1[2 {"id":"C1","text":"The closed-form competitive equilibrium relative price is p1/p2 = 0.875 (7/8).","results_keys":["price_ratio_p1_over_p2"],"status":"supported","caveat":"Assumes aggregate endowment of good 1 = 12 (sum of individual endowments), not the summary-sheet value 14."},3 {"id":"C2","text":"Independent numerical root-finding of the good-1 excess demand gives the same price to machine precision.","results_keys":["price_ratio_numerical","abs_diff_closed_form_vs_numerical"],"status":"supported","caveat":"Validated only for these parameters on the bracket [1e-6, 1e6]."},4 {"id":"C3","text":"Equilibrium allocation: A consumes (4.1143, 5.4), B consumes (7.8857, 4.6).","results_keys":["x1_A","x2_A","x1_B","x2_B"],"status":"supported","caveat":"Interior Cobb-Douglas solution."},5 {"id":"C4","text":"Both markets clear and the Walras' law residual is zero at the equilibrium price.","results_keys":["excess_demand_good1","excess_demand_good2","walras_law_residual","aggregate_endowment_good1","aggregate_endowment_good2"],"status":"supported","caveat":"Zero in floating point."},6 {"id":"C5","text":"The summary-sheet aggregate endowment of good 1 (14) is inconsistent with the individual endowments (12); imposing it yields a non-zero Walras residual, so it was not used.","results_keys":["data_issues","sensitivity_summary_sheet_E1","sensitivity_walras_residual_with_sheet_E1","sensitivity_excess_demand_good2_with_sheet_E1","sensitivity_price_clearing_good1_with_sheet_E1"],"status":"supported","caveat":"Data cannot reveal which input is erroneous; endowments.csv treated as primary."}7]8