @@ -36,5 +37,6 @@ $C_{3a} \geq 1 + \log( \lvert U-U \rvert /\lvert U+U \rvert )/\log(2 \max(U)+1)$
- [GGSWT2025] Georgiev, Bogdan; Gómez-Serrano, Javier; Tao, Terence; Wagner, Adam Zsolt. Mathematical exploration and discovery at scale. [arXiv:2511.02864](https://arxiv.org/abs/2511.02864)
- [G2025] Gerbicz, Robert. Sums and differences of sets (improvement over AlphaEvolve), 2025. [arXiv:2505.16105](https://arxiv.org/abs/2505.16105).
- [GHR2007] Gyarmati, Katalin; Hennecart, François; Ruzsa, Imre Z. Sums and differences of finite sets. Functiones et Approximatio Commentarii Mathematici, 37(1):175–186, 2007.
- [MI2026] Mosaic Intelligence ([@111111](https://x.com/111111)). Exact-count certificate for problem 3a, [submitted to this repository](https://github.com/teorth/optimizationproblems/pull/95) (2026).
- [Z2025] Zheng, Fan. Sums and differences of sets: a further improvement over AlphaEvolve, 2025. [arXiv:2506.01896](https://arxiv.org/abs/2506.01896).
- [G2026] Griego, Sebastian. Base-$21$ digit construction certificate for $C_{3a}$, [submitted to this repository](https://github.com/teorth/optimizationproblems/pull/71) (2026).