\section{Synthesis: theory, data, and rival explanations}
\label{sec:synth}

\subsection{What is observable and what is not}
\label{sec:synth-observable}

Table~\ref{tab:observable} sets the framework's mechanisms against the two kinds of evidence. The coding gain, the stale-code penalty and the routing bounds are measured in the simulation and are not observable in Seshat, which records whether writing, coins or courts existed and never how long a message was or how many tasks waited. The break-even condition is reflected in the historical record only through the association of capacity with scale (H1), which is consistent with institutions being built where they pay but equally consistent with the reverse. Backlog dynamics are observable nowhere in history. The one mechanism that the historical tests address, sustained overload leading to breakdown (Conjecture~\ref{conj:c2}), is addressed only through the proxy $P$, and the proxy's claim to track utilization (Conjecture~\ref{conj:c1}) is what the collinearity and placebo results undermine.

\begin{table}[H]
\centering\small
\caption{Mechanisms of the framework against the two kinds of evidence.}
\label{tab:observable}
\begin{tabular}{L{4.4cm} L{5.4cm} L{5.4cm}}
\toprule
Mechanism & Historical record (\EMP) & Simulation (\SIM) \\
\midrule
Coding gain (Thm.~\ref{thm:coding}) & Not observable: presence of codes, not message lengths & Reproduced in every cell; Shannon code longer than raw in one near-uniform cell \\
Break-even (Thm.~\ref{thm:breakeven}) & Indirect: capacity rises with scale (H1) & Code repaid only with large concentrated plan space and long horizon \\
Stale code (Thm.~\ref{thm:stale}) & Not observable & Extra bits $1.90$ vs divergence $1.98$ \\
Routing and root load (Thm.~\ref{thm:routing}) & Partially: administrative levels coded, loads not & At equal budgets, central collapses below budget multiple 1; federated keeps most of its success \\
Backlog (Thm.~\ref{thm:backlog}) & Not observable; $P$ is a proxy under C1 & By construction \\
Overload $\to$ breakdown (C2) & Tested through $P$: positive but not beyond components & Not modelled \\
Smooth vs threshold (C3) & No threshold in Seshat; negligible nonlinearity in modern panel & Convex latency in utilization \\
\bottomrule
\end{tabular}
\end{table}

\subsection{The model against simpler rivals}
\label{sec:synth-rivals}

The pre-registration named the rivals and the results rank them. In Seshat, a scale-only model explains crisis severity as well as the mismatch model, in and out of sample; the placebo built from production infrastructure is not distinguishable from $P$; capacity alone does nothing, and the equal-and-opposite restriction is not rejected only because $\beta_K$ is imprecise. The simplest reading is \citeauthor{johnson1982}'s: larger polities face more that can go wrong when a crisis strikes, and whether their administrations were ``adequate'' is not something the presence codes can tell us. In the modern panel, a capacity-only model explains instability onsets as well as or better than the mismatch model; so does development; population adds little. The simplest reading is the state-capacity literature's \citep{besley2009,hanson2021,goldstone2010}: states with impartial administrations, predictable law and fiscal and territorial reach experience fewer civil wars, coups and irregular transitions, and the mismatch index inherits that association with its sign reversed. In neither panel does the \emph{difference} between scale and capacity carry information that its components do not.

The rival mechanisms named in the mandate fare as follows. Military competition: the warfare-technology index is included as a covariate in every specification and does not displace the scale association; it is not itself associated with severity once scale is in the model. Environmental shocks: an epidemic accompanying the crisis is a covariate; the climate-mediated pathway of \citet{hoyer2023} is not testable with Polaris alone. Geography: absorbed by region effects, and the leave-one-region-out results show no region driving the estimates. Resource base: the production-infrastructure index is a covariate and, used as a placebo, mimics capacity. Inequality and elite conflict: not measurable at the polity level in Polaris and only through regime-type proxies in V-Dem; the structural-demographic mechanism \citep{turchin2003,turchin2009} remains an open rival that this paper cannot distinguish from scale. Cultural diffusion and selection: addressed by region and family controls for inference and by the crisis-selection caveat, not for identification. Coercion: the military professionalization index is a covariate in H1 and was not associated with severity.

\subsection{Consistency with simulation-derived predictions}
\label{sec:synth-consistency}

The simulation predicts that institutions lower operating cost per successful task (and raise success by the construction of their error parameters), which agrees with the positive association of capacity with scale and, in the modern panel, with the negative association of capacity with instability; agreement of this kind is weak evidence because the data cannot distinguish capacity enabling scale from scale demanding capacity. The simulation also predicts a sharp utilization effect---hierarchies fail when relayed load exceeds administrative capacity---whose historical analogue would be a threshold in the mismatch index. The historical tests find no threshold in Seshat and, in the modern panel, a nonlinearity that meets the pre-registered rule but is negligible in size. Either there is no utilization threshold in history, or the proxy does not measure utilization; the collinearity of the proxy's components makes the second reading at least as likely, and the paper cannot tell them apart. Disagreement is more informative than agreement here: it marks the precise place where better data would be decisive.

\subsection{Scope conditions and failed predictions}
\label{sec:synth-scope}

Three statements survive, each with its scope. First, capacity and scale are positively associated across 317 historical polities, 579 ethnographic societies and 14,647 modern country-years, with the sign stable within regions and eras and over fifty-year differences; the direction is not identified. Second, among the 127 historical crises with a defined pre-crisis index, a larger polity's crisis is recorded with more adverse consequences, at about 0.42--0.44 log-odds per standard deviation of scale on the common sample; this is a statement about scale, not about mismatch. Third, modern states with higher administrative, legal, fiscal and territorial capacity experience fewer instability onsets in the following five years, at about $-0.63$ log-odds per standard deviation; this replicates a known result and is as strongly related to past as to future instability. Five predictions failed or fell short. The mismatch index does not outperform its components out of sample in either panel. The restriction it imposes is rejected in the modern panel. The placebo index is not distinguishable from it in Seshat. The negative control in the modern panel passes by the letter but by less than one standard error. There is no threshold in Seshat and only a small nonlinearity in the modern panel; and the secondary polity-duration outcome runs against the hypothesis. By the rule written before the data were examined, the universal theory of coordination, institutions and civilizational complexity is not supported by the historical and modern evidence available in 2026, and the paper is written as the test that did not confirm it.