# Contract (P0)
**Question.** In a one-way random-effects clustered design with few clusters, how close to 95% is the actual coverage of three cluster-robust intervals for the mean (CR0+normal, CR1+t(G-1), wild cluster bootstrap-t with Rademacher weights)?

**Estimands (per cell of G∈{5,10,30} × ICC∈{0,0.2,0.5}, per procedure):**
(a) coverage probability of the nominal 95% interval for μ=0; (b) for CR0/CR1, E[V̂]/Var(ȳ) with exact Var(ȳ)=[ICC Σn_g² + (1−ICC)N]/N²; (c) MC SE √(p̂(1−p̂)/R); (d) failure regimes: coverage < 0.90; "nominal": |p̂−0.95| ≤ 2 MC SE.
Meaningful under the stated Gaussian DGP with the fixed unbalanced cluster sizes (8,16,32,64 repeated); R=2000, B=399 fixed; per-cell seeds from design.csv.

**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.

**Information rules.** Use only data/design.csv; DGP and procedures exactly as specified; do not change grid, R, B or seeds. No observed data exist.

**Invalidity/impossibility.** Changing R/B/grid/seeds; deviating from the procedure formulas; non-determinism; runtime >10 min. Degenerate bootstrap variance (zero V̂*) would need handling (none expected: all-equal weights give V̂*=V̂>0).