\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. Four scenarios of the catalogue are not in the table because they were not solved to
tolerance after the direct solve and the homotopy fallback: the Cobb--Douglas and substitutes cells (the compute
stock grows by factors the terminal conditions cannot accommodate on a 275-year horizon) and the two scenarios
in which utilization of compute capacity switches between idle and full across periods (fast Moore without
efficiency gains; Moore's law without end). Their logs are in the replication package; the text relies on the
propositions for those cells.

\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}).