1\section{Additional tables and experiment register}2\label{app:extra}34\paragraph{Experiment register.} Each experiment was pre-registered with the following hypothesis before it was run; the outcome5column records whether the stored results support it.6\begin{enumerate}[label=E\arabic*.]7\item Baseline: unique equilibrium, durations of a few months, urgency discount of a few percent, positive between-type dispersion,8decreasing population hazard. Supported (Tables~\ref{tab:baseline}--\ref{tab:types}, Figures~\ref{fig:equilibrium}, \ref{fig:survival}).9\item Urgency gradient: monotone schedules, attenuation $|\bar p'|<|V'|$, steeper when arrivals fall. Supported (Figures~\ref{fig:urgency_price}--\ref{fig:urgency_hazard}).10\item Arrival collapse: lower prices and tightness, longer durations, more inventory, wider discount; GE exceeds PE; $\Gamma$ changes sign. Supported (Table~\ref{tab:compstat}, Figure~\ref{fig:discount}).11\item Financing: screen equivalent to $A$; mortgage deals need better matches; three-term gap; $\Delta_b$ rising in urgency. Supported except that mortgage deals need better matches only for urgent sellers (selection term negative for patient sellers), and the extension is inadmissible for $\phi_m\le0.6$ (Table~\ref{tab:financing}).12\item Bargaining power: hump-shaped welfare near the Hosios value; heterogeneity shifts the optimum. Supported for the hump; the optimum is at 0.55 for both economies, so the heterogeneity shift is not detectable (Table~\ref{tab:welfare}).13\item Matching versus approval: distinct signatures in the extension. Supported (Table~\ref{tab:match_vs_approval}).14\item Entry: monotone residual, amplification, entry costs. Supported (Tables~\ref{tab:entry}, \ref{tab:uniqueness_draws}).15\item Heterogeneity: dispersion rises with the spread of $F$ and when liquidity falls. Supported (Table~\ref{tab:heterogeneity}).16\item Dynamics: impact fall of the index, inventory build-up, slow volume; composition transitory; sign depends on $G$. Supported, with the qualification that prices adjust fully on impact (Table~\ref{tab:dynamics}).17\item Selection: small composition term, sign governed by $h_GM$. Supported (Table~\ref{tab:selection}).18\item Posted prices: pickier sellers, between-type dispersion only, gradient preserved. Supported (Table~\ref{tab:protocols}).19\item Sensitivity and convergence: signs robust, objects converge, Monte Carlo agrees. Supported (Tables~\ref{tab:sensitivity}--\ref{tab:distributions}, Appendix~\ref{app:computation}).20\end{enumerate}2122\begin{table}[H]23\centering24\caption{Qualification screen $\phi$ in the baseline (model-generated, general equilibrium)}25\label{tab:screen}26\footnotesize27\input{tables/tab04a_qualification_screen}28\end{table}2930\begin{table}[H]31\centering32\caption{Financing extension: approval delay (model-generated)}33\label{tab:fin_delay}34\footnotesize35\resizebox{\textwidth}{!}{\input{tables/tab04c_financing_delay}}36\end{table}3738\begin{table}[H]39\centering40\caption{Financing extension: bargaining power and the delay-bargaining term (model-generated)}41\label{tab:fin_beta}42\footnotesize43\resizebox{\textwidth}{!}{\input{tables/tab04d_financing_bargaining}}44\end{table}4546\begin{table}[H]47\centering48\caption{Entry and search costs (model-generated, general equilibrium)}49\label{tab:entry}50\footnotesize51\resizebox{\textwidth}{!}{\input{tables/tab07e_entry_costs}}52\end{table}5354\begin{table}[H]55\centering56\caption{Uniqueness check: number of roots of the free-entry residual in 60 random parameter draws (model-generated)}57\label{tab:uniqueness_draws}58\footnotesize59\input{tables/tab07f_uniqueness}60\end{table}6162\begin{table}[H]63\centering64\caption{Dispersion decomposition as a function of the seller's bargaining share (model-generated)}65\label{tab:disp_beta}66\footnotesize67\input{tables/tab05b_dispersion_beta}68\end{table}6970\begin{table}[H]71\centering72\caption{Planner's steady-state flow optimum versus the decentralised equilibrium (model-generated)}73\label{tab:planner}74\footnotesize75\resizebox{\textwidth}{!}{\input{tables/tab08b_planner}}76\end{table}7778\begin{table}[H]79\centering80\caption{One-at-a-time sensitivity of baseline moments (model-generated)}81\label{tab:sensitivity}82\scriptsize83\input{tables/tab07_sensitivity}84\end{table}8586\begin{table}[H]87\centering88\caption{Alternative match-value distributions at the baseline parameters (model-generated)}89\label{tab:distributions}90\footnotesize91\resizebox{\textwidth}{!}{\input{tables/tab07b_distributions}}92\end{table}93