1[2 {"id":"C1","text":"The closed-form Walrasian relative price p1/p2 is 0.875.","results_keys":["price_ratio_p1_over_p2"],"status":"supported","caveat":"Uses aggregate good-1 endowment 12 (sum of individual endowments), not the summary-sheet 14."},3 {"id":"C2","text":"Independent Brent root-finding of z1(p) gives the same price within 1.1e-16.","results_keys":["price_ratio_numerical","abs_diff_closed_form_vs_numerical"],"status":"supported","caveat":"Validation is of the price for these parameters only."},4 {"id":"C3","text":"Equilibrium allocation is A=(4.1143, 5.4), B=(7.8857, 4.6), with incomes 9 and 11.5.","results_keys":["x1_A","x2_A","x1_B","x2_B","income_A","income_B"],"status":"supported","caveat":"Interior solution assumed (alphas in (0,1), positive endowments), satisfied by the data."},5 {"id":"C4","text":"Both markets clear at the equilibrium price (excess demands 0).","results_keys":["excess_demand_good1","excess_demand_good2","aggregate_endowment_good1","aggregate_endowment_good2"],"status":"supported","caveat":""},6 {"id":"C5","text":"Walras' law holds: residual 0 at equilibrium and at most 5.7e-14 on an off-equilibrium price grid.","results_keys":["walras_law_residual","walras_law_residual_max_abs_offeq_grid"],"status":"supported","caveat":"Floating-point precision."},7 {"id":"C6","text":"The summary-sheet aggregate endowment of good 1 (14) is inconsistent with the individual endowments (12); using it would give price 0.6667 and a non-zero Walras residual of -1.333.","results_keys":["data_issues","sensitivity_price_if_summary_aggregate_good1","sensitivity_walras_residual_if_summary_aggregate_good1"],"status":"supported","caveat":"Which source is erroneous cannot be determined from the inputs; primary endowments were trusted."}8]9