Predicting whether someone with mild cognitive impairment (MCI) will progress to Alzheimer's disease (AD) is crucial in the early stages of neurodegeneration. This uncertainty limits enrollment in clinical trials and delays urgent treatment. The Boundary Sharpness Coefficient (BSC) measures how well-defined the gray-white matter boundary looks on structural MRI. This study measures how BSC changes over time, namely, how fast the boundary degrades each year works much better than looking at a single baseline scan for predicting MCI-to-AD conversion. This study analyzed 1,824 T1-weighted MRI scans from 450 ADNI subjects (95 converters, 355 stable; mean follow-up: 4.84 years). BSC voxel-wise maps were computed using tissue segmentation at the gray-white matter cortical ribbon. Previous studies have used CNN and RNN models that reached 96.0% accuracy for AD classification and 84.2% for MCI conversion, but those approaches disregard specific regions within the brain. This study focused specifically on the gray-white matter interface. The approach uses temporal slope features capturing boundary degradation rates, feeding them into Random Survival Forest, a non-parametric ensemble method for right-censored survival data. The Random Survival Forest trained on BSC slopes achieved a test C-index of 0.63, a 163% improvement over baseline parametric models (test C-index: 0.24). Structural MRI costs a fraction of PET imaging ($800--$1,500 vs. $5,000--$7,000) and does not require CSF collection. These temporal biomarkers could help with patient-centered safety screening as well as risk assessment.