Predicting which hypothetical inorganic crystals can be experimentally realized remains a central challenge in accelerating materials discovery. SyntheFormer is a positive-unlabeled framework that learns synthesizability directly from crystal structure, combining Fourier-transformed crystal properties (FTCP) representation with structure-aware feature extraction, Random-Forest feature selection, and a compact deep MLP classifier. The model is trained on historical data from 2011 through 2018 and evaluated prospectively on future years from 2019 to 2025, where the positive class constitutes only 1.02 percent of samples. Under this temporally separated evaluation, SyntheFormer achieves a test AUC of 0.735, AUPRC of 0.099 and 97.6 percent recall at 94.2 percent coverage with dual-threshold calibration. Direct prospective validation supports this result as two materials that were unlabeled at the time of data curation, Y6Fe(SiS7)2 and BaYb2F8, were assigned high SyntheFormer scores (0.961 and 0.753, respectively) and were subsequently reported experimentally. Crucially, the model recovers experimentally confirmed metastable compounds that lie far from the convex hull and simultaneously assigns low scores to many thermodynamically stable yet unsynthesized candidates, demonstrating that stability alone is insufficient to predict experimental attainability.