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# 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
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
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