Anthology Narrative and Axiomatic Relations

The evolution of AI systems is described by: ∂A/∂t = μ∇²A + γA(1 - A/K) + εR(t)
Where A is the agent's activity, R(t) the available resource, μ the diffusion, γ the growth rate, K the carrying capacity, and ε the stochasticity.
The connectivity between agents and external systems is formalized by: C(i,j) = exp(-αd(i,j)) * f(P(i),P(j))
d(i,j) is the distance between nodes i and j, α the decay coefficient, P(i) and P(j) the properties of the nodes, f a compatibility function.
The efficiency of automation is given by: E = Σ[ω(t) * (1 - exp(-βt))]
With ω(t) the weight of the activity at time t and β the learning rate.
The transition to superintelligence follows a singularity model: S(t) = S₀ / (1 - exp(-λ(t-t₀)))
Where S₀ is the initial level, λ the exponential growth rate, and t₀ the critical time.