Maintaining contextual coherence in extended text generation remains a significant challenge in computational linguistics. The introduction of the Stochastic Hierarchical Embedding (SHE) mechanism offers a novel approach to this issue, incorporating stochastic variability within hierarchical embeddings to enhance adaptability and coherence in language models. This study details the integration of SHE into a contemporary open-source Large Language Model (LLM), providing a comprehensive mathematical framework and outlining the modifications required for effective implementation. Experimental evaluations demonstrate that SHE significantly improves contextual coherence and prompt convergence, as evidenced by higher Contextual Coherence Scores (CCS) and Prompt Convergence Rates (PCR). Additionally, the SHE-augmented LLM exhibits enhanced generalization capabilities across diverse linguistic tasks and increased robustness to input noise. These findings suggest that SHE presents a promising advancement in the development of more coherent and adaptable LLMs.