Narrative Anthology and Axiomatic Relations:

Result: The evolution of AI can be formalized through the following equation: AI(t) = ∫[B(t) + C(t) + M(t)]dt, where B(t) represents integration into business, C(t) creative capacity, and M(t) complexity of multi-agent models. The derivative dAI/dt > 0 indicates accelerated growth across all sectors. The optimization function O(AI) = max[Σ(Ei * Wi)], where Ei are the efficiencies in various domains and Wi the relative weights, aims to maximize overall impact. The pervasiveness P of AI follows a logistic curve: P(t) = K / (1 + e^(-r(t-t0))), with K as the upper saturation limit. The interaction between domains is described by a coupling matrix Mij, where non-diagonal elements represent intersectoral synergies. The democratization D of AI is proportional to the logarithm of the available tools: D ∝ log(N), where N is the number of accessible platforms. These axiomatic relations describe a rapidly evolving AI ecosystem characterized by increasing complexity and interconnection among technological and application sectors.