# Expected Emergence of Algorithmic Information from a Lower Bound for Stationary Prevalence

## TL;DR

This paper demonstrates that in scale-free networks with a contagion model, a certain threshold of infection prevalence leads to unbounded growth in the expected algorithmic complexity of nodes as the network expands.

## Contribution

It establishes a lower bound for stationary prevalence that causes unbounded emergent information in networked computable systems following a contagion process.

## Key findings

- A lower bound for stationary prevalence triggers unbounded complexity growth.
- Scale-free networks exhibit this threshold behavior.
- Emergent information increases with network size.

## Abstract

We study emergent information in populations of randomly generated networked computable systems that follow a Susceptible-Infected-Susceptible contagion (or infection) model of imitation of the fittest neighbor. These networks have a scale-free degree distribution in the form of a power-law following the Barab\'{a}si-Albert model. We show that there is a lower bound for the stationary prevalence (or average density of infected nodes) that triggers an unlimited increase of the expected emergent algorithmic complexity (or information) of a node as the population size grows.