The extreme volatility of Bitcoin poses significant challenges for traditional forecasting models. This study introduces a scalable hypothesis-driven feature extraction framework combined with a Random Forest classifier to predict Bitcoin price curvature patterns instead of absolute price levels. Using daily OHLCV data from August 10, 2023, to August 10, 2025, a 14-day sliding window and dual-segment slope comparison are applied for binary labeling. Automated feature engineering is performed using the TSFRESH library with MinimalFCParameters. Model performance is rigorously evaluated via 5-fold cross-validation. The proposed Random Forest model achieves an accuracy of 0.8043 and an F1-score of 0.8072, significantly outperforming Support Vector Machines (linear, RBF, and polynomial kernels) and Long Short-Term Memory (LSTM) networks. In addition, a transaction-cost-aware backtesting experiment demonstrates that the predictive signals retain practical value under realistic trading conditions. The results highlight the effectiveness of curvature-based prediction empowered by scalable hypothesis features, providing a more reliable and interpretable approach for anticipating regime shifts in highly volatile cryptocurrency markets.