Each state (or bloc, e.g. the EU under its Sovereign Tech Fund) accumulates AI compute capacity — GPU/accelerator stock, shown as stacked rack units — through logistic growth toward a national capacity ceiling, plus diffusion of know-how and hardware from other states.
dCi/dt = ri·Ci·(1 − Ci/K) + T·Σ(Cj − Ci)
T = T0·(1 − L/100)·(1 − E)
- Compute investment — scales the leading state's growth rate ri, modeling national AI-strategy CAPEX (data centers, chip fabs, GPU reserves).
- Data localization / sovereignty rules (L) — the more a state restricts cross-border data and model flows, the lower the diffusion coefficient T, slowing everyone's catch-up but raising independence.
- Chip export controls (E) — a binary embargo: when on, T drops to zero and no compute or know-how diffuses between blocs at all.
- Capability threshold (K-line) — the frontier-model compute level a state must reach to be considered AI-sovereign; shown as a glowing ring.
This mirrors real dynamics discussed around sovereign AI: national strategies and GPU reserves (US, China), the EU Sovereign Tech Fund pooling investment to catch up, and export-control regimes on advanced chips that widen or narrow the gap between leading and lagging states.