A Theory of Special Solutions: Bounded Conditions, Problem Transformation, and Dramaturgical Architecture in Unsolvable Systems

Complex multi-agent interactions, irreversible temporal dynamics, and structural paradoxes often render general solutions—defined as global, perpetual, and universal resolutions—mathematically and practically impossible. When encountering such unsolvable states, insistence on discovering a general solution leads to computational paralysis or reliance on ungrounded deus ex machina constructs. Building upon foundations in bounded rationality, problem space theory, cognitive framing, and insight research, this paper establishes the Theory of Special Solutions. Rather than searching for an elusive global optimum, this framework systematically abandons global solution searches and constructs local, conditional, and transient analytical resolutions. We formalize the Theorem of Conditional Existence, introduce the Conditional Resolution Framework (CRF) as a five-axis dimensionality reduction methodology, and articulate four conviction vectors and twenty primitive operators that govern structural and narrative integration.