WP35 — Phase 6: theory-to-data integration
Numbers quoted here are copied from results/empirical/*.csv|json and results/simulated/simulation_summary.json.
1. Which mechanisms are observable in the historical record, and which are not
| Mechanism (framework) | Observable in Seshat / V-Dem? | Observable in the simulation? |
|---|---|---|
| Coding gain of shared codes (T1) | No: presence of writing, coins, legal codes is observed; message lengths are not | Yes: $H(p) \le L < H(p)+1$ holds in every cell; code longer than raw in one weakly-concentrated cell |
| Break-even scale of institutions (T2) | Only indirectly: H1 (capacity rises with scale) | Yes: a 200-bit learning cost is repaid only with $s=256$, Zipf 1.5 and $T=160$ |
| Stale-code penalty after shocks (T3) | No: no measure of task distributions or of code adaptation | Yes: extra bits per recipient 1.90 vs $D_{KL}$ 1.98 (within ±1) |
| Routing and root load in hierarchies (T4) | Partially: administrative levels are coded, loads are not | Yes: central regimes fail when capacity ratio < 1; federated regimes keep 84% success at ratio 0.5 |
| Backlog dynamics / utilization (T5) | Not observed; $P$ is a proxy for $\log\rho$ only under C1 | Yes by construction (queue) |
| Sustained overload → breakdown (C2) | This is what H2 tests, through $P$ | Not modelled (no breakdown process) |
| Smooth vs threshold (C3) | H4: no threshold in Seshat; marginal, economically negligible nonlinearity in the modern panel | Convex latency in $\rho$ (T5) |
2. The model against simpler rivals (EMPIRICAL)
- Seshat crisis severity. $\beta_P = 0.20$ (SE 0.06, n = 127) in the primary spec and 0.20 (SE 0.09, n = 87) with covariates; stable across leave-one-region-out (0.18–0.33) and leave-one-era-out (0.20–0.32). But the D-only baseline gives 0.26 (SE 0.14) and D and K entered separately give D = 0.34 (p = 0.04), K = −0.21 (p = 0.27): the capacity component has the predicted sign but is not distinguishable from zero. Out of sample, P beats the FE-only, K-only and complexity-PC1 baselines in ≥ 80% of 10×5 folds, but not the D-only (75%), persistence (69%) or D+K (75%) baselines, and it loses to D-only in 7 of 10 leave-one-region-out folds. The placebo index built from production infrastructure instead of K yields 0.26 (SE 0.14). Verdict: the association is driven by scale; the mismatch adds nothing identifiable beyond population size.
- Seshat polity hazard and succession. No association of P with polity duration (HR 1.00–1.03) or with discontinuous succession (p > 0.4). Higher K is associated with a higher hazard of polity end (HR 1.75, p = 0.005), which we read as a periodization artifact (complex polities are split into more, shorter Seshat polities).
- Modern panel. $\beta_P = 0.40$ (SE 0.09, n = 14,637, 2,692 events), stable across regions and periods, strongest for civil-war onsets (1.01) and weak for coups (0.20, n.s.). But K alone gives −0.63 (SE 0.13) and D alone 0.13 (p = 0.08): the signal is capacity, not mismatch. Out of sample P never beats the K-only baseline (forward chaining 0/2 on log-likelihood and AUC; leave-one-region-out 1/6). The reverse-window negative control (past events on current P) gives 0.44 vs 0.48 for future events: P marks chronically unstable countries. Oster-adjusted coefficient −0.02; RV = 0.07.
- H1. Capacity and scale are positively associated everywhere: Seshat 0.75 SD of D per SD of K (primary), 0.39 with rival covariates; EA 0.70 log units of community size per jurisdictional level (Conley SE 0.09–0.10); modern within-country 0.15 (p = 0.02) and 50-year differences 0.13 (p = 0.01), pooled n.s. (p = 0.43). Sign stable; direction not identified.
3. Consistency of historical patterns with simulation-derived predictions
The simulation predicts (i) institutions raise success and lower operating cost per success in essentially every cell (norms 99%, records 100% of paired comparisons), which is consistent with H1's positive association but says nothing about causation; (ii) hierarchies collapse when relayed load exceeds administrative capacity (ratio < 1), i.e. a sharp utilization effect; the historical analogue would be a threshold in P, which H4 does not find in Seshat and finds only marginally in the modern panel — the proxy may simply not measure utilization (C1); (iii) distribution shocks raise cost by the divergence without lowering success, so "shock → breakdown" needs a capacity constraint that binds, which again the historical proxies do not measure. Agreement on (i) is weak evidence; disagreement on (ii) is informative: either there is no utilization threshold in history, or P does not track utilization. We cannot tell which.
4. Scope conditions and failed predictions (stated for the abstract)
- Failed: H2 as pre-registered ("beyond conventional baselines") fails in both panels. H4 fails in Seshat and is marginal in the modern panel. C1 is undermined by the collinearity and placebo results.
- Held: H1 as an association in all three datasets; H3 in simulation for the operating cost of coordination, with the explicit exceptions (set-up costs, saturated hierarchies, weakly concentrated plan spaces) found by the fragility search.
- Scope: the only historical claim that survives is that scale predicts crisis severity among crisis cases (β ≈ 0.26–0.34 per SD) and that capacity predicts fewer instability onsets in modern states (−0.63 per SD) — neither is new, and neither is the Social Compression Hypothesis. The paper is therefore written as a pre-registered test that does not support the universal framing, with the theory and simulations as the constructive part.