\section{Limitations}
\label{sec:limits}

The limitations were written down during the analysis and before this section; the full list is in the replication package. The ones that bear on how the results should be read are these.

\paragraph{Data.} The CrisisDB outcome is crisis-selected (150 of 626 polities), so the Seshat test concerns the severity of recorded crises, not their occurrence. Only 6\% of Polaris facts are dated, so pre-crisis capacity is in practice whole-polity capacity and temporal precedence is weak; a dated-only test was not estimable. Seshat capacity items record the existence of institutions, not their reach, quality or cost, and the demand side is scale only because the databank has no usable indicator of division of labour or dispersion. Institutional codes and crisis codes come from the same project and overlapping historiography, which permits circularity that the inferred-code and late-crisis sensitivities can only partly address. Seshat polity boundaries are periodization decisions, so polity duration is not an instability outcome. In the modern panel, the six capacity items correlate 0.75 with electoral democracy and are rated by experts who know what came later; population begins in 1820 for most countries and there is no dispersion measure; 39 V-Dem entities without Maddison population drop out. The Ethnographic Atlas is a cross-section with coarse ordinal community sizes (the top category is bounded at 50,000) and no outcome; jurisdictional levels are themselves a response to scale in the scalar-stress tradition \citep{johnson1982,carneiro1967}, so the H1 association there replicates a known size--hierarchy regularity rather than testing compression. The severity share aggregates fourteen weakly correlated consequences (Section~\ref{sec:hist-h2}).

\paragraph{Design.} Nothing is identified causally. The modern negative control passes the pre-registered letter (past 0.44 against future 0.48 log-odds per SD) by a margin within one standard error; the Oster adjustment under proportional selection crosses zero, with the caveat that proportional selection is a strong assumption when one control (electoral democracy) correlates 0.75 with a component of the regressor, and the robustness value is 0.07 against a partial $R^2$ of 0.006. The Seshat binary outcome was underpowered in advance. There are 42 regions and ten macro-regions, so cluster-robust inference is anti-conservative and alternative clusterings are reported. The verdict on H2 rests on a pre-registered out-of-sample rule against baselines, which is the right test of ``beyond conventional baselines'' but is also a demanding one at $n=93$--127, and one of the baselines (scale and capacity entered separately) nests the mismatch model, so that $P$ cannot do better than it in expectation; we report the fold-level results and the Wald test of the restriction so that readers who prefer a different rule can apply it. Several specification errors found by the adversarial reviews (a placebo that reparametrized the scale-only baseline, a consequence item used as a covariate, silently failed cross-validation folds, mislabelled rows) were corrected and are listed as amendments A-004 to A-007. The Equinox-2020 replication listed in the pre-registration was not executed (not blocked: the raw file is in the package, the parser was not written) and is recorded as such in the audit.

\paragraph{Theory.} The theorems describe an idealized communication system in which capacity is exogenous; historically it is built in response to demand. The conjectures that link the framework to the proxies are exactly what the measurement results call into question: with scale and capacity correlated 0.84, the proxy $P$ retains 17\% of their joint variance, and a residual of that kind cannot be assumed to track utilization.

\paragraph{Simulation.} Regimes are imposed; the model says nothing about emergence. The success ranking of regimes is the ranking of their decoding-error parameters (0.25 per unit of dialect distance without a code, 0.02 with a code, zero with records) and reverses when heterogeneity is low; only the cost side is measured rather than assumed. Bit and message accounting is stylized (one-bit acknowledgements, four-bit records, codewords repeated on every relay hop), and only within-simulation comparisons are meaningful. Decoding success does not depend on the plan drawn, so distribution shocks affect cost but not success by construction; link removal does not touch the administrative tree. The saturation of hierarchies follows from the budget multiple, a free parameter swept across its range; it is confirmed, not discovered, and its position depends on the ``capacity follows load'' allocation rule. Shannon rather than Huffman codes are used so that the stale-code penalty is comparable to the theorem; an optimal code would never be longer than fixed-length coding. Several of these choices were corrected after the computational review (amendment A-005).

\paragraph{Process.} The study was executed autonomously by a language-model agent under a human mandate in a single session: the pre-registration, code, analyses and text were produced by the agent, with the mandate's prohibitions on fabrication, imputation of missing data as zero and unapproved spending enforced by the execution log and the replication package. The principal investigator has not yet reviewed the code or the text at the time of writing; three adversarial reviews commissioned from independent reviewer personas and the responses to them are included in the package. Reference verification relied on Crossref metadata and primary-source abstracts; the chapter contents of \citet{johnson1982} and the published tables of \citet{sng2014} were not read.