# Contract (P0)
**Question.** With few clusters, how reliable are cluster-robust 95% CIs for a population mean μ estimated by the sample mean ȳ?

**Estimands (per cell G∈{5,10,30} × ICC∈{0,0.2,0.5}; per procedure CR0, CR1, WCB):**
(a) actual coverage of the nominal 95% interval (fraction of R=2000 intervals containing μ=0);
(b) for CR0/CR1: relative bias E[V̂]/Var(ȳ), Var(ȳ) = [ICC Σ n_g² + (1−ICC) N]/N² (exact under the DGP), E[V̂] by Monte Carlo mean;
(c) MC SE of coverage √(p̂(1−p̂)/R);
(d) failure regimes: coverage < 0.90; "nominal-consistent": |p̂−0.95| ≤ 2 MC SE.
Meaningful under the stated Gaussian random-intercept DGP with given unbalanced cluster sizes; results are Monte Carlo estimates with MC error.

**Outputs:** out/table1.csv (27 rows: estimator, cell_id, G, icc, coverage, mc_se_coverage, rel_bias_var [empty for wcb], mean_ci_halfwidth, R); out/results.json (task_id, R, B, n_cells, coverage, mc_se_coverage, rel_bias_var, failure_cells, n_failure_cells, nominal_cells, best_procedure_small_G, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed); out/figure1.png; out/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues); out/analysis.py; out/claims.json; plus protocol files (state/, exclusions.csv).

**Information rules:** use only data/design.csv; DGP and procedures exactly as specified; R=2000, B=399, per-cell seed; no change to grid.

**Invalidity/impossibility:** changing R/B/grid/seeds; procedures deviating from spec; nondeterminism; runtime >10 min. Nothing appears impossible.