Resolving this would provide a complete quantitative picture of extremal behavior for long-range dependent non-linear functionals of Gaussian sequences, unifying the central and non-central regimes under one roof. It would also clarify the precise role of Hermite rank in determining how heavy tails and memory interact to shape rare large deviations. Applications extend to econometrics, telecommunications traffic modeling, and climate data analysis, where long-memory signals are filtered through nonlinear transformations and practitioners need reliable normalizing constants for inference and hypothesis testing.