# Contract (P0)
**Question.** In a Gaussian AR(1) y_t = c + rho*y_{t-1} + e_t (c=0 in DGP), OLS of y_t on (1, y_{t-1}) is biased in finite samples. Compare the Marriott–Pope/Kendall approximation -(1+3rho)/n with the Monte Carlo bias at the design (n, rho).

**Estimands.** (i) bias_analytical = -(1+3rho)/n at design values (a first-order, O(1/n) asymptotic-expansion approximation; meaningful for stationary |rho|<1, Gaussian errors, intercept estimated). (ii) bias_mc = mean(rho_hat) - rho over R replications, with MC SE sd(rho_hat)/sqrt(R). Also discrepancy in SE units and baseline se_asymptotic = sqrt((1-rho^2)/n).

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

**Information rules.** Use only data/design.csv; follow design exactly (n=30, rho, sigma, intercept, stationary y_1, R, seed with numpy default_rng); c=0; fresh series per replication; OLS for t=2..n.

**Invalidity.** Missing/contradictory design values; nonstationary rho (|rho|>=1) with "stationary" init; not using the seed; dropping replications without ledger.