# Verification checks

1. Reproducibility: deleted results.json/exclusions.csv, re-ran analysis.py, cmp byte-identical -> PASS.
2. Closed form vs independent Brent root of z1(p) on [1e-6,1e6]: |diff| = 1.1e-16 (price_abs_diff_closed_vs_numerical) -> PASS.
3. Market clearing: excess_demand_good1 = 0.0, excess_demand_good2 = 0.0 -> PASS.
4. Allocation sums: x1_A+x1_B = 12 = aggregate_endowment_good1; x2_A+x2_B = 10 = aggregate_endowment_good2 -> PASS.
5. Walras' law: residual 0.0 at equilibrium; max |p z1 + z2| over 41-point log grid p in [0.01,100] = 5.7e-14 -> PASS (holds identically up to float rounding).
6. Budget: wealth_A = 0.8758+2 = 9; 0.8754.1143+5.4 = 9.0; wealth_B = 11.5; 0.875*7.8857+4.6 = 11.5 -> PASS.
7. Hand derivation: p = (0.42+0.68)/(0.68+0.44) = 5.6/6.4 = 0.875 -> PASS.
8. Positivity / interiority: all consumptions > 0 -> PASS.
9. Exclusion ledger: 2 raw - 0 removed = 2 = n_analysed -> PASS.
10. Data-consistency check: sheet aggregate good1 (14) inconsistent with rows (12) -> FLAGGED, handled (data_issues).