The Economic Singularity: Dimensional Reduction, Invariants, and Stability Analysis of the Financialization Threshold

Анотація

Background: The possibility of an economic singularity---a finite‑time explosion of AI capability, financial capital, and inequality---has been discussed in futurist and economic literature, but endogenous feedback loops between AI, finance, and labour markets remain underexplored. Methods: This paper presents a dimensional reduction of a dynamical systems model of an economy with recursively self‑improving artificial intelligence and financial autocatalysis. By transforming to three economically meaningful ratios---financial depth per AI capability ($x = K_f/A$), AI capital per financial capital ($u = K_{ai}/K_f$), and employment odds ($z = L_p/(1-L_p)$)---the original four‑variable explosive system reduces to a bounded, analytically tractable three‑dimensional system. Results: The reduced model possesses a saddle‑type equilibrium that separates two asymptotic regimes: one in which AI dominates ($x\to0$) and one in which finance explodes ($x\to\infty$, Neofeudalism). The critical financial depth is $x_c = (\lambda+\beta)/\gamma_F$, so that the economy tips into Neofeudalism whenever the initial $x_0 > x_c$. Numerical simulations confirm the saddle structure and the threshold behaviour. Conclusions: The analysis yields sharp policy recommendations: regulate financial autocatalysis to raise the safety threshold, and intervene early to keep the financial‑to‑AI ratio below the critical value. Redistribution alone cannot substitute for structural regulation.

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