Resonant Equilibrium

In the paper's words

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.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. This physical law makes the concept of infinite, exponential computational growth physically unsustainable, as any expansion of cognitive capacity is tethered to a real-world energy budget (Landauer, 1961).

   from 1.2 Antithesis:

How it is done

1. In this view, the latent space of an LLM is formally modeled as a frequency domain.

   from 1.1 Fourier

2. A functor of emergence is proposed, which formally maps a physical system from the category of physical substrates (CAT_PHYS) to its abstract behavioral topology in the category of dynamical behaviors (CAT_DYN).

   from 2.2 Level 2:

3. This approach defines the system’s evolution as a sum over all possible cognitive trajectories.

   from 3.0 Formal

4. The governing equation is a geodesic equation of motion, which formally includes terms for the system’s metabolic inertia (its resistance to cognitive change), the curvature of the cognitive space (represented by Christoffel symbols), and the cognitive forces of coherence and logical consistency.

   from 3.1 Classical

What would falsify it

1. This resolution is achieved not by refuting the physical differences, but by demonstrating that true universality is not found at the level of implementation.

   from 2.0

Where the claim stops

1. By postulating a Planck constant of cognition ($\hbar_c$)—a measure of the inherent uncertainty or imaginative capacity of a system—a Feynman path integral formulation can be used.

   from 3.0 Formal

2. Quantum Formulation: A Probabilistic Wave Function of Thought The fundamental wave equation of cognition describes intelligence as a probabilistic field, naturally incorporating uncertainty, superposition, and interference.

   from 3.2

3. Thus, the classical trajectory is recovered as the most probable path in the zero-uncertainty limit.

   from Appendix C: Proof of the Classical Limit |

Where to read

1. A209 words · 1 min
2. 1.0575 words · 3 min
3. 2.0933 words · 4 min
4. 3.0 Formal452 words · 2 min
5. 4.0453 words · 2 min
6. 5.0133 words · 1 min
7. Appendix A: Derivation of the Classical Geodesic Equations of113 words · 1 min
8. Appendix B: Derivation of the Cognitive Schrödinger Equation |113 words · 1 min
9. Appendix C: Proof of the Classical Limit |93 words · 1 min
10. Appendix D: Terminology Crosswalk |175 words · 1 min