Narrative Anthology and Axiomatic Relations:

Result: The evolution of AI models can be formalized through an exponential growth function: C(t) = C₀ * e^(rt), where C(t) represents the model's capacity at time t, C₀ the initial capacity, r the growth rate, and t the time. Multimodal convergence is expressed as M = ∫(L + V + A) dt, where M is the multimodal capacity, L, V, and A represent the functions of language, vision, and audio over time, respectively. Self-improvement of AI systems follows an iterative process described by S(n+1) = f(S(n)), where S(n) is the system's state at iteration n and f the improvement function. The pervasiveness of AI agents can be modeled as a logistic function: P(t) = K / (1 + e^(-r(t-t₀))), where P(t) is market penetration, K the maximum capacity, r the growth rate, and t₀ the inflection point. The acceleration of innovation manifests as a positive second derivative of the technological progress function: d²T/dt² > 0, where T is a measure of technological progress. Finally, the development feedback loop can be represented as a system of coupled differential equations: dA/dt = f(A,B) and dB/dt = g(A,B), where A and B are measures of advancement in interconnected areas of AI.