{"abstract":"Crossing the 232600 break raises the tax on the entire base by two points.","category":"Tax bracket computation","checks":6,"contract":"solve(amti, regular_cents, status): stipulated AMT, whole dollars. Exemption: single 85700 (phase-out threshold 609350), mfj 133300 (threshold 1218700). The exemption is reduced by 25% of AMTI above the threshold, with the reduction rounded down to whole dollars, never below 0. Base = max(0, amti - exemption). Tentative minimum tax = 26% of base up to 232600 plus 28% of base above 232600 (in cents: dollars times percent). AMT = max(0, TMT - regular tax). Return [exemption, tmt_cents, amt_cents].","evaluation_group":"w2-tax_bracket_computation-alternative-minimum-tax","failed_approach":"Splitting at 232600 of AMTI rather than of the base puts the break in the wrong place.","family":"w2-tax_bracket_computation-alternative-minimum-tax-rate-break","id":"FA-62541","implementations":{"attempt":{"sha256":"57024dc4ba1e3e5cbd5459eee7a3ed0d44fde2557b92ae6c31545270d48f8da6","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(amti, regular_cents, status):\n    ex, thr = {'single': (85700, 609350), 'mfj': (133300, 1218700)}[status]\n    if amti > thr: ex = max(0, ex - (amti - thr) // 4)\n    base = max(0, amti - ex)\n    tmt = min(base, max(0, 232600 - ex)) * 26 + max(0, base - max(0, 232600 - ex)) * 28\n    return [ex, tmt, max(0, tmt - regular_cents)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('regression rate-break 1', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),\n  ('regression rate-break 2', (700000, 0, 'single'), [63038, 17369736, 17369736]),\n  ('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),\n  ('control: no exemption left', (1000000, 99999999, 'single'), [0, 27534800, 0]),\n  ('control: below exemption', (100000, 0, 'mfj'), [133300, 0, 0]),\n  ('control: odd excess', (609353, 5000000, 'single'), [85700, 14197084, 9197084])],\n [('regression rate-break 1', (1000000, 99999999, 'single'), [0, 27534800, 0]),\n  ('regression rate-break 2', (609353, 5000000, 'single'), [85700, 14197084, 9197084]),\n  ('partial repair guard 2', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500]),\n  ('control: below exemption', (100000, 0, 'mfj'), [133300, 0, 0]),\n  ('control: rate break', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),\n  ('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),\n  ('control: partial phase-out', (700000, 0, 'single'), [63038, 17369736, 17369736])],\n [('regression rate-break 1', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500]),\n  ('regression rate-break 2', (365900, 10000000, 'single'), [85700, 7380400, 0]),\n  ('partial repair guard 2', (832985, 0, 'single'), [29792, 22024204, 22024204]),\n  ('control: rate break', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),\n  ('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),\n  ('control: partial phase-out', (700000, 0, 'single'), [63038, 17369736, 17369736]),\n  ('control: no exemption left', (1000000, 99999999, 'single'), [0, 27534800, 0])],\n [('regression rate-break 1', (832985, 0, 'single'), [29792, 22024204, 22024204]),\n  ('regression rate-break 2', (1122405, 10000000, 'mfj'), [133300, 27229740, 17229740]),\n  ('partial repair guard 1', (365900, 35622995, 'mfj'), [133300, 6047600, 0]),\n  ('control: no exemption left', (1000000, 99999999, 'single'), [0, 27534800, 0]),\n  ('control: below exemption', (100000, 0, 'mfj'), [133300, 0, 0]),\n  ('control: odd excess', (609353, 5000000, 'single'), [85700, 14197084, 9197084]),\n  ('control: joint high', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500])],\n [('regression rate-break 1', (1526866, 0, 'single'), [0, 42287048, 42287048]),\n  ('regression rate-break 2', (510076, 1928999, 'mfj'), [133300, 10084528, 8155529]),\n  ('partial repair guard 1', (365900, 7499416, 'mfj'), [133300, 6047600, 0]),\n  ('control: joint high', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500]),\n  ('control: rate break', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),\n  ('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),\n  ('control: partial phase-out', (700000, 0, 'single'), [63038, 17369736, 17369736])]]\nfor label, args, expected in cases[N - 1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"f6130f3ae640d4b4c8b378f5145bfd508c4c991be3838ebbe7df7ad74f58eeaf","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(amti, regular_cents, status):\n    ex, thr = {'single': (85700, 609350), 'mfj': (133300, 1218700)}[status]\n    if amti > thr: ex = max(0, ex - (amti - thr) // 4)\n    base = max(0, amti - ex)\n    tmt = base * (28 if base > 232600 else 26)\n    return [ex, tmt, max(0, tmt - regular_cents)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('regression rate-break 1', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),\n  ('regression rate-break 2', (700000, 0, 'single'), [63038, 17369736, 17369736]),\n  ('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),\n  ('control: no exemption left', (1000000, 99999999, 'single'), [0, 27534800, 0]),\n  ('control: below exemption', (100000, 0, 'mfj'), [133300, 0, 0]),\n  ('control: odd excess', (609353, 5000000, 'single'), [85700, 14197084, 9197084])],\n [('regression rate-break 1', (1000000, 99999999, 'single'), [0, 27534800, 0]),\n  ('regression rate-break 2', (609353, 5000000, 'single'), [85700, 14197084, 9197084]),\n  ('partial repair guard 2', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500]),\n  ('control: below exemption', (100000, 0, 'mfj'), [133300, 0, 0]),\n  ('control: rate break', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),\n  ('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),\n  ('control: partial phase-out', (700000, 0, 'single'), [63038, 17369736, 17369736])],\n [('regression rate-break 1', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500]),\n  ('regression rate-break 2', (365900, 10000000, 'single'), [85700, 7380400, 0]),\n  ('partial repair guard 2', (832985, 0, 'single'), [29792, 22024204, 22024204]),\n  ('control: rate break', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),\n  ('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),\n  ('control: partial phase-out', (700000, 0, 'single'), [63038, 17369736, 17369736]),\n  ('control: no exemption left', (1000000, 99999999, 'single'), [0, 27534800, 0])],\n [('regression rate-break 1', (832985, 0, 'single'), [29792, 22024204, 22024204]),\n  ('regression rate-break 2', (1122405, 10000000, 'mfj'), [133300, 27229740, 17229740]),\n  ('partial repair guard 1', (365900, 35622995, 'mfj'), [133300, 6047600, 0]),\n  ('control: no exemption left', (1000000, 99999999, 'single'), [0, 27534800, 0]),\n  ('control: below exemption', (100000, 0, 'mfj'), [133300, 0, 0]),\n  ('control: odd excess', (609353, 5000000, 'single'), [85700, 14197084, 9197084]),\n  ('control: joint high', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500])],\n [('regression rate-break 1', (1526866, 0, 'single'), [0, 42287048, 42287048]),\n  ('regression rate-break 2', (510076, 1928999, 'mfj'), [133300, 10084528, 8155529]),\n  ('partial repair guard 1', (365900, 7499416, 'mfj'), [133300, 6047600, 0]),\n  ('control: joint high', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500]),\n  ('control: rate break', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),\n  ('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),\n  ('control: partial phase-out', (700000, 0, 'single'), [63038, 17369736, 17369736])]]\nfor label, args, expected in cases[N - 1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"fixed":{"sha256":"62d46d8fce32d343effe01351567b34e9253c77d36e1477e5012aeb078d7f6b8","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(amti, regular_cents, status):\n    ex, thr = {'single': (85700, 609350), 'mfj': (133300, 1218700)}[status]\n    if amti > thr: ex = max(0, ex - (amti - thr) // 4)\n    base = max(0, amti - ex)\n    tmt = min(base, 232600) * 26 + max(0, base - 232600) * 28\n    return [ex, tmt, max(0, tmt - regular_cents)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('regression rate-break 1', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),\n  ('regression rate-break 2', (700000, 0, 'single'), [63038, 17369736, 17369736]),\n  ('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),\n  ('control: no exemption left', (1000000, 99999999, 'single'), [0, 27534800, 0]),\n  ('control: below exemption', (100000, 0, 'mfj'), [133300, 0, 0]),\n  ('control: odd excess', (609353, 5000000, 'single'), [85700, 14197084, 9197084])],\n [('regression rate-break 1', (1000000, 99999999, 'single'), [0, 27534800, 0]),\n  ('regression rate-break 2', (609353, 5000000, 'single'), [85700, 14197084, 9197084]),\n  ('partial repair guard 2', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500]),\n  ('control: below exemption', (100000, 0, 'mfj'), [133300, 0, 0]),\n  ('control: rate break', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),\n  ('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),\n  ('control: partial phase-out', (700000, 0, 'single'), [63038, 17369736, 17369736])],\n [('regression rate-break 1', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500]),\n  ('regression rate-break 2', (365900, 10000000, 'single'), [85700, 7380400, 0]),\n  ('partial repair guard 2', (832985, 0, 'single'), [29792, 22024204, 22024204]),\n  ('control: rate break', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),\n  ('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),\n  ('control: partial phase-out', (700000, 0, 'single'), [63038, 17369736, 17369736]),\n  ('control: no exemption left', (1000000, 99999999, 'single'), [0, 27534800, 0])],\n [('regression rate-break 1', (832985, 0, 'single'), [29792, 22024204, 22024204]),\n  ('regression rate-break 2', (1122405, 10000000, 'mfj'), [133300, 27229740, 17229740]),\n  ('partial repair guard 1', (365900, 35622995, 'mfj'), [133300, 6047600, 0]),\n  ('control: no exemption left', (1000000, 99999999, 'single'), [0, 27534800, 0]),\n  ('control: below exemption', (100000, 0, 'mfj'), [133300, 0, 0]),\n  ('control: odd excess', (609353, 5000000, 'single'), [85700, 14197084, 9197084]),\n  ('control: joint high', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500])],\n [('regression rate-break 1', (1526866, 0, 'single'), [0, 42287048, 42287048]),\n  ('regression rate-break 2', (510076, 1928999, 'mfj'), [133300, 10084528, 8155529]),\n  ('partial repair guard 1', (365900, 7499416, 'mfj'), [133300, 6047600, 0]),\n  ('control: joint high', (1300000, 30000000, 'mfj'), [112975, 32771500, 2771500]),\n  ('control: rate break', (400000, 0, 'mfj'), [133300, 7002400, 7002400]),\n  ('control: moderate single', (200000, 2500000, 'single'), [85700, 2971800, 471800]),\n  ('control: partial phase-out', (700000, 0, 'single'), [63038, 17369736, 17369736])]]\nfor label, args, expected in cases[N - 1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"A deterministic, bounded teaching model with a stipulated toy contract; it makes no claim of conformance to any real regulation, standard, or institution's rules. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-tax_bracket_computation-alternative-minimum-tax-rate-break","generated_at":"2026-09-29T14:47:05.596838+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Tax computations hinge on which slice, threshold, ordering and rounding rule applies at each step; a misplaced boundary silently misstates liabilities.","repair":"Tax the base up to 232600 at 26% and only the excess at 28%.","root_cause":"The base is taxed at a single rate chosen by the base size.","sha256":"5b2956465b07b24ae33705c7758ec9a00e1359ea42d4bd73f68cf8bebbe36e79","title":"The 28% AMT rate is applied to the whole base once it crosses the break · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":38.566,"exit_code":1,"observations":[{"actual":[133300,7269000,7269000],"check":"regression rate-break 1","expected":[133300,7002400,7002400],"passed":false},{"actual":[63038,17495812,17495812],"check":"regression rate-break 2","expected":[63038,17369736,17369736],"passed":false},{"actual":[85700,2971800,471800],"check":"control: moderate single","expected":[85700,2971800,471800],"passed":true},{"actual":[0,27534800,0],"check":"control: no exemption left","expected":[0,27534800,0],"passed":true},{"actual":[133300,0,0],"check":"control: below exemption","expected":[133300,0,0],"passed":true},{"actual":[85700,14368484,9368484],"check":"control: odd excess","expected":[85700,14197084,9197084],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression rate-break 1\", \"actual\": [133300, 7269000, 7269000], \"expected\": [133300, 7002400, 7002400], \"passed\": false}, {\"check\": \"regression rate-break 2\", \"actual\": [63038, 17495812, 17495812], \"expected\": [63038, 17369736, 17369736], \"passed\": false}, {\"check\": \"control: moderate single\", \"actual\": [85700, 2971800, 471800], \"expected\": [85700, 2971800, 471800], \"passed\": true}, {\"check\": \"control: no exemption left\", \"actual\": [0, 27534800, 0], \"expected\": [0, 27534800, 0], \"passed\": true}, {\"check\": \"control: below exemption\", \"actual\": [133300, 0, 0], \"expected\": [133300, 0, 0], \"passed\": true}, {\"check\": \"control: odd excess\", \"actual\": [85700, 14368484, 9368484], \"expected\": [85700, 14197084, 9197084], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.967,"exit_code":1,"observations":[{"actual":[133300,7467600,7467600],"check":"regression rate-break 1","expected":[133300,7002400,7002400],"passed":false},{"actual":[63038,17834936,17834936],"check":"regression rate-break 2","expected":[63038,17369736,17369736],"passed":false},{"actual":[85700,2971800,471800],"check":"control: moderate single","expected":[85700,2971800,471800],"passed":true},{"actual":[0,28000000,0],"check":"control: no exemption left","expected":[0,27534800,0],"passed":false},{"actual":[133300,0,0],"check":"control: below exemption","expected":[133300,0,0],"passed":true},{"actual":[85700,14662284,9662284],"check":"control: odd excess","expected":[85700,14197084,9197084],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression rate-break 1\", \"actual\": [133300, 7467600, 7467600], \"expected\": [133300, 7002400, 7002400], \"passed\": false}, {\"check\": \"regression rate-break 2\", \"actual\": [63038, 17834936, 17834936], \"expected\": [63038, 17369736, 17369736], \"passed\": false}, {\"check\": \"control: moderate single\", \"actual\": [85700, 2971800, 471800], \"expected\": [85700, 2971800, 471800], \"passed\": true}, {\"check\": \"control: no exemption left\", \"actual\": [0, 28000000, 0], \"expected\": [0, 27534800, 0], \"passed\": false}, {\"check\": \"control: below exemption\", \"actual\": [133300, 0, 0], \"expected\": [133300, 0, 0], \"passed\": true}, {\"check\": \"control: odd excess\", \"actual\": [85700, 14662284, 9662284], \"expected\": [85700, 14197084, 9197084], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":40.738,"exit_code":0,"observations":[{"actual":[133300,7002400,7002400],"check":"regression rate-break 1","expected":[133300,7002400,7002400],"passed":true},{"actual":[63038,17369736,17369736],"check":"regression rate-break 2","expected":[63038,17369736,17369736],"passed":true},{"actual":[85700,2971800,471800],"check":"control: moderate single","expected":[85700,2971800,471800],"passed":true},{"actual":[0,27534800,0],"check":"control: no exemption left","expected":[0,27534800,0],"passed":true},{"actual":[133300,0,0],"check":"control: below exemption","expected":[133300,0,0],"passed":true},{"actual":[85700,14197084,9197084],"check":"control: odd excess","expected":[85700,14197084,9197084],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression rate-break 1\", \"actual\": [133300, 7002400, 7002400], \"expected\": [133300, 7002400, 7002400], \"passed\": true}, {\"check\": \"regression rate-break 2\", \"actual\": [63038, 17369736, 17369736], \"expected\": [63038, 17369736, 17369736], \"passed\": true}, {\"check\": \"control: moderate single\", \"actual\": [85700, 2971800, 471800], \"expected\": [85700, 2971800, 471800], \"passed\": true}, {\"check\": \"control: no exemption left\", \"actual\": [0, 27534800, 0], \"expected\": [0, 27534800, 0], \"passed\": true}, {\"check\": \"control: below exemption\", \"actual\": [133300, 0, 0], \"expected\": [133300, 0, 0], \"passed\": true}, {\"check\": \"control: odd excess\", \"actual\": [85700, 14197084, 9197084], \"expected\": [85700, 14197084, 9197084], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}