From 8bf98936c04468a640ef81fb593c55d6218f789b Mon Sep 17 00:00:00 2001
From: Taksh <takshkothari09@gmail.com>
Date: Sun, 6 Sep 2026 22:37:41 +0530
Subject: [PATCH] Label the Romanoff certificate as Griego's superseded bound.

The printed object recomputes 0.490249, not the Yoo record on the table.
---
 README.md        | 2 ++
 constants/45a.md | 5 ++++-
 2 files changed, 6 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index c2c630fc..38bb333f 100644
--- a/README.md
+++ b/README.md
@@ -159,6 +159,8 @@ Bounds for which the level of available verification is currently at minimal lev
 - [43](https://teorth.github.io/optimizationproblems/constants/43a.html) **improved lower bound (unverified):** $C_{43} \geq 0.860*$ (exact $43/50$; certificate-layer result conditional on the lemma set of [KHSHGW2026](https://arxiv.org/abs/2601.22365)) by [J. Savva](https://doi.org/10.5281/zenodo.22223485), 1 Sep 2026.
 - [88a](https://teorth.github.io/optimizationproblems/constants/88a.html) **improved upper bound:** $C_{88a} \leq 186$ via $\mathrm{DHL}[40,2]$, by [OpenAI](https://cdn.openai.com/pdf/51126fac-1b68-4128-9666-c908bcc16033/short_gaps.pdf), 30 Aug 2026, with a Lean 4 formalization conditional on three declared axioms.
 
+- [45](https://teorth.github.io/optimizationproblems/constants/45a.html) **presentation:** the printed certificate is Griego's $0.490249407811155$, not Yoo's record $0.490180063290061$.
+
 ## Maintainers
 
 This site is maintained by Damek Davis, Paata Ivanisvili and Terence Tao.
diff --git a/constants/45a.md b/constants/45a.md
index f9f73165..ec610e5a 100644
--- a/constants/45a.md
+++ b/constants/45a.md
@@ -27,7 +27,9 @@ $C_{45}$ is the asymptotic density (if it exists) of the set of odd integers tha
 | $0.107648$ | [CE2018] |  |
 
 
-## Certificate for the $0.490249407811155$ upper-density bound
+## Certificate for the superseded $0.490249407811155$ Griego bound
+
+The current record is Yoo's $0.490180063290061$ ([Y2026]); that bound has no printed certificate on this page. The object below recomputes Griego's earlier value.
 
 Let
 $$
@@ -90,3 +92,4 @@ The external verifier independently recomputes the 13-prime seed histogram from
 
 Prepared with assistance from Gemini.
 This update was prepared with assistance from GPT-5.5 Pro; the construction, arithmetic, and verification script were reviewed by the human contributor.
+AI assistance was used to reword the certificate heading so it is not mistaken for the record bound.