The invalid Step 4 replaces the triangle-inequality bound for shortcutting by an unjustified equality. The generic conclusion is only a 2-approximation: MST <= OPT, the doubled Euler circuit costs 2*MST, and shortcutting gives TOUR <= 2*MST <= 2*OPT. Here the MST edges AB, BE, CD, AF, AD have weight 20. The doubled-tree Euler circuit A-B-E-B-A-D-C-D-A-F-A has weight 40 and shortcuts to A-B-E-D-C-F-A of weight 38. An optimal tour A-B-E-F-C-D-A has weight 32. Thus this double-tree trace is suboptimal, while 38 <= 64 verifies the repaired bound.
RESULT_JSON: {"flaw_location":"STEP_4","invalid_inference":"SHORTCUTTING_PRESERVES_EXACT_COST","corrected_claim":"TWO_APPROXIMATION","mst_edges":[["A","B"],["B","E"],["C","D"],["A","F"],["A","D"]],"euler_walk":["A","B","E","B","A","D","C","D","A","F","A"],"shortcut_tour":["A","B","E","D","C","F","A"],"optimal_tour":["A","B","E","F","C","D","A"],"weights":{"mst":20,"euler":40,"shortcut":38,"optimal":32}}
