Triple-negative breast cancer (TNBC) lacks effective molecular targets, leading to poor prognosis. Previous computational methods to identify targets have suffered from low druggability, high complexity, and lack of robust validation. We propose a hybrid methodology combining Boolean network modeling with semidefinite programming (SDP) to analyze a TNBC cell line network. The resulting therapeutic pair underwent a multi-level validation framework, including Boolean simulations, statistical uncertainty quantification (bootstrap), sensitivity analysis, and independent verification by AlphaGenome v2, a deep learning model from Google DeepMind. Our analysis identified TK1 and VIM as a robust therapeutic pair. Dual inhibition achieved 99.03% similarity to the apoptotic state with a 95% confidence interval of [98.79%, 99.26%], and was statistically superior to alternative pairs (p < 0.001). The selection remained optimal across all tested model parameters, demonstrating high robustness. Importantly, the pair has full druggability because both targets have available specific inhibitors. AlphaGenome v2 validation in normal mammary tissue revealed that TK1 exhibits moderate expression while VIM shows low baseline expression. This differential pattern, combined with strong VIM upregulation in the mesenchymal-like TNBC phenotype, supports the synergistic mechanism of the dual-target strategy. Our methodology identified TK1-VIM as a high-confidence and druggable therapeutic pair for TNBC with strong biological plausibility. This work provides a clinically actionable strategy and establishes a new benchmark for computational rigor in drug target identification.