Constraint-Driven Contexts: Engineering the Solution Space of Large Language Models

As Large Language Models (LLMs) become integral to software architecture, the pre-
vailing practice of ”Prompt Engineering” remains largely heuristic. This paper proposes a
shift towards ”Context Engineering”, rigorously defining prompts as a set of constraints
within 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 or
conflicting 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 learning
mechanics [?, ?]. Finally, we introduce ”Context Refactoring” as a methodology to manage
constraint density and maintain a healthy solution space.