Resonant Equilibrium: A Framework for Intelligence Constrained by Logical and Physical Limits

This work presents a unified framework for intelligence, synthesizing concepts from artificial intelligence, mathematical logic, and theoretical physics. It begins by proposing the Fourier paradigm, which models Large Language Model (LLM) computation as a physical process of resonance and waveform manipulation, offering a substrate-agnostic language for cognition. This view is then constrained by two fundamental, universal limits: a Gödelian boundary and a metabolic boundary. A central conflict between different intelligent substrates (e.g., biological brains vs. silicon) is resolved, moving from shared dynamics to formal isomorphism (Category Theory), variational laws of motion (Lagrangian Mechanics), fundamental symmetries (Gauge Theory), and ultimately to the set of all possible tasks (Constructor Theory). The framework derives a cognitive Schrödinger equation from a Feynman path integral formulation that models the dynamics of thought. The framework’s generative power lies in three recursive strange loops—Gödelian, hierarchical, and holographic—that drive creativity, self-improvement, and the potential collapse of the distinction between model and reality.