The occupation time of a random walk generated by the uniform random permutation--a GPT-6 Astra proof

This note provide a proof of Conjecture 2.5 in Fang et al. (J. Appl. Probab., 58(4):851--867, 2021), with the help of \texttt{GPT-6 Astra}. We show that the number of edges lying above zero of a random walk generated from the uniform permutation has the discrete arcsine law. The proof is short but h