1[2 {"id":"C1","text":"The closed-form competitive equilibrium relative price is p1/p2 = 0.875.","results_keys":["price_ratio_p1_over_p2"],"status":"supported","caveat":"Uses aggregate endowment of good 1 = 12 (sum of individual endowments), not the inconsistent sheet value 14."},3 {"id":"C2","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 with strictly positive endowments."},4 {"id":"C3","text":"Market for good 1 clears and Walras' law holds at the equilibrium price (residuals 0 to machine precision).","results_keys":["excess_demand_good1","walras_law_residual","aggregate_endowment_good1","aggregate_endowment_good2"],"status":"supported","caveat":"Against the sheet aggregate of 14, z1 would be -2; that value was rejected as inconsistent."},5 {"id":"C4","text":"Independent Brent root-finding of z1(p) reproduces the closed-form price (|difference| ~1e-16).","results_keys":["price_ratio_numerical","price_ratio_p1_over_p2"],"status":"supported","caveat":"Validates the algebra for this parameter set only."},6 {"id":"C5","text":"The summary-sheet aggregate endowment of good 1 (14) is inconsistent with the individual endowments (12).","results_keys":["data_issues"],"status":"supported","caveat":"Which source is erroneous cannot be determined from the data; individual endowments treated as primary."}7]8