1\section{Econometric methods and identification}2\label{sec:methods}34\subsection{Pre-registration}5\label{sec:methods-prereg}67The analysis plan was frozen before any predictor--outcome association was computed; its SHA-256 hash is recorded in the decision log and every deviation is a numbered amendment. The plan fixes five hypotheses with falsifiers (H1: capacity and scale are positively associated conditional on era, region and rival covariates, with no direction claimed; H2: lagged mismatch predicts subsequent instability \emph{beyond} scale-only, capacity-only, complexity-only and persistence baselines, judged out of sample; H3: in simulation, shared protocols and institutions lower communication cost per successfully coordinated task; H4: a threshold form outperforms a smooth form out of sample; H5: estimates keep their sign in every held-out macro-region and era, otherwise the domain is narrowed), the samples and exclusions, the disjoint indicator sets of Section~\ref{sec:data-measurement}, three primary tests with a Holm correction (H1 in Seshat, H2 on Seshat crisis severity, H2 on the modern composite outcome), a robustness set, and the rule for abandoning the universal framing: if H2 fails in both panels, the paper reports the hypothesis as not supported and keeps only what survived.89\subsection{Historical polities}10\label{sec:methods-hist}1112For H1 we regress the scale component on the capacity index with macro-region and era fixed effects (ten macro-regions grouping the 42 Seshat regions; six era blocks on the polity midpoint), with and without the rival covariates (warfare-technology index, production-infrastructure index, military professionalization), with standard errors clustered by Seshat region, and we repeat the exercise with a region random intercept, with the latent capacity score, with the four blocks entered separately, and without quasi-polities.1314For H2 the primary outcome is crisis severity $Y_1$, the share of the fourteen instability consequences coded present among those coded at all for a CrisisDB record (unknown codes are missing, never zero). The model is a fractional logit,15\begin{equation}16\mathbb{E}[Y_{1,c}] = \Lambda\!\left(\alpha + \beta\, P_{i(c)} + \gamma' X_{i(c)} + \mu_{r(c)} + \tau_{e(c)}\right),17\label{eq:h2a}18\end{equation}19where $P_{i(c)}$ is the pre-crisis mismatch of the polity of crisis $c$, $X$ contains the warfare-technology and production-infrastructure indices and an indicator that an epidemic accompanied the crisis, and $\mu$ and $\tau$ are macro-region and era effects; standard errors are clustered by Seshat region (alternatively by natural geographic area and by polity). The binary secondary outcome $Y_{1b}$---any of collapse, fragmentation, century-long conflict, conquest or civil war coded present, defined only when all five are coded---is fitted by logit; several region--era cells are all-severe, so era effects are dropped for that outcome and heteroskedasticity-robust errors are used. Baselines are fitted on the same observations: fixed effects only, scale only, capacity only, a Turchin-style complexity component, a persistence indicator (an earlier CrisisDB crisis in the same natural geographic area), and scale and capacity entered separately. A placebo index replaces $K$ with the production-infrastructure share that was excluded from $K$ by design. Out-of-sample comparison uses leave-one-macro-region-out folds (region effects removed) and ten repetitions of five-fold cross-validation; the pre-registered rule is that $P$ ``beats'' a baseline if its mean out-of-sample log-likelihood is higher in at least 80\% of folds. For H4, a hinge model whose knot is chosen by profile likelihood on the training fold only and a natural cubic spline with three degrees of freedom are compared with the linear form on the same folds. For H5, $\beta$ is re-estimated with each macro-region and each era held out, and, where the held-out block has at least twelve crisis records, within the block.2021Two secondary historical outcomes use all polities. Polity duration (end year minus start year) is modelled by a Cox proportional-hazards regression stratified by macro-region, with the polity's end as the event and right-censoring for polities that reach 1900, robust errors clustered by region and a Schoenfeld test \citep{cox1972,boxsteffensmeier2004}; discontinuous succession---the successor polity's relationship to its predecessor coded as anything other than continuity---is modelled by logit. Both are reported with the caveat that Seshat polity boundaries are periodization decisions.2223\subsection{Ethnographic societies}24\label{sec:methods-ea}2526Log community size is regressed on jurisdictional levels with subsistence, agricultural intensity, class differentiation and region controls; standard errors are Conley spatial HAC with 500 and 1{,}000 km cut-offs \citep{conley1999} and, alternatively, clustered by Glottolog language family. The reverse specification, an ordered logit of jurisdictional levels on log community size, is reported with family-clustered errors.2728\subsection{Modern states}29\label{sec:methods-modern}3031The modern outcome $Y_{456}$ equals one if a civil-war onset, a coup or an irregular regime end occurs in $(t, t+5]$ and is missing if no year in the window is coded. The primary model is a pooled logit with region and year fixed effects and country-clustered standard errors,32\begin{equation}33\Pr(Y_{456,i,t+1..t+5} = 1) = \Lambda\!\left(\alpha + \beta P_{it} + \gamma' X_{it} + \mu_{r(i)} + \tau_t\right),34\label{eq:h2c}35\end{equation}36with $X$ containing log GDP per capita, the V-Dem electoral-democracy index (because the capacity items correlate 0.75 with it) and a cubic in years since the last event \citep{carter2010,beck1998}; a conditional logit with country and decade effects and a linear probability model with country and year effects are secondary \citep{cameron2015}. Baselines are population only, capacity only, development only, persistence (an event in the previous five years), and population and capacity entered separately; the placebo index replaces $K$ with the democracy index. Two negative controls are pre-registered: events in $[t-5, t-1]$ regressed on $P_t$ with the same controls should not load more strongly than future events, and the placebo should not perform as well as $P$. Out-of-sample validation is by forward chaining (train to 1945, test 1946--1975; train to 1975, test 1976--2005; train to 2005, test 2006 onward; year effects replaced by decade effects so that test years have a fitted level) and by leave-one-region-out on the six V-Dem politico-geographic regions, with log-likelihood, area under the ROC curve, Brier score and calibration slope \citep{goldstone2010}. H4 and H5 proceed as in the historical panel with country-blocked folds and with the six regions and four periods (pre-1900, 1900--1945, 1946--1989, 1990 onward) as blocks. The robustness set varies the horizon (1, 3, 10 years), the outcome components, the capacity aggregation, the standardization window, the inclusion of land area, the sample period and the control set, and reports Oster's bias-adjusted coefficient and the Cinelli--Hazlett robustness value on the linear-probability version of the primary model \citep{oster2019,cinelli2020}.3738\subsection{What the designs identify}39\label{sec:identification}4041Nothing in this paper is causal, and the text does not use causal language for H1 or H2. The estimands are conditional associations with pre-specified direction, baselines, out-of-sample validation and falsification tests. The reasons are stated in advance in the identification note of the replication package and summarized here. Scale creates the demand for administration and administration enables scale, so H1 is symmetric by construction. The historical outcome is crisis-selected, most Seshat facts are undated so that ``pre-crisis'' capacity is mostly whole-polity capacity, the institutional codes and the crisis codes are produced by the same project from overlapping historiography, and the mismatch index is a residual of two indices that correlate 0.84. In the modern panel the capacity items are expert-coded with knowledge of later events and compete with regime type as an explanation, which the pre-registered placebo, negative control and sensitivity analysis are designed to expose rather than to remove. A credible design would move demand or capacity for reasons unrelated to local instability; no such variation is coded at the polity level in Seshat, and the candidate instruments in the modern panel (printing, railways, telegraphy) do not satisfy an exclusion restriction for instability. The paper therefore claims association, prediction and robustness, and declines a causal claim.42