Fractal Alignment- A Mathematical Framework for Stable and Safe AGI Cognition

This article introduces Fractal Alignment, a formal mathematical framework for achieving structural stability and safety in Artificial General Intelligence (AGI).

Current alignment methods (e.g., RLHF) fail to control the internal geometric instability of deep learning systems, leading to representational drift, hallucinations, and vulnerabilities to mesa-optimizers.

We propose Fractal Cognitive Dynamics (FCD), which treats cognitive states as multi-level, self-similar dynamic systems. The core of FCD is a set of cross-layer mappings that enforce recursive coherence—a fractal structure analogous to stable biological cognition.

The framework derives key constructs such as informational stability (S) and cognitive temperature (T) to enforce a Gibbs-like distribution over cognitive transitions. This design structurally makes internally incoherent and unsafe states mathematically unstable, providing an architectural guarantee for robust and coherent AGI operation.

This work is part of a unified research program, including the Fractal Observer Interpretation (FOI) and The Fractal Constitution, focused on designing AGI based on fundamental laws of information and coherence.