\section{Additional results}
\label{app:extra}

\subsection{Diagnostics of every scenario}

Table~\ref{tab:diagnostics} reports, for each solved scenario, the maximum absolute residual of the dynamic
system (four capital Euler equations, goods-market clearing, capitalists' Euler equation), the maximum gap of the
income identity \eqref{eq:identity} relative to GDP, the truncation check (maximum change in the interest-rate
path and in the log capital stocks over the first 225 years when the horizon is extended by 50 years) and the
solution time on one core.

\begin{table}[htbp]
\centering\scriptsize
\caption{Numerical diagnostics by scenario.}
\label{tab:diagnostics}
\resizebox{\textwidth}{!}{\input{tables/tab08_diagnostics}}
\end{table}

\subsection{The two reference economies}

The scenario ``AI frozen'' holds capability, the compute price and energy efficiency at their 2026 values; it is
the exact balanced growth path of Section~\ref{sec:calibration} and the reference for the valuation
decomposition. The scenario ``no capability'' holds capability only: hardware keeps cheapening at 15\% a year to
the same floor. The gap between the two (Table~\ref{tab:scenarios}) is the contribution of Moore's law alone at
2026 algorithms: three of the four task classes are automated by 2060 and the labor share halves, because the
2026 compute requirements are finite and a hundredfold cheaper compute eventually meets them. The source's
Premise~1 (finite $\alpha$) is already satisfied for every task in 2026 in our calibration --- the question is
only at what price.

\subsection{Price--earnings ratios and user costs}

On the baseline path the price--earnings ratio of compute capital is $V^Q_t/(R^Q_tK^Q_t)$; by the Euler
equation \eqref{eq:capital_euler} it equals $(1+g^Q_{t+1})\,q^Q_t/R^Q_{t+1}$ up to adjustment-cost terms, and on
the terminal balanced path $(1+g)/[(1+r)(1+\pi_Q)-(1-\delta_Q)]$ with $\pi_Q=0$ once the floor is reached: 3.6 at
$r=3.5\%$, $\delta_Q=0.25$, $g=1.5\%$. During the transition it is lower (near 2) because the price is still
falling ($\pi_Q=0.15$) and the real rate is high. The corresponding earnings yield, 30--50\%, is the number a
financial analyst would see as the ``return on compute'': it is a user cost, not a rate of return, and the
return to the owner is $r_{t+1}$ like on every other claim.

\subsection{The news effect in 2026}

Because the whole path is anticipated, the baseline differs from the frozen economy already in 2026:
Tobin's $q$ of compute is 1.5, the real return is \rBase\% against 3.5\%, and the compute investment share is
two to three times its frozen value. These are the model's implications for a world that learns in 2026 that
the baseline scenario is certain. The size of the effect is a measure of how much of the scenario the marginal
investor would have to believe; the sign --- anticipation of AI raises real rates and compute investment at once
--- is a testable implication (Section~\ref{sec:empirical}).