Example. A maintained stock can finance training forever [ftip-00OK]
Example. A maintained stock can finance training forever [ftip-00OK]
In Definition [ftip-00O5], choose constant expenditure \(v(t)=gh_0/\eta \) and maintenance \(m(t)=\delta h_0/\eta \). Since \(g=\eta A-\delta >0\), these are nonnegative and sum to \(Ah_0\). The stock equation gives \(h(t)=h_0\geq h_{\min }\) for all \(t\geq 0\), so the allocation is admissible on every finite interval and
\[\int _0^T v(t)\,dt=\frac {gh_0}{\eta }T\longrightarrow \infty .\]At a fixed compute price \(p>0\), a service with constant physical capacity at least \(gh_0/(\eta p)\) can supply that positive compute rate indefinitely. Thus maintenance dependence and a finite bound for each deadline are compatible with infinite lifetime compute. No conclusion about unbounded capability follows without a learning model.