arXiv:2605.31416v3 Announce Type: replace Abstract: Fractional Gaussian noise and $\FARIMA(0,d,0)$ have the same long-memory pole $|\theta|^{-2d}$ and hence the same leading PACF law $\alpha(n)\sim d/n$. We show that this agreement breaks at the first non-universal order. For $0Source:https://arxiv.org/abs/2605.31416