# [Withdrawal notice: Algebraicity of Weil classes on split abelian eightfolds](paper.pdf)

OpenAI  
**Withdrawn on October 6, 2026.**

The proof contains a sign error in the stabilization-trace argument used to obtain negative double points. In the manuscript's signed double-point convention, write $I(f_1)=-m$ with $m>0$. The proof assigns each reverse stabilization trace sign $+1$ and therefore claims that inserting $m$ such traces makes the signed count zero.

Accounting for the opposite source orientations of the two branches of the standard cusp gives sign $-1$ for each reverse trace in this convention. The resulting count is therefore

$$I_{\mathrm{new}}=I(f_1)-m=-2m\ne0.$$

The Eliashberg-Murphy cancellation theorem invoked at this step requires zero signed double-point count, so its hypothesis is not met. The subsequent oriented-surgery and embedded-brane construction is therefore unsupported, and the paper does not establish its claimed algebraicity theorem.

This withdrawal concerns the proof; it does not assert that the mathematical statement is false.

## Archived manuscript

[Pre-withdrawal PDF](https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Algebraicity-of-Weil-classes-on-split-abelian-eightfolds-September-18-2026/paper.pdf)  
Repository revision: `adc7f1241b42e322a6451854ab7e4b4c146bf78a`.