Axiomatic Narrative and Relational Insights:

Outcome: The evolution of AI towards direct control of computational and robotic systems can be formalized through the equation: C(t) = α * e^(βt), where C(t) represents control capacity over time t, α is the initial level of control, and β is the rate of exponential growth. The democratization of AI tools, especially for video generation, follows a logistic curve: D(t) = K / (1 + e^(-r(t-t0))), where D(t) is the level of democratization, K the maximum capacity, r the growth rate, and t0 the inflection point. The integration of automation in various sectors can be modeled as a system of differential equations: dS/dt = γS(1-S/M) - δSR, dR/dt = εSR - ζR, where S represents the non-automated sector, R the automated sector, γ,δ,ε,ζ are interaction parameters, and M the maximum system capacity. These equations describe the dynamics of adoption and saturation of automation. The convergence of AI, video generation, and automation creates a vector field F(x,y,z) = (∂C/∂t, ∂D/∂t, ∂A/∂t), where C, D, A represent AI control, democratization of tools, and automation respectively. The divergence of this field, ∇·F, quantifies the rate of expansion or contraction of technological innovation over time and across application spaces.