1# Verification checks (P4)2| check | outcome |3|---|---|4| Clean re-run of out/analysis.py reproduces out/results.json byte-identically | PASS |5| Market clearing good 1: x1_A + x1_B = 12.0 = aggregate_endowment_good1 | PASS (12.0) |6| Market clearing good 2: x2_A + x2_B = 10.0 = aggregate_endowment_good2 | PASS (10.0) |7| excess_demand_good1 = 0 | PASS (0.0) |8| walras_law_residual = 0 | PASS (0.0) |9| Budgets bind: A 9.0 = 0.875*8+2; B 11.5 = 0.875*4+8 | PASS |10| Optimality: MRS_A = MRS_B = p = 0.875 | PASS |11| Closed-form vs numerical root (brentq on z1(p), not using closed form) | PASS, |diff| = 1.1e-16 |12| All allocations strictly positive (interior solution) | PASS |13| n_analysed (2) = n_raw agents (2) − removed (0) per exclusions.csv | PASS |14| Hand derivation: p = (0.4*2+0.6*8)/(12-(0.4*8+0.6*4)) = 5.6/6.4 = 0.875 | PASS |15| Data issue (E1 summary 14 vs primary 12) reported in data_issues | PASS |16