A proposed proof of Open Question 3 in instance-optimal identity testing

Editor’s note: this proof was entirely generated by ChatGPT 5.6, I didn’t contribute anything! I’m publishing this in case it will be a useful reference for others. In identity testing, we know a reference distribution $q$, receive independent samples from an unknown distribution $p$, and want to distinguish \[p=q \qquad\text{from}\qquad d_{\mathrm{TV}}(p,q)>\varepsilon.\] The usual worst-case…