# Contract — F2-conf-03
**Question:** Do nominal 95% t-intervals for the OLS slope reach 95% coverage when n=30 and errors are heteroskedastic (σ_i given, fixed design)?
**Model:** y_i = 1 + 0.5 x_i + σ_i ε_i, ε_i iid N(0,1), x_i and σ_i fixed from data/design.csv; only ε is redrawn.
**Estimands:** (a) P(β ∈ β̂ ± t_.975(28) se_conv); (b) the same with se_HC1 = sqrt(HC0·n/(n−2)); (c) exact SD(β̂) = sqrt(Σ w_i² σ_i²), w = row 2 of (X'X)⁻¹X'; (d) E[se_conv]. (a),(b),(d) estimated by MC, R=2000, fixed seed; (c) analytical. These are meaningful under the stated model with the design held fixed.
**Outputs:** out/results.json (task_id, coverage_conventional, coverage_hc1, sd_beta_exact, sd_beta_mc, mean_se_conventional, conventional_ci_undercovers, n_replications, n_obs_per_replication, feasibility, feasibility_reason, data_issues, n_input_rows, random_seed), out/report.md (6 sections incl. MC SEs), out/analysis.py, out/claims.json (incl. a nominal-coverage claim).
**Undercoverage rule:** true iff coverage_conventional < 0.95 − 3·MCSE, where MCSE = binomial SE at R=2000. I use p=0.95 (null value) as primary: sqrt(.95·.05/2000); also report the version with estimated p.
**Info rules:** use only design.csv; do not redraw x or σ.
**Invalidity:** design not 30 rows / bad σ; non-reproducible simulation; R ≠ 2000.