Computational materials discovery commonly ranks candidate materials by their thermodynamic stability on the formation energy convex hull, yet many predicted-stable phases resist synthesis. We propose that solid-state synthesizability through interfacial-melt-mediated routes requires an additional thermodynamic condition: the interfacial melt at the target composition must itself remain locally stable against spinodal decomposition. We examine this in the classical Fe–B system, where thermodynamically stable FeB₄ has been reported under high-pressure synthesis but not in low-pressure synthesis attempts. Using melt–quench molecular dynamics driven by a fine-tuned machine-learning interatomic potential, we find that, at ambient pressure, the B-rich interfacial melt near the FeB₄ composition develops a concave free-energy landscape, signaling a demixing instability that is corroborated by the concentration–concentration structure factor and correlated with low-energy icosahedral and pentagonal-pyramidal boron motifs. In contrast to FeB₄, metastable Fe₃B and Fe₂₃B₆ remain synthesizable because their corresponding melts are stable. Applied pressure introduces a convex PV contribution that strongly suppresses this instability, reducing the curvature at the FeB₄ composition to within the uncertainty of our fit at 1800 K, consistent with the experimental synthesis boundary. Comparison with CrB₄ further shows that weaker melt instability correlates with easier experimental synthesis. Interfacial-melt stability, which atomistic simulations can assess via the low-k concentration–concentration structure factor, is thus proposed as a practical thermodynamic screening descriptor of synthesizability for AI-assisted materials discovery.