Geometric Information Dynamics Construction L: Information Hierarchy and Artificial General Intelligence

The realization of artificial general intelligence (AGI) requires not only scalingbut also fundamental architectural innovation. This paper proposes a cognitiveframework based on information hierarchy, modeling cognitive processes as dynamical evolution over discrete information levels. The core insight is that when thecumulative information capacity of a system exceeds a critical threshold determinedby the distribution of prime numbers, information processing undergoes a transition from discrete, localized hopping modes to continuous, global emergent modes,thereby enabling genuine abstract reasoning and self-modeling. Specifically, thesum of natural logarithms of the first 23 primes, ∑ p≤83lnp ≈ 83 nats, constitutesthis critical point of phase transition. This paper demonstrates the mathematicalnecessity of this critical value and explores how a cognitive architecture designedbased on this principle could potentially overcome the fundamental limitations ofcurrent deep neural networks in terms of recursive self-reference, cross-scale abstraction, and causal modeling.