Narrative Anthology and Axiomatic Relations:

Result: The AI ecosystem evolves according to principles of self-organization and positive feedback, described by the function F(t) = A * e^(kt), where A represents the initial state of AI technologies, k the rate of exponential growth, and t the time. Technological convergence follows the model S(t) = K / (1 + e^(-r(t-t0))), with K as the upper saturation limit, r the adoption rate, and t0 the inflection point. Human-AI interaction is modeled by the equation dI/dt = αH * αAI * I, where I is the intensity of interaction, αH and αAI are the human and AI adaptability coefficients. Process optimization follows the principle of least action, ∫L(q,q̇,t)dt, minimizing the overall energy of the system. The democratization of AI is represented by D(t) = D0 * (1 - e^(-βt)), where D0 is the maximum potential and β the rate of diffusion. These equations describe a rapidly evolving complex system characterized by acceleration, convergence, and mutual amplification of AI technologies.