# Verification checks

1. Clean re-run of analysis.py reproduces results.json byte-identically: PASS (cmp).
2. Closed form vs brentq root of z1(p) on [1e-6,1e6]: |diff| = 1.1e-16 (abs_diff_closed_form_vs_numerical): PASS.
3. Hand derivation: p = (0.42+0.68)/(0.68+0.44) = 5.6/6.4 = 0.875: matches.
4. Market clearing: x1_A+x1_B = 12 = W1, x2_A+x2_B = 10 = W2; z1 = z2 = 0 (floating point): PASS.
5. Walras law residual = 0: PASS.
6. Budget: px1_A + x2_A = 0.8754.1143+5.4 = 9.0 = 0.875*8+2: PASS (checked below in log).
7. All allocations > 0 (interior): PASS.
8. Exclusions: n_raw 2 - 0 removed = n_analysed 2: PASS.