Skip to content

Improve lower bound for the Gyarmati–Hennecart–Ruzsa sum-difference constant to 1.187326127925948 (base-89 capped digit construction, limit certificate) #131

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
unnir wants to merge 1 commit into
base: main
Choose a base branch
from
Open

Improve lower bound for the Gyarmati–Hennecart–Ruzsa sum-difference constant to 1.187326127925948 (base-89 capped digit construction, limit certificate) #131

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
2 changes: 2 additions & 0 deletions constants/3a.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -24,6 +24,7 @@ $$ |A-B| \gg |A+B|^{C_{3a}}.$$
| $1.173077$ |[Z2025]|
| $1.1740744$ | [G2026] | Base-$21$ digit construction with exact counting certificate. |
| $1.1835129324$ | [MI2026] | Base-$33$ digit construction with exact counting certificate. |
| $1.187326127925948$ | [Num2026] | Capped base-$89$ digit construction (max digit $44$, sparse 29-letter alphabet); certified as the large-deviation LIMIT of the exact per-depth lemma values $\theta(U_d)$, each valid for every $d$ and increasing to the limit (the same limit-as-lower-bound principle as [Z2025]); interval-arithmetic certificate, replayable checker included. |


## Additional comments and links
Expand All @@ -38,5 +39,6 @@ $C_{3a} \geq 1 + \log( \lvert U-U \rvert /\lvert U+U \rvert )/\log(2 \max(U)+1)$
- [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, [certificate archive](https://doi.org/10.5281/zenodo.20794135), [submitted to this repository](https://github.com/teorth/optimizationproblems/pull/95) (2026).
- [Num2026] Numaro ([numaro.tech](https://numaro.tech)). Large-deviation limit certificate for a base-89 capped digit construction, [certificate archive](https://doi.org/10.5281/zenodo.21504058), submitted to this repository (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).