1\section{Data and historical measurement}2\label{sec:data}34Every source was downloaded by a script that records the release, URL, retrieval time, licence, size and SHA-256 hash of the raw file (Table~\ref{tab:sources}); raw files are preserved unmodified and never redistributed. All counts in this section are produced by the parsers and written to machine-readable diagnostics from which the tables are generated. Missing values are never recoded as absent, no fact is forward-filled across polities or periods, and no outcome is imputed---the lesson of the moralizing-gods episode \citep{beheim2021,whitehouse2023}.56\begin{table}[H]7\centering\footnotesize8\caption{Sources, releases and provenance. Hashes are the first twelve hexadecimal digits of the SHA-256 of the raw file as downloaded on 2026-11-01; the full registry is in the replication package.}9\label{tab:sources}10\begin{tabular}{L{4.6cm} L{4.0cm} L{3.0cm} r l}11\toprule12Dataset & Release & Licence & Bytes & SHA-256 \\13\midrule14\input tables/tab_sources 15\bottomrule16\end{tabular}17\end{table}1819\subsection{Three panels, kept separate}20\label{sec:data-panels}2122\paragraph{Historical polities (Seshat Polaris-2026).} The Seshat Global History Databank codes historical polities on hundreds of variables from the published historiography \citep{turchin2015,francois2016}. We use the Polaris-2026 snapshot, the current official release, which contains 626 polities in 42 regions (35 natural geographic areas) spanning $-13{,}600$ to 2020 CE, and 56,274 coded facts in the social-complexity, warfare, religion and general sheets. Each fact carries a value or a value range (\texttt{value\_from}, \texttt{value\_to}), an optional date range, and flags for disputed and uncertain codes; presence variables are coded present (P), absent (A), inferred present (IP), inferred absent (IA) or unknown (SU). Two structural features of the release shape the design. First, only 2,503 facts carry a date; the other 93.7\% describe the whole polity period. A polity-year panel would therefore be an interpolation that the data do not support, and the historical unit of analysis is the polity, with region and era effects. Second, the release contains the CrisisDB ``crisis consequences'' table \citep{hoyer2023,hoyer2024}: for 166 crisis episodes in 150 polities, historians coded whether each of 21 consequences occurred, among them decline, collapse, civil war, uprising, fragmentation, loss of the capital, conquest, assassination and deposition. This is the independently coded instability outcome. It is also a crisis-selected sample: a polity without a CrisisDB record is one for which no crisis was coded, not one that had no crisis, so the outcome measures how badly a recorded crisis unfolded rather than whether one occurred. Table~\ref{tab:coverage} summarizes coverage; Figure~\ref{fig:coverage} shows the temporal distribution of polities and crises and the pattern of coded and missing indicators.2324\paragraph{Ethnographic societies (D-PLACE Ethnographic Atlas v3.3).} The Ethnographic Atlas \citep{murdock1967}, as curated in D-PLACE \citep{kirby2016}, describes 1,291 societies at an ethnographic focal year (between $-2000$ and 1965, most in the nineteenth and twentieth centuries) on a fixed set of categorical variables. We use mean size of local communities (EA031, eight ordinal categories converted to geometric midpoints of the category ranges printed in the codebook), population size (EA202, continuous), and jurisdictional hierarchy beyond the local community (EA033, from acephalous to four levels), with subsistence, agricultural intensity and class differentiation as covariates. Galton's problem---societies are related by descent and diffusion---is handled with Glottolog 5.3 language families (173 families among the 1,291 societies), regions, and spatial heteroskedasticity-and-autocorrelation-consistent standard errors \citep{conley1999,mace1994,dow2007}. The Atlas has no instability outcome and is used only for the capacity--scale association.2526\paragraph{Modern states (V-Dem v16 and Maddison 2023).} The Varieties of Democracy country-year dataset \citep{coppedge2020,pemstein2018} provides expert-coded institutional variables for 202 countries from 1789 to 2025; the Maddison Project Database 2023 \citep{bolt2024} provides population and GDP per capita, which we merge by ISO3 code (163 countries matched; the 39 unmatched V-Dem entities are mostly historical polities and micro-states and drop out of the population-based index). Outcomes are the first year of a civil war (Correlates-of-War coding carried in V-Dem, 1816--2006), a coup (1789--2008), and the last year of a V-Dem regime whose coded end type is a military or non-military coup, a self-coup, an assassination, a loss in civil or inter-state war, a foreign intervention or a popular uprising (1789--2025); natural deaths and guided or negotiated transitions are not events. We never map modern countries onto historical polities: the two panels answer the same hypotheses separately.2728\begin{table}[H]29\centering\small30\caption{Coverage of the three panels after parsing (counts produced by the build script).}31\label{tab:coverage}32\begin{tabular}{L{5.6cm} L{3.6cm} L{6.2cm}}33\toprule34Quantity & Value & Detail \\35\midrule36\input tables/tab_coverage 37\bottomrule38\end{tabular}39\end{table}4041\begin{figure}[H]42\centering43\includegraphics[width=\textwidth]{figures/fig_seshat_temporal_coverage.pdf}\\[2mm]44\includegraphics[width=0.9\textwidth]{figures/fig_seshat_missingness.pdf}45\caption{Seshat Polaris-2026. Top: polity time spans by macro-region (left) and CrisisDB crisis start years (right). Bottom: coded (dark) versus missing (white) pre-registered indicators, polities sorted by number of coded indicators. Missing is never treated as absent.}46\label{fig:coverage}47\end{figure}4849\subsection{Coding rules and uncertainty}50\label{sec:data-coding}5152Presence codes are mapped to 1 (P, IP), 0 (A, IA) and 0.5 (disputed codes of the form A$\sim$P), with inferred codes flagged so that a sensitivity run can drop them; unknown (SU), blank and unparseable values are missing (132 of 56,274 facts were unparseable and are logged). Numeric ranges are summarized by their geometric midpoint for population, territory and largest-settlement population and by the arithmetic midpoint for level counts, and the bounds are kept: the paper re-estimates its main model at the lower and upper bounds. Dates are kept as intervals; a crisis is dated by the start of its coded interval; nothing is interpolated. When several facts exist for a polity and a variable, the polity value is the mean over facts (the mean log for logged variables); for each crisis record, ``pre-crisis'' aggregates use dated facts ending before the crisis start together with the undated whole-polity facts; only 3.6\% of the facts entering these aggregates are dated, so ``pre-crisis'' means, in practice, ``whole-polity'', and temporal precedence is weak. We keep the label for consistency with the pre-registration and flag it wherever it is used.5354\subsection{Demand, capacity, and the mismatch index}55\label{sec:data-measurement}5657The pre-registration fixed disjoint indicator sets before any outcome was examined. Coordination demand $D$ is scale: the first principal component of the pairwise-complete correlation matrix of log population, log territory, log largest-settlement population and settlement-hierarchy levels, scored as the loading-weighted mean of whatever is available for a polity (at least two of the four), with log population alone as the secondary measure. The component explains 82\% of the variance with nearly equal loadings and is defined for 442 polities. Coordination capacity $K$ is the unweighted mean of four block scores, each the share of coded indicators present and each requiring at least half of its indicators coded, with at least three blocks present: administration (full-time bureaucrats, specialized government buildings, merit promotion, examination system, rank-scaled administrative levels), standardized rules and money (legal code, judges, courts, professional lawyers, indigenous and foreign coins, paper currency, tokens, precious metals, articles), communication infrastructure (couriers, postal stations, general postal service, roads, bridges, canals, ports) and record-keeping (written records, script, phonetic and non-phonetic writing, lists and tables, calendar, practical literature, non-written records, mnemonic devices). $K$ is defined for 344 polities. Military, religious and production-infrastructure indicators are excluded from $K$ by design and serve as rival-explanation covariates. The mismatch index is $P = z(\log D) - z(K)$, standardized over the polity sample; because $K$ is a bounded share that can be zero, it is standardized rather than logged, a pre-registered deviation from the candidate formula in the mandate. In the modern panel $D$ is log population and $K$ the mean of six standardized V-Dem items---rigorous and impartial public administration, meritocratic appointment, transparent and predictably enforced laws, fiscal capacity, territorial control and election-management capacity---none of which is a democracy index; in the Atlas the capacity-side measure is the number of jurisdictional levels.5859\begin{table}[H]60\centering\small61\caption{Measurement model: construction and diagnostics. Values from the measurement diagnostics written by the index-building script; no outcome variable was read by that script.}62\label{tab:measurement}63\begin{tabular}{L{6.0cm} L{9.4cm}}64\toprule65Index & Construction and diagnostics \\66\midrule67\input tables/tab_measurement 68\bottomrule69\end{tabular}70\end{table}7172Two alternatives to the block mean were pre-registered and are reported side by side: the first principal component of the four blocks, which correlates 0.999 with the mean, and a two-parameter logistic item-response model estimated by marginal maximum likelihood with mild priors on the thirty binary items, which handles item missingness through the likelihood rather than by imputation, is defined for 579 polities, and correlates 0.96 with the block mean. The latent score carries a median posterior standard deviation of 0.34 on a unit-variance scale, which is the honest measure of how uncertain an individual polity's capacity is. Item parameters refitted separately on the Old World and on the Americas and Oceania have difficulties correlated 0.88, so the ordering of institutions by rarity is similar across the two worlds, although the New-World sample (94 polities) is too small for a strict invariance test and the leave-region-out analyses are the operational safeguard. The block structure is stable: inter-block correlations are 0.75--0.79 overall, Cronbach's $\alpha$ across the four blocks is between 0.83 and 0.97 in every macro-region, and dropping any block leaves $K$ correlated at least 0.98 with the full index.7374The central measurement fact of the paper is collinearity (Figure~\ref{fig:measurement}, Table~\ref{tab:measurement}). Scale and capacity correlate 0.84 across polities, as the single-dimension result of \citet{turchin2018} implies, so the mismatch index retains only 17\% of the variance of $z(D)+z(K)$; it correlates 0.39 with $D$, $-0.18$ with $K$ and $-0.04$ with a Turchin-style first principal component of 57 social-complexity indicators. $P$ is a residual, nearly orthogonal to overall complexity. That is what would make it informative if it carried signal, and what makes it fragile: measurement error in either index leaks into it, and any association with $P$ can be a disguised association with one of its components. The pre-registered baselines (scale only, capacity only, complexity only, scale and capacity entered separately) exist to detect exactly this. The problem is sharper in the crisis sample: polities with a CrisisDB record are better documented and more complex than the average polity, their mean capacity share is 0.71 against 0.58 overall, and 40\% of records have $K$ above 0.8, so within that sample $P$ correlates 0.63 with $D$ and 0.02 with $K$---the mismatch index is, among crisis cases, close to a rescaled measure of scale (last row of Table~\ref{tab:measurement}).7576\begin{figure}[H]77\centering78\includegraphics[width=\textwidth]{figures/fig_measurement_DK.pdf}79\caption{Measurement. Left: capacity index against the scale component across Seshat polities. Middle: block-mean against latent (IRT) capacity. Right: item difficulties from the two-parameter model (items ordered by block).}80\label{fig:measurement}81\end{figure}8283\subsection{A-priori power}84\label{sec:data-power}8586Before estimation, we drew random outcomes with the actual distribution of pre-crisis $P$ among the 127 crisis records with a defined index and computed power at the 5\% level with region-clustered standard errors (Table~\ref{tab:power}). For the binary ``severe outcome'' indicator (base rate 0.77) the minimum detectable effect at 80\% power is about 0.6 log-odds per standard deviation, above the pre-registered threshold of 0.5, so that outcome was declared underpowered before any result was seen and is reported as secondary. For the fractional severity share (base rate 0.29 over fourteen items) the minimum detectable effect is about 0.15, and that outcome is primary.8788\begin{table}[H]89\centering\small90\caption{A-priori power for the Seshat crisis-severity test (random outcomes, actual $P$ distribution, $n=127$, 400 replications per effect size).}91\label{tab:power}92\begin{tabular}{l r r r}93\toprule94Outcome & $\beta$ per SD of $P$ & Power & $n$ \\95\midrule96\input tables/tab_power 97\bottomrule98\end{tabular}99\end{table}100