# Contract (P0)

Question: In the fixed-design 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 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 mean.
• Also sd_beta_mc (divisor R-1) and decision conventional_ci_undercovers = cov_conv < 0.95 - 3sqrt(0.950.05/2000). Meaningful under: fixed design, normal errors, known sigma_i only used by the DGP (not by estimators).

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 (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues), out/analysis.py, out/claims.json, plus protocol files.

Information rules: only data/design.csv; never redraw x or sigma; constants as given.

Invalidity: design file missing/malformed (not 30 rows, non-positive sigma, constant x), R != 2000, non-reproducible seed.