A Mathematical Theory of Creativity in Artificial Intelligence Deterministic State Evolution, Semantic Novelty and Value Optimization

Creativity in artificial intelligence is commonly treated as an emergent property of stochastic generative systems. While such systems can produce diverse outputs, they do not inherently provide guarantees of reproducibility, auditability, or monotonic improvement under fixed objectives. This paper develops a mathematically explicit framework for creativity grounded in deterministic state evolution, consistent with the Deterministic Computation Law. Creativity is formalized as the generation of semantically novel and high-value artifacts under explicit constraints, using deterministic transformation operators acting over structured, canonicalized memory states. We introduce a formal model defining memory spaces, transformation operators, semantic novelty predicates, and deterministic value functionals, and we establish theoretical guarantees for reproducibility, traceability, and monotonic improvement that follow directly from determinism. Rather than asserting expressive superiority over stochastic methods, we show that deterministic creativity systems admit guarantee classes-including long-horizon coherence and stable creative identity-that stochastic sampling methods cannot provide without additional deterministic control assumptions. The framework clarifies the role of determinism in creative reasoning and auditable innovation, and provides a foundational basis for deterministic creative AI systems.