This paper proposes a new way to think about artificial intelligence. Instead of judging AI only by how well models perform, the authors define a regime they call AI‑Native Autonomous Infrastructure, or ANAI. In ANAI, decision‑making by AI becomes built into the critical systems that run society. The paper offers a formal, mathematical way to describe and test that shift.

To make the idea concrete, the researchers introduce three quantitative measures. The Autonomy Index (AIx) is meant to capture how much decision power is embedded in systems. The Infrastructure Coupling Coefficient (ICC) measures how tightly AI is linked to the physical and organizational infrastructure that supports it. The Technological Transition Potential (TTP) combines these ideas to express how close a system is to crossing into a new technological regime. The paper then writes equations for how these quantities can scale together.

The authors go on to analyze how autonomy and infrastructure embedding coevolve over time. They derive threshold conditions that mark a paradigm transition and sketch a phase‑space picture of systemic change. A temporal model in the paper shows that the joint dynamics can produce super‑linear growth in transition potential. In plain terms, once autonomy and coupling reinforce each other, change can accelerate faster than simple, steady growth.

One novel point the paper highlights is a recursive feedback loop between energy, computation, and infrastructure. AI systems can raise their own computational needs while at the same time optimizing the networks and power that sustain them. That loop can speed up the process by which AI becomes a core part of infrastructure, and it helps explain how an AI‑driven transformation might differ from past general‑purpose technologies.