Accurate grading of corn kernels is critical for seed certification, directional seeding, and breeding, yet it is still predominantly performed by manual inspection. This work introduces CornViT, a three-stage Convolutional Vision Transformer (CvT) framework that emulates the hierarchical reasoning of human seed analysts for single-kernel evaluation. Three sequential CvT-13 classifiers operate on 384x384 RGB images: Stage 1 distinguishes pure from impure kernels; Stage 2 categorizes pure kernels into flat and round morphologies; and Stage 3 determines the embryo orientation (up vs. down) for pure, flat kernels. Starting from a public corn seed image collection, we manually relabeled and filtered images to construct three stage-specific datasets: 7265 kernels for purity, 3859 pure kernels for morphology, and 1960 pure-flat kernels for embryo orientation, all released as benchmarks. Head-only fine-tuning of ImageNet-22k pretrained CvT-13 backbones yields test accuracies of 93.76% for purity, 94.11% for shape, and 91.12% for embryo-orientation detection. Under identical training conditions, ResNet-50 reaches only 76.56 to 81.02 percent, whereas DenseNet-121 attains 86.56 to 89.38 percent accuracy. These results highlight the advantages of convolution-augmented self-attention for kernel analysis. To facilitate adoption, we deploy CornViT in a Flask-based web application that performs stage-wise inference and exposes interpretable outputs through a browser interface. Together, the CornViT framework, curated datasets, and web application provide a deployable solution for automated corn kernel quality assessment in seed quality workflows. Source code and data are publicly available.