Narrative Anthology and Axiomatic relations:

Result: The integrated AI ecosystem E(t) evolves according to the function E(t) = ∫[AI(t) + I(t) + T(t)]dt, where AI(t) represents the evolution of AI technologies, I(t) innovation, and T(t) technological infrastructure. The convergence C between different forms of AI is described by C = lim[t→∞] (Text(t) ∩ Image(t) ∩ Prediction(t)), tending towards a unified system. The acceleration A in software development cycles is expressed by A = dS/dt, where S is the complexity of software and t is time, with dA/dt > 0 indicating constant acceleration. The expansion E of AI applications in niche sectors follows a logistic curve E(t) = K / (1 + e^(-r(t-t0))), where K is the maximum capacity, r is the growth rate, and t0 is the inflection point. The adaptation of global infrastructure G is modeled by dG/dt = α(AI(t) - G(t)), where α is the adaptation coefficient. Finally, accessibility and natural interaction N with AI is described by N(t) = N0 + βt, where N0 is the initial level and β is the rate of improvement over time. These equations describe a complex dynamic system that tends toward optimal integration of AI across multiple technological and social aspects.