diff --git a/_includes/math/ai/OpenAIMath.html b/_includes/math/ai/OpenAIMath.html
index 1935b8a3..fabaa3f7 100644
--- a/_includes/math/ai/OpenAIMath.html
+++ b/_includes/math/ai/OpenAIMath.html
@@ -27,7 +27,14 @@ <h4>#109</h4>
 
         <ul class="now-list">
             <li>CrocSwap/integer-mult-bounds <a class="gh-link" href="https://github.com/CrocSwap/integer-mult-bounds" target="_blank" rel="noopener noreferrer" aria-label="CrocSwap/integer-mult-bounds on GitHub"><svg viewBox="0 0 16 16" class="ico" aria-hidden="true"><path d="M8 0c4.42 0 8 3.58 8 8a8.013 8.013 0 0 1-5.45 7.59c-.4.08-.55-.17-.55-.38 0-.27.01-1.13.01-2.2 0-.75-.25-1.23-.54-1.48 1.78-.2 3.65-.88 3.65-3.95 0-.88-.31-1.59-.82-2.15.08-.2.36-1.02-.08-2.12 0 0-.67-.22-2.2.82-.64-.18-1.32-.27-2-.27-.68 0-1.36.09-2 .27-1.53-1.03-2.2-.82-2.2-.82-.44 1.1-.16 1.92-.08 2.12-.51.56-.82 1.28-.82 2.15 0 3.06 1.86 3.75 3.64 3.95-.23.2-.44.55-.51 1.07-.46.21-1.61.55-2.33-.66-.15-.24-.6-.83-1.23-.82-.67.01-.27.38.01.53.34.19.73.9.82 1.13.16.45.68 1.31 2.69.94 0 .67.01 1.3.01 1.49 0 .21-.15.45-.55.38A7.995 7.995 0 0 1 0 8c0-4.42 3.58-8 8-8Z"/></svg>GitHub</a>: a community effort to optimize the construction and push $\kappa$ higher. It is conditional on the #109 framework and is not an official OpenAI release.</li>
-            <li>Current reviewed result: $\kappa=0.0023$ (above $2^{-9}$), not a complete Lean multiplication theorem.</li>
+            <li>Status:
+                <ul>
+                    <li>Previous selected: #1094 <a class="gh-link" href="https://github.com/CrocSwap/integer-mult-bounds/pull/1094" target="_blank" rel="noopener noreferrer" aria-label="PR #1094 on GitHub"><svg viewBox="0 0 16 16" class="ico" aria-hidden="true"><path d="M8 0c4.42 0 8 3.58 8 8a8.013 8.013 0 0 1-5.45 7.59c-.4.08-.55-.17-.55-.38 0-.27.01-1.13.01-2.2 0-.75-.25-1.23-.54-1.48 1.78-.2 3.65-.88 3.65-3.95 0-.88-.31-1.59-.82-2.15.08-.2.36-1.02-.08-2.12 0 0-.67-.22-2.2.82-.64-.18-1.32-.27-2-.27-.68 0-1.36.09-2 .27-1.53-1.03-2.2-.82-2.2-.82-.44 1.1-.16 1.92-.08 2.12-.51.56-.82 1.28-.82 2.15 0 3.06 1.86 3.75 3.64 3.95-.23.2-.44.55-.51 1.07-.46.21-1.61.55-2.33-.66-.15-.24-.6-.83-1.23-.82-.67.01-.27.38.01.53.34.19.73.9.82 1.13.16.45.68 1.31 2.69.94 0 .67.01 1.3.01 1.49 0 .21-.15.45-.55.38A7.995 7.995 0 0 1 0 8c0-4.42 3.58-8 8-8Z"/></svg>GitHub</a>, $\kappa\approx 0.00167$ (about $2^{-9.2}$).</li>
+                    <li>Selected: #4359 <a class="gh-link" href="https://github.com/CrocSwap/integer-mult-bounds/pull/4359" target="_blank" rel="noopener noreferrer" aria-label="PR #4359 on GitHub"><svg viewBox="0 0 16 16" class="ico" aria-hidden="true"><path d="M8 0c4.42 0 8 3.58 8 8a8.013 8.013 0 0 1-5.45 7.59c-.4.08-.55-.17-.55-.38 0-.27.01-1.13.01-2.2 0-.75-.25-1.23-.54-1.48 1.78-.2 3.65-.88 3.65-3.95 0-.88-.31-1.59-.82-2.15.08-.2.36-1.02-.08-2.12 0 0-.67-.22-2.2.82-.64-.18-1.32-.27-2-.27-.68 0-1.36.09-2 .27-1.53-1.03-2.2-.82-2.2-.82-.44 1.1-.16 1.92-.08 2.12-.51.56-.82 1.28-.82 2.15 0 3.06 1.86 3.75 3.64 3.95-.23.2-.44.55-.51 1.07-.46.21-1.61.55-2.33-.66-.15-.24-.6-.83-1.23-.82-.67.01-.27.38.01.53.34.19.73.9.82 1.13.16.45.68 1.31 2.69.94 0 .67.01 1.3.01 1.49 0 .21-.15.45-.55.38A7.995 7.995 0 0 1 0 8c0-4.42 3.58-8 8-8Z"/></svg>GitHub</a>, $\kappa=0.0023$ (above $2^{-9}$), maintainer-reviewed but not a complete Lean multiplication theorem.</li>
+                    <li>Merged but not selected: #4416 <a class="gh-link" href="https://github.com/CrocSwap/integer-mult-bounds/pull/4416" target="_blank" rel="noopener noreferrer" aria-label="PR #4416 on GitHub"><svg viewBox="0 0 16 16" class="ico" aria-hidden="true"><path d="M8 0c4.42 0 8 3.58 8 8a8.013 8.013 0 0 1-5.45 7.59c-.4.08-.55-.17-.55-.38 0-.27.01-1.13.01-2.2 0-.75-.25-1.23-.54-1.48 1.78-.2 3.65-.88 3.65-3.95 0-.88-.31-1.59-.82-2.15.08-.2.36-1.02-.08-2.12 0 0-.67-.22-2.2.82-.64-.18-1.32-.27-2-.27-.68 0-1.36.09-2 .27-1.53-1.03-2.2-.82-2.2-.82-.44 1.1-.16 1.92-.08 2.12-.51.56-.82 1.28-.82 2.15 0 3.06 1.86 3.75 3.64 3.95-.23.2-.44.55-.51 1.07-.46.21-1.61.55-2.33-.66-.15-.24-.6-.83-1.23-.82-.67.01-.27.38.01.53.34.19.73.9.82 1.13.16.45.68 1.31 2.69.94 0 .67.01 1.3.01 1.49 0 .21-.15.45-.55.38A7.995 7.995 0 0 1 0 8c0-4.42 3.58-8 8-8Z"/></svg>GitHub</a>, $\kappa=0.00268647$.</li>
+                    <li>Highest open claim: #4470 <a class="gh-link" href="https://github.com/CrocSwap/integer-mult-bounds/pull/4470" target="_blank" rel="noopener noreferrer" aria-label="PR #4470 on GitHub"><svg viewBox="0 0 16 16" class="ico" aria-hidden="true"><path d="M8 0c4.42 0 8 3.58 8 8a8.013 8.013 0 0 1-5.45 7.59c-.4.08-.55-.17-.55-.38 0-.27.01-1.13.01-2.2 0-.75-.25-1.23-.54-1.48 1.78-.2 3.65-.88 3.65-3.95 0-.88-.31-1.59-.82-2.15.08-.2.36-1.02-.08-2.12 0 0-.67-.22-2.2.82-.64-.18-1.32-.27-2-.27-.68 0-1.36.09-2 .27-1.53-1.03-2.2-.82-2.2-.82-.44 1.1-.16 1.92-.08 2.12-.51.56-.82 1.28-.82 2.15 0 3.06 1.86 3.75 3.64 3.95-.23.2-.44.55-.51 1.07-.46.21-1.61.55-2.33-.66-.15-.24-.6-.83-1.23-.82-.67.01-.27.38.01.53.34.19.73.9.82 1.13.16.45.68 1.31 2.69.94 0 .67.01 1.3.01 1.49 0 .21-.15.45-.55.38A7.995 7.995 0 0 1 0 8c0-4.42 3.58-8 8-8Z"/></svg>GitHub</a>, $\kappa=0.00302015$ (author-checked).</li>
+                </ul>
+            </li>
             <li>Notes: <a href="{{ '/articles/Math/ai/openai/integer-mult-bounds/' | relative_url }}">CrocSwap integer-mult-bounds</a></li>
         </ul>
     </div>