From dfbfe4b00ac40a5fcb035d16ff5fc6816f4b513e Mon Sep 17 00:00:00 2001 From: Mosaic Intelligence <463464q435q43@users.noreply.github.com> Date: Wed, 10 Jun 2026 22:05:48 +0200 Subject: [PATCH 1/4] Improve lower bound for C_3a --- constants/3a.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/constants/3a.md b/constants/3a.md index 80f37ad..75de847 100644 --- a/constants/3a.md +++ b/constants/3a.md @@ -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. | +| $1.1823357212$ | [MI2026] | Base-$33$ digit construction with exact counting certificate. | ## Additional comments and links @@ -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/NNN) (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). From e67ae9ed9c25485ea3fd43ab39402cf9a8f15418 Mon Sep 17 00:00:00 2001 From: Mosaic Intelligence <463464q435q43@users.noreply.github.com> Date: Wed, 10 Jun 2026 22:06:20 +0200 Subject: [PATCH 2/4] Fill in PR number in C_3a reference --- constants/3a.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/constants/3a.md b/constants/3a.md index 75de847..bf41972 100644 --- a/constants/3a.md +++ b/constants/3a.md @@ -37,6 +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/NNN) (2026). +- [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). From b9ec963551b445c93b91fee08b86b66ac19b543d Mon Sep 17 00:00:00 2001 From: Mosaic Intelligence <463464q435q43@users.noreply.github.com> Date: Thu, 11 Jun 2026 20:43:24 +0200 Subject: [PATCH 3/4] Improve C_3a lower bound to 1.1830053419... (d=320 rung of the same certificate family) --- constants/3a.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/constants/3a.md b/constants/3a.md index bf41972..95cadae 100644 --- a/constants/3a.md +++ b/constants/3a.md @@ -23,7 +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. | -| $1.1823357212$ | [MI2026] | Base-$33$ digit construction with exact counting certificate. | +| $1.1830053419$ | [MI2026] | Base-$33$ digit construction with exact counting certificate. | ## Additional comments and links From 1aaa0c8d26304ea5bf49e74918ea679d09e4b1cf Mon Sep 17 00:00:00 2001 From: Mosaic Intelligence <463464q435q43@users.noreply.github.com> Date: Thu, 11 Jun 2026 22:07:31 +0200 Subject: [PATCH 4/4] Improve C_3a lower bound to 1.1835129324... (d=420 rung of the same certificate family) --- constants/3a.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/constants/3a.md b/constants/3a.md index 95cadae..362b409 100644 --- a/constants/3a.md +++ b/constants/3a.md @@ -23,7 +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. | -| $1.1830053419$ | [MI2026] | Base-$33$ digit construction with exact counting certificate. | +| $1.1835129324$ | [MI2026] | Base-$33$ digit construction with exact counting certificate. | ## Additional comments and links