The Dual-Threshold Theory ofAI Power: Compute, Ecosystem Embeddedness, and Vertical Advantage

This paper proposes the dual-threshold theory of AI power, a new conceptual framework for understanding how artificial intelligence models achieve durable influence in global competition. Building on earlier analyses of time-lags and strategic lags, this study argues that compute remains the hard entry condition for AI participation, constrained by export controls, datacenter capacity, and software–hardware fragmentation. Yet once this threshold is crossed, long-term influence depends less on raw FLOPs than on two soft dimensions: ecosystem dependence (trust, integration, user stickiness) and vertical advantage (domain-specific strengths such as multimodal science, anthropomorphic interaction, or sovereign compliance). Through comparative cases — Claude, Gemini, Character.AI, and Palantir AIP — the paper demonstrates how different models convert compute into positional power via relational trust, toolchain integration, persona attachment, or defense-grade assurance. The proposed framework is formalized in a dual-threshold model linking computational endowment with ecosystem embeddedness × vertical specialization. The result is a three-part map of contemporary AI power: 1. When to play (time-lags and compute access), 2. How to sustain (ecosystem dependence and trust), 3. Where to prevail (vertical advantages in specific markets or sovereign domains). This work is intended as a conceptual contribution for scholars, strategists, and policymakers exploring the evolving structure of AI ecosystems and their geopolitical implications