1[2 {"id": "C1", "text": "The competitive equilibrium relative price p1/p2 is 0.875 (closed form 5.6/6.4).", "results_keys": ["price_ratio_p1_over_p2"], "status": "supported", "caveat": "Relies on aggregate good-1 endowment = 12 (sum of individual endowments), not the summary-sheet value 14."},3 {"id": "C2", "text": "Independent root-finding of aggregate excess demand for good 1 reproduces the closed-form price to machine precision.", "results_keys": ["price_ratio_numerical", "abs_diff_closed_form_vs_numerical"], "status": "supported", "caveat": "Brent bracketing on [1e-8, 1e8]; single-market check."},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 demands at p*."},5 {"id": "C4", "text": "Both markets clear at p* and Walras' law holds (residual 0 at p*, <1e-13 on an off-equilibrium price grid).", "results_keys": ["excess_demand_good1", "excess_demand_good2", "walras_law_residual", "walras_law_max_abs_residual_offequilibrium_grid"], "status": "supported", "caveat": "Floating-point precision."},6 {"id": "C5", "text": "The summary-sheet aggregate endowment of good 1 (14) is inconsistent with the individual endowments (12); the latter was used.", "results_keys": ["data_issues", "aggregate_endowment_good1", "sensitivity_excess_demand_good1_vs_summary_sheet_aggregate"], "status": "supported", "caveat": "Which source is wrong cannot be verified; resolution is an assumption."}7]8