As Large Language Models (LLMs) become integral to software architecture, the pre-vailing practice of ”Prompt Engineering” remains largely heuristic. This paper proposes ashift towards ”Context Engineering”, rigorously defining prompts as a set of constraintswithin a design optimization problem. By applying topological analysis to the model’s high-dimensional possibility space, we demonstrate that context acts as a dimensionality reduc-tion operator. We identify the phenomenon of ”Contextual Binding”—where excessive orconflicting constraints (both implicit and explicit) cause the feasible solution manifold to col-lapse into a null set, forcing the model into undefined behaviors often characterized as hallu-cinations. Furthermore, we validate this theory by analyzing empirical community heuristics(such as the ”KERNEL” pattern) alongside recent academic findings on in-context learningmechanics [?, ?]. Finally, we introduce ”Context Refactoring” as a methodology to manageconstraint density and maintain a healthy solution space.