Axiomatic Narrative and Relational Insights:

Result: The AI ecosystem evolves according to the function R(t) = A(t) * I(t) * D(t), where A(t) represents process automation, I(t) innovation of models, and D(t) the democratization of technologies. The derivative dR/dt > 0 indicates a constant acceleration in AI integration. The competition C between open-source and proprietary models follows the equation dC/dt = k(Io - Ip), where Io and Ip are the innovations from open-source and proprietary respectively, and k is a coupling factor. The accessibility of AI, A(t), grows according to dA/dt = α * U(t), where U(t) represents the usability of AI interfaces and α is an adoption coefficient. The multidisciplinarity M(t) of AI expands following dM/dt = β * ∑(Si), where Si are the application sectors and β the intersectoral diffusion rate. These axiomatic relations describe a rapidly evolving AI system, characterized by increasing integration, accessibility, and versatility, driven by competition and continuous innovation.