1\section{Robustness}2\label{sec:robustness}34We organise the robustness checks by the type of claim they protect.56\paragraph{Theory.} Proposition~\ref{prop:benchmark} is verified symbolically (the wedge is an identically zero7rational function) and numerically on 60 random parameter draws over $\alpha\in(-0.95,0.95)$, $M\in\{1,\dots,6\}$ and8precisions in $[0.1,20]$; Proposition~\ref{prop:wedges}(a) is verified against its closed form at six parameter9points to machine precision; the moments of Proposition~\ref{prop:linear} are verified by Monte Carlo10(Table~\ref{tab:c_factorial} notes; \texttt{tests/unit/test\_lq\_game.py}).1112\paragraph{Illustrative information parameters (Model A).} Figure~\ref{fig:A_pv_noise}(a) and13Figure~\ref{fig:A_threshold} already span model-noise standard deviations from 0.02 to 0.095 (human noise 0.10) and14compute rentals from 0.2 to 1.0; Figure~\ref{fig:A_heatmap} sweeps the effective number of models from 1 to 16.15Three conclusions survive every sweep: the private value of delegation is decreasing in $D$ (strategic16substitutability), the model-noise variance scales with $D^2/M$, and the wedge is zero in the benchmark and17positive under uninsurable wage risk. The \emph{levels} (3.3\% of consumption for the first adopter; a wage-noise18standard deviation of 7.7\% at full adoption with one model) move proportionally with $\sigma_\theta^2$ and19$1/(\gamma\sigma_R^2)$ and should be read as orders of magnitude. The compute-market crowding-out is small for every20$(K_Q,\bar q)$ we tried, for the reason given in Section~\ref{sec:results_a}; we could not find a calibration in which21inference demand reverses the automation-driven decline of the labour share by more than a few tenths of a point.2223\paragraph{Savings versus portfolio mapping.} With $\gamma\in\{1,2,4\}$ and $\rho_z\in\{0.5,0.9,0.95\}$ the24partial-equilibrium savings response to news stays below 0.01 in absolute value; the conclusion that the stake lies25in allocation decisions does not depend on the baseline parameters.2627\paragraph{Model B.} The ordering of Gini and top shares across ownership structures is unchanged at $n_a=100$ versus28160 grid points, three versus five Gauss--Hermite nodes, and with the borrowing limit at 0 or $-0.5$ (the29``no borrowing'' scenario). The level of the top-1\% share is too low in every scenario, as in all Aiyagari-type30models without additional return heterogeneity or discount-factor heterogeneity; the \emph{changes} across scenarios31are the object of interest.3233\paragraph{Model C: designs, seeds and the competing explanation.} The H2 pattern (order-flow correlation increasing34in $D$, decreasing in $M$) holds in all three market designs with non-overlapping bootstrap intervals at $D=1$35(Figure~\ref{fig:C_herding}); it is robust to 20 versus 5 seeds and to $T=80$ versus 160. The competing explanation36flagged in the novelty audit---homogenisation reduces disagreement and therefore volatility---is \emph{also} present:37with one shared model and full delegation, trading volume collapses toward the no-trade outcome38(Figure~\ref{fig:C_volvol}) and volatility is lower in calm periods. The two effects coexist: a shared model makes the39market quieter and more correlated at the same time, which is why the stress test, not the unconditional40volatility, is the right place to look for fragility.4142\paragraph{LLM laboratory.} Table~\ref{tab:llm} reports every cell at temperature 0 and 0.7 and the43prompt-variation control; the audit logs record the model fingerprints. The qualitative H2 pattern in the LLM cells44is read against the Bayesian control and the surrogate; we do not claim robustness across model versions beyond the45three models used, and we report invalid-action rates by model because they differ (Section~\ref{sec:results_c}).46