# Verification checks (P4)
| check | outcome |
|---|---|
| Clean re-run of out/analysis.py (results.json deleted, regenerated) byte-identical | PASS |
| Market clearing good 1: x1_A+x1_B-12 | 0.0 PASS |
| Market clearing good 2: x2_A+x2_B-10 | 0.0 PASS |
| Budget constraints A and B hold at p | 0.0, 0.0 PASS |
| MRS_A = MRS_B = p (Pareto efficiency / tangency) | 0.875, 0.875 PASS |
| Closed form vs hand computation 5.6/6.4 = 0.875 | PASS |
| Numerical root (brentq on z1, bracket [1e-9,1e9]) vs closed form | |diff| = 2.2e-16 PASS |
| Walras residual p*z1+z2 | 0.0 PASS |
| Interior allocation (all x > 0) | PASS |
| Aggregate endowment consistency with summary sheet | FAIL for good 1 (14 vs 12) -> handled, reported in data_issues |