= Discounted one-capacity climate pulse damage
{title2=$\mathrm{PV}=\alpha\beta/[Ck_D(k_D+\lambda/C)]$}
A persistent forcing increment $\alpha$ from a unit emission pulse drives $C\dot T=\alpha-\lambda T$, with $T(0)=0$. Linear annual damage $\beta T$ discounted at positive rate $k_D$ integrates to the displayed value. It assumes constant coefficients, a permanent forcing step and damage valued relative to the emission date. A decaying carbon burden or a different damage law changes the result.
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