<p>Vision foundation models such as prompt-conditioned segmenters carry rich open-world semantic priors, but transferring those priors into closed-class convolutional neural network (CNN) detectors is fundamentally a cross-task problem, not a cross-architecture one. We identify three coupled asymmetries that govern this transfer: a semantic asymmetry between pixel-region and box-class supervision, a statistical asymmetry between globally-balanced Vision Transformer (ViT) activations and locally-sparse CNN activations, and a gradient conflict between dense distillation supervision and the sparse detection objective. We argue, and empirically observe, that value-level alignment saturates in this setting: whether through concept-guided response matching or a learnable projection, the supervision target remains segmentation-shaped, so bridging activations does not resolve the underlying mismatch. We therefore propose Structural Semantic Organization Distillation (SSOD), which aligns the organization of representations rather than their values. SSOD places three structural channels in one-to-one correspondence with the asymmetries: an object-token contrastive channel with an explicit background prototype, a relation-affinity channel matching symmetric Kullback–Leibler (KL)-normalized token affinities, and a confidence-gated box-attention channel that restricts supervision to teacher-confident regions. On closed-class detection benchmarks with a strong YOLOv5m baseline, SSOD delivers stable and consistent improvements, and ablations confirm that each channel contributes a distinct inductive bias.</p>