Recent advances in prompting techniques and multi-agent systems for Large Language Models (LLMs) have produced increasingly complex approaches. However, we lack a framework for characterizing and comparing prompting techniques or understanding their relationship to multi-agent LLM systems. This position paper introduces and explains the concepts of linear contexts (a single, continuous sequence of interactions) and non-linear contexts (branching or multi-path) in LLM systems. These concepts enable the development of an agent-centric projection of prompting techniques, a framework that can reveal deep connections between prompting strategies and multi-agent systems. We propose three conjectures based on this framework: (1) results from non-linear prompting techniques can predict outcomes in equivalent multi-agent systems, (2) multi-agent system architectures can be replicated through single-LLM prompting techniques that simulate equivalent interaction patterns, and (3) these equivalences suggest novel approaches for generating synthetic training data. We argue that this perspective enables systematic cross-pollination of research findings between prompting and multi-agent domains, while providing new directions for improving both the design and training of future LLM systems.