This research explores the theoretical alignment between self-supervised contrastive learning (CL) and supervised learning, specifically investigating why label-agnostic training produces organized semantic clusters. The authors prove that standard CL objectives implicitly approximate a negatives-only supervised contrastive loss (NSCL), with the gap between the two vanishing as the number of dataset classes increases. Their analysis identifies that global minimizers of this loss exhibit augmentation collapse, within-class collapse, and a simplex equiangular tight frame structure, mirroring the "neural collapse" found in supervised models. The paper introduces a new few-shot error bound based on directional feature variability, which explains how these models support high-accuracy label recovery with minimal supervision. Empirical tests across diverse vision datasets confirm that minimizing the unsupervised CL loss effectively drives down the supervised NSCL loss. Ultimately, the study provides a robust mathematical framework to justify the success of contrastive pre-training in downstream classification tasks.