A Mathematical Theory of General Intelligence: State-Space Compression as a Variational Framework for Problem Solving

We propose a mathematical framework that measures intelligence as the efficiency with which a system discovers and uses task-relevant state-space compressions under declared cost and capacity constraints. Starting from state-space compression (SSC), we define tasks, admissible representations, a resource-weighted loss functional, and Cognitive Compression Cost (CCC): the lowest achievable task cost under a declared modeling policy. An agent's task-local intelligence is its efficiency relative to this optimum, and general intelligence is the expectation of that score over a declared task distribution. We establish existence, rate-distortion, monotonicity, dominance, information-bottleneck, and no-free-lunch properties under explicit assumptions. The framework separates task difficulty from agent capability and makes resource assumptions visible, enabling conditional cross-substrate comparison when task, loss, representation, and resource policies are shared. It does not claim a theory of consciousness, personhood, or context-free intelligence ranking.