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We employ first-principles density functional theory to investigate the structural, electronic, and optical properties of 2H-Ge$_{1-x}$Sn$_{x}$ random alloys in the dilute Sn regime ($x \\le 0.10$). The extended alloy disorder is modeled using 48-atom special quasirandom structure (SQS) supercells, and the coherent effective band structure is recovered via spectral band unfolding. We show that 2H-Ge$_{1-x}$Sn$_{x}$ ma"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that 2H-Ge_{1-x}Sn_{x} maintains a direct bandgap at the Γ point across the studied composition range, exhibiting a strong bandgap bowing that shifts the fundamental absorption edge into the mid-infrared. 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