Improve C_3a exact-count lower bound to 1.1873823054 (budgeted semigroup-mask certificate)

README.md

@@ -17,7 +17,7 @@ Bounds for which the level of available verification is currently at minimal lev
 | [1a](https://teorth.github.io/optimizationproblems/constants/1a.html) | Sidon set autocorrelation constant | 1.2802 (1.292*) | 1.502862 |
 | [1b](https://teorth.github.io/optimizationproblems/constants/1b.html) | Erdős minimum overlap constant | 0.379005 | 0.380868 |
 | [2](https://teorth.github.io/optimizationproblems/constants/2a.html) | Crouzeix constant | 2 | $1+\sqrt{2} \approx 2.4142$ |
-| [3a](https://teorth.github.io/optimizationproblems/constants/3a.html) | Gyarmati-Hennecart-Ruzsa sum-difference constant | 1.1835129324 (1.19102809*) | 1.33333 |
+| [3a](https://teorth.github.io/optimizationproblems/constants/3a.html) | Gyarmati-Hennecart-Ruzsa sum-difference constant | 1.1873823054 (1.19102809*) | 1.33333 |
 | [3b](https://teorth.github.io/optimizationproblems/constants/3b.html) | Kakeya sums-differences constant | >1.77898 | 1.83333 |
 | [3c](https://teorth.github.io/optimizationproblems/constants/3c.html) | 4-slope Kakeya-type sum-difference constant | 1.67473389 | 1.75 |
 | [3d](https://teorth.github.io/optimizationproblems/constants/3d.html) | Single-set sum-difference exponent | 2 | 2 |
@@ -147,6 +147,7 @@ Bounds for which the level of available verification is currently at minimal lev
 - [3a](https://teorth.github.io/optimizationproblems/constants/3a.html) **improved lower bound (limit value):** $C_{3a} \geq 1.187326127925948*$ by [Numaro](https://numaro.tech), 23 Jul 2026.
 - [3a](https://teorth.github.io/optimizationproblems/constants/3a.html) **improved lower bound (limit value):** $C_{3a} \geq 1.19102809*$ by [L. Kleinwaks](https://github.com/kleinwaks/masked-digit-sum-difference-bound), 24 Jul 2026.
 - [3d](https://teorth.github.io/optimizationproblems/constants/3d.html) **solved:** $C_{3d} = 2$ by [H. Lin and S. Li](https://arxiv.org/abs/2607.27199), 29 Jul 2026.
+- [3a](https://teorth.github.io/optimizationproblems/constants/3a.html) **improved lower bound (exact-count certificate):** $C_{3a} \geq 1.1873823054$ by [C. Barnett](https://github.com/barnettcaleb1/c3a-exact-count-certificate), 5 Aug 2026.
 
 ## Maintainers
 

constants/3a.md

@@ -31,6 +31,7 @@ $$ |A-B| \gg |A+B|^{C_{3a}}.$$
 | $1.1835129324$ | [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. |
 | $1.19102809$* | [K2026] | Base-$34065$ masked-digit limit construction with $M=\langle1518,1524,1587,2024,2032,2116\rangle\cap[0,17032]$ and a directed-rounding certificate. |
+| $1.1873823054$ | [Ba2026] | Finite exact-count certificate: $U=\\{\sum\_{i=0}^{255} a\_i\,379^i : a\_i \in M,\ \sum\_i a\_i \le 11923\\}$ with $M=\langle24,26,36,39\rangle\cap[0,189]$ from the [K2026] progression ($\lvert M\rvert=99$, $\lvert M+M\rvert=288$, $\lvert M-M\rvert=377$, $Q=379$, carry-free), i.e. the budgeted truncation of that mask at $m=256$ digits. Certified by digit-string DPs with every quantity bounded in the safe direction: $\lvert U+U\rvert \le N = 6.40031822639\ldots\times 10^{493}$, $T = 3.18558899774\ldots\times 10^{617} \le \lvert U-U\rvert \le D = 1.01085191601\ldots\times 10^{619} < 2\max U+1 = 1.35405951034\ldots\times 10^{660}$ ($\max U$ exact), giving $\theta(U) > 1.187382305438637$; the exact integers and a re-runnable checker are in the [certificate archive](https://github.com/barnettcaleb1/c3a-exact-count-certificate). This finite value exceeds the [Num2026] limit. The limit of the present family is $1.1893936243$, approached by deeper truncations. |
 
 
 ## Additional comments and links
@@ -55,3 +56,8 @@ $C_{3a} \geq 1 + \log( \lvert U-U \rvert /\lvert U+U \rvert )/\log(2 \max(U)+1)$
 - [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).
 - [K2026] Kleinwaks, Logan. A masked-digit lower bound for the Gyarmati–Hennecart–Ruzsa sum–difference constant, [proof and verification package](https://github.com/kleinwaks/masked-digit-sum-difference-bound), [submitted to this repository](https://github.com/teorth/optimizationproblems/pull/134) (2026).
+- [Ba2026] Barnett, Caleb. Finite exact-count certificate for $C_{3a}$ via a budgeted semigroup-mask construction, [verification package](https://github.com/barnettcaleb1/c3a-exact-count-certificate), submitted to this repository (2026).
+
+## Contribution notes
+
+The [Ba2026] certificate and its verification package were prepared with substantial AI assistance (Anthropic Claude), directed and reviewed by the human contributor.