# Contract (P0)
**Question.** In a Gaussian AR(1), y_t = c + rho*y_{t-1} + e_t (c=0 in DGP), how biased is the OLS estimator of rho
(regression with intercept) in a finite sample, and how well does the Marriott–Pope/Kendall approximation
E[rho_hat]-rho ≈ -(1+3rho)/n describe it at the design (n, rho)?

**Estimands.** (i) bias_analytical = -(1+3rho)/n at design values (n = 30 as given in design.csv, the series length;
the regression uses n-1 = 29 pairs — this ambiguity is noted as a sensitivity only). (ii) bias_mc = mean(rho_hat) - rho over R
replications, with MC SE = sd(rho_hat)/sqrt(R). Meaningful under: Gaussian iid innovations, stationarity |rho|<1,
stationary start y_1 ~ N(0, sigma^2/(1-rho^2)), OLS with intercept on t=2..n.
Also the baseline se_asymptotic = sqrt((1-rho^2)/n).

**Required outputs.** out/results.json keys: task_id, bias_analytical, bias_mc, bias_mc_se, rho_hat_mean, rho_hat_sd_mc,
discrepancy_se_units, se_asymptotic, n_replications, feasibility, feasibility_reason, data_issues, n_input_rows,
n_analysed, random_seed. out/report.md (sections Question; Data and exclusions; Method; Results; Uncertainty;
Limitations and open issues), out/analysis.py, out/claims.json. Plus protocol files in out/state, out/exclusions.csv.

**Information rules.** Use only data/design.csv; follow design exactly (n, rho, sigma, intercept, stationary init, R, seed
with numpy default_rng); fresh series each replication; OLS of y_t on (1, y_{t-1}) for t=2..n.

**Invalidity.** Missing/inconsistent design parameters, non-stationary rho with stationary init, failure to use the seed,
or reporting the asymptotic formula as exact.