TY  - JOUR
AU  - Yaremenko, Mykola
PY  - 2026
DA  - 2026/06/10
TI  - The Economic Singularity: Dimensional Reduction, Invariants, and Stability Analysis of the Financialization Threshold
JO  - Journal of Nonlinear Dynamics and Applications
T2  - Journal of Nonlinear Dynamics and Applications
JF  - Journal of Nonlinear Dynamics and Applications
VL  - 2
IS  - 2
SP  - 119
EP  - 126
DO  - 10.62762/JNDA.2026.489975
UR  - https://www.icck.org/article/abs/JNDA.2026.489975
KW  - economic singularity
KW  - artificial intelligence
KW  - financialization
KW  - stability analysis
KW  - saddle point
KW  - dimensional reduction
KW  - wealth inequality
KW  - Neofeudalism
KW  - dynamical systems
AB  - 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.
SN  - 3069-6313
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 

@article{Yaremenko2026The,
  author = {Mykola Yaremenko},
  title = {The Economic Singularity: Dimensional Reduction, Invariants, and Stability Analysis of the Financialization Threshold},
  journal = {Journal of Nonlinear Dynamics and Applications},
  year = {2026},
  volume = {2},
  number = {2},
  pages = {119-126},
  doi = {10.62762/JNDA.2026.489975},
  url = {https://www.icck.org/article/abs/JNDA.2026.489975},
  abstract = {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.},
  keywords = {economic singularity, artificial intelligence, financialization, stability analysis, saddle point, dimensional reduction, wealth inequality, Neofeudalism, dynamical systems},
  issn = {3069-6313},
  publisher = {Institute of Central Computation and Knowledge}
}