Verification checks (P4)
- Clean re-run of out/analysis.py (results.json deleted first) -> byte-identical output (cmp). PASS
- Market clearing: x1_A+x1_B = 12.0 = aggregate_endowment_good1; x2_A+x2_B = 10.0 = aggregate_endowment_good2. PASS
- excess_demand_good1 = 0.0, excess_demand_good2 = 0.0, walras_law_residual = 0.0. PASS
- Budget constraints hold exactly for A and B (residual 0.0). PASS
- Pareto efficiency: MRS_A = MRS_B = 0.875 = price_ratio_p1_over_p2. PASS
- Closed form vs independent brentq root of z1(p): |diff| = 2.2e-16 (abs_diff_closed_form_vs_numerical). PASS
- Numerical root uses only the demand functions and z1(p) on bracket [1e-8,1e8]; it does not evaluate the closed-form formula. PASS
- All allocations strictly positive (interior). PASS
- Exclusion ledger: n_raw 2 - removed 0 = n_analysed 2. PASS
- Data inconsistency (recorded E1=14 vs 12) recorded in data_issues; diagnostic price with 14 = 0.6667. PASS (reported)