# Contract (P0)
**Question:** In a fixed-design linear model y_i = 1 + 0.5 x_i + sigma_i eps_i (n=30, x and sigma from data/design.csv, eps iid N(0,1)), do nominal 95% t(28) intervals for the OLS slope achieve 95% coverage, using (i) conventional OLS SE and (ii) HC1 robust SE?

**Estimands**
- (a) P(beta in betahat ± t_.975(28) se_conv) — MC, R=2000, fixed seed.
- (b) same with se_HC1 = sqrt(n/(n-2) * HC0) — MC.
- (c) exact SD of betahat = sqrt(sum w_i^2 sigma_i^2), w_i = (x_i - xbar)/Sxx — analytic.
- (d) E[se_conv] — MC average.
- Also sd_beta_mc (ddof=1) and conventional_ci_undercovers = (0.95 - cov_conv) > 3*sqrt(0.95*0.05/2000).
Assumptions: model is correctly specified as stated; x, sigma fixed; only eps redrawn.

**Outputs:** out/results.json (keys 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 (sections Question, Data and exclusions, Method, Results, Uncertainty, Limitations and open issues); out/analysis.py; out/claims.json; plus state files and out/exclusions.csv.

**Information rules:** only data/design.csv; constants given; do not redraw x or sigma.

**Invalidity conditions:** design file missing/malformed (not 30 rows, nonpositive sigma, missing values, constant x); non-reproducible simulation; R != 2000.

**MC SE choice for the undercoverage rule:** the binomial SE at the nominal level, sqrt(0.95*0.05/2000) (test of H0 coverage=0.95). The SE at the estimated coverage is also reported in the report.