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# Verification checks (P4)

# check outcome
1 Clean rerun (delete results.json, rerun analysis.py, byte compare) PASS: identical
2 Market clearing good 1: x1_A+x1_B-12 PASS: 0.0
3 Market clearing good 2: x2_A+x2_B-10 PASS: 0.0
4 Budget constraints A and B hold with equality PASS: 0.0, 0.0
5 MRS_A = MRS_B = p (Pareto efficiency / tangency) PASS: 0.875 each
6 Closed form vs Brent root of z1(p) on [1e-6,1e6] PASS: abs diff 1.1e-16
7 Walras' law at eq. (0.0) and on 41-point off-equilibrium grid p in [0.01,100] PASS: max abs 5.7e-14
8 Hand calculation p = (0.42+0.68)/(0.68+0.44) = 5.6/6.4 PASS: 0.875
9 All allocations strictly positive (interior) PASS
10 n_raw(2) - removed(0) = n_analysed(2) PASS
11 Uniqueness: Cobb-Douglas z1(p) strictly decreasing (z1 = 5.6/p - 6.4 with sum-of-endowment data), so there is a single root PASS (analytic)
12 Input inconsistency (aggregate good1 14 vs 12) recorded in data_issues PASS
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