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

The realization of artificial general intelligence (AGI) requires not only scaling
but also fundamental architectural innovation. This paper proposes a cognitive
framework based on information hierarchy, modeling cognitive processes as dynam
ical evolution over discrete information levels. The core insight is that when the
cumulative information capacity of a system exceeds a critical threshold determined
by the distribution of prime numbers, information processing undergoes a transi
tion from discrete, localized hopping modes to continuous, global emergent modes,
thereby enabling genuine abstract reasoning and self-modeling. Specifically, the
sum of natural logarithms of the first 23 primes, ∑ p≤83lnp ≈ 83 nats, constitutes
this critical point of phase transition. This paper demonstrates the mathematical
necessity of this critical value and explores how a cognitive architecture designed
based on this principle could potentially overcome the fundamental limitations of
current deep neural networks in terms of recursive self-reference, cross-scale ab
straction, and causal modeling.