1[2 {"id":"C1","text":"The closed-form equilibrium relative price is p1/p2 = 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's 14."},3 {"id":"C2","text":"Independent Brent root-finding of good-1 excess demand gives the same price, to within 1e-16.","results_keys":["price_ratio_numerical","price_ratio_p1_over_p2"],"status":"supported","caveat":"Validation covers these parameter values only."},4 {"id":"C3","text":"The equilibrium allocation is A = (4.1143, 5.4), B = (7.8857, 4.6), and both markets clear.","results_keys":["x1_A","x2_A","x1_B","x2_B","excess_demand_good1"],"status":"supported","caveat":"Assumes an interior Cobb-Douglas solution."},5 {"id":"C4","text":"The Walras' law residual is zero at equilibrium, and zero to within 1e-12 across a grid of prices.","results_keys":["walras_law_residual"],"status":"supported","caveat":"Grid result is in out/diagnostics.json."},6 {"id":"C5","text":"The summary sheet's aggregate good-1 endowment (14) conflicts with the individual endowments (12); the latter was used.","results_keys":["data_issues","aggregate_endowment_good1"],"status":"supported","caveat":"The inputs cannot show which value is correct."}7]8