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Millimeter-wave (mmWave) links are increasingly utilized in wireless x-haul transport to meet growing service demands. However, the inherent susceptibility of mmWave links to weather-related attenuation creates uncertainty about future network capacity which can significantly affect Quality of Service (QoS). This creates a critical challenge: how to make admission control decisions for slices with QoS requirements, balancing acceptance rewards against the risk of future QoS-violation penalties due to capacity uncertainty? To address this, we develop a proactive slice admission control framework that tightly integrates: (i) a predictor that leverages historical link measurements to forecast short-term attenuation and quantify uncertainty; and (ii) an admission control algorithm that incorporates both the predictions and uncertainties to maximize rewards and minimize QoS-violation penalties. We compare our framework against baseline, state-of-the-art, and idealized oracle algorithms using real-world mmWave x-haul data and residential traffic traces. Simulations suggest that our framework can achieve revenues that are 250% larger than baseline algorithms and 75% larger than state-of-the-art algorithms.