diff --git a/constants/3a.md b/constants/3a.md
index 7c84b23..9a9368e 100644
--- a/constants/3a.md
+++ b/constants/3a.md
@@ -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
@@ -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).