Systematic Underestimation of Defect and Alloy Band Gaps by DFT Endpoint Interpolation: A 549-Entry Experimental Benchmark with a Hypothesis-Driven Correction Model

DFT endpoint interpolation underestimates defect/alloy band gaps in 81% of 274 gold-standard systems (median +0.80 eV, MAE 0.87 eV), with monotone growth in the alloy gap (38% to 100% underestimation) and endpoint-quality dependence (physically gapless +0.45 eV vs computationally gapless +1.19 eV). Mainstream DFT databases are verified to contain zero defective systems - a structural blind spot for infrared, thermoelectric and optoelectronic materials. A falsifiable hypothesis framework survives in-sample falsification of half its predictions and yields a correction model (R2 = 0.79, MAE 0.28 eV). Forward predictions for 275 unresolved systems provided for external testing.