Abstract:Despite their impressive performance, large language models (LLMs) remain fundamentally associative — they recombine patterns rather than autonomously forge new conceptual invariants.This preprint introduces the Universal Correspondence Framework (UCF), a protocol bridging physical entropy and cognitive complexity.It establishes the Universal Correspondence Law (LU) linking the physical amplification of informational noise (γ) to the cognitive cost of reasoning and creation (β).Evidence from SAT benchmarks, quantum-inspired coherence simulations, and cross-domain validation (deep learning, optimization, graphs) shows that both physical decoherence and cognitive effort follow the same exponential law, offering a measurable thermodynamic foundation for reasoning and creativity. Keywords: Entropy, Cognitive Complexity, Signal-to-Noise Ratio, Universal Correspondence Law, AI Reasoning, Thermodynamics of Computation.