Seizure prediction from Electroencephalogram (EEG) signals is a critical task for proactive intervention in epilepsy management. Existing models often struggle to capture high-order inter-channel dependencies dynamically and adapt to the spectral variations preceding seizure onset, especially in cross-patient scenarios. To address these issues, a novel Unified Hypergraph-Mamba (UHM) framework, which for the first time integrates hypergraph-based spatial modeling with Mamba-based adaptive spectral modeling. Specifically, a hypergraph attention mechanism is designed to capture high-order spatial interactions among EEG channels, enabling dynamic representation of inter-channel dependencies. Concurrently, an adaptive spectral modeling module based on the Mamba architecture selectively emphasizes frequency components most indicative of preictal states. Together, these components form a unified architecture capable of jointly modeling spatiotemporal EEG dynamics. Extensive experiments conducted on both patient-specific and cross-patient settings demonstrate that our model consistently outperforms state-of-the-art baselines, achieving superior sensitivity and AUC.