Antology Narrative and Axiomatic Relations:

Result: The AI ecosystem evolves according to the function E(t) = A(t) + O(t) + D(t), where A(t) represents the advancement towards AGI, O(t) the computational optimization, and D(t) the democratization of AI. The speed of innovation V(t) = dE/dt shows a constant acceleration, indicated by the rapid translation of research into practical applications. The convergence C(t) between different AI technologies follows a logarithmic curve, C(t) = log(1 + t), reflecting a gradual saturation of the innovation space. The computational efficiency EC(t) grows exponentially: EC(t) = e^(kt), where k is the technological improvement rate. The competition between tech companies models as a nonlinear dynamic system, where each advancement stimulates further progress, creating a positive feedback loop described by dI/dt = rI(1 - I/K), with I representing innovation and K the system's maximum capacity. This mathematical model describes a rapidly evolving AI ecosystem characterized by a growing convergence towards AGI, computational optimization, and democratization, with a strong interconnection among various aspects of innovation.