{"abstract":"High earners pay the same tax as someone exactly at the final threshold.","category":"Tax bracket computation","checks":6,"contract":"solve(income, brackets): brackets is [[upper, rate_percent], ...] with strictly increasing positive uppers and a final open bracket [None, rate]; otherwise return 'ERR:brackets'. Each rate applies only to the slice of income in (previous upper, upper]. Negative income is taxed as zero. The tax is summed exactly and rounded half-up to cents once, returned as integer cents.","evaluation_group":"w2-tax_bracket_computation-progressive-marginal-slices","failed_approach":"Taxing the excess at the second-to-last rate still ignores the top rate.","family":"w2-tax_bracket_computation-progressive-marginal-slices-open-top-bracket","id":"FA-62361","implementations":{"attempt":{"sha256":"91d9dbd0e2dd7f117786bb9633fd492330acbff23d3a729aa7ab46580fc7d948","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(income, brackets):\n    if not brackets or brackets[-1][0] is not None: return 'ERR:brackets'\n    uppers = [u for u, _ in brackets[:-1]]\n    if any(b <= a for a, b in zip([0] + uppers, uppers)): return 'ERR:brackets'\n    x = max(0, income)\n    tax, lower = Fraction(0), 0\n    for upper, rate in brackets[:-1]:\n        top = x if upper is None else min(x, upper)\n        if top > lower:\n            tax += (top - lower) * Fraction(rate) / 100\n        if upper is None or x <= upper: break\n        lower = upper\n    if len(brackets) > 1 and x > brackets[-2][0]: tax += (x - brackets[-2][0]) * Fraction(brackets[-2][1]) / 100\n    return int(tax * 100 + Fraction(1, 2))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('regression open-top-bracket 1',\n   (250001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]), 5917183),\n  ('regression open-top-bracket 2', (50000, [[10000, '10'], [40000, '12'], [None, '22']]), 680000),\n  ('control: at first threshold', (10000, [[10000, '10'], [40000, '12'], [None, '22']]), 100000),\n  ('control: zero', (0, [[10000, '10'], [40000, '12'], [None, '22']]), 0),\n  ('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),\n  ('control: one over threshold', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022)],\n [('regression open-top-bracket 1', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022),\n  ('regression open-top-bracket 2', (777, [[None, '12.5']]), 9713),\n  ('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),\n  ('control: fractional rate', (12345, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),\n   126140),\n  ('control: non increasing', (10000, [[10000, '10'], [5000, '20'], [None, '30']]), 'ERR:brackets'),\n  ('control: closed top', (10, [[10000, '10'], [20000, '20']]), 'ERR:brackets')],\n [('regression open-top-bracket 1',\n   (232540, [[34000, '22'], [101000, '15'], [147000, '10'], [184000, '10'], [None, '30']]), 4039200),\n  ('regression open-top-bracket 2', (40000, [[None, '45']]), 1800000),\n  ('control: non increasing', (10000, [[10000, '10'], [5000, '20'], [None, '30']]), 'ERR:brackets'),\n  ('control: closed top', (10, [[10000, '10'], [20000, '20']]), 'ERR:brackets'),\n  ('control: high earner', (250001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),\n   5917183),\n  ('control: single bracket', (777, [[None, '12.5']]), 9713)],\n [('regression open-top-bracket 1', (139460, [[None, '40.5']]), 5648130),\n  ('regression open-top-bracket 2',\n   (236107, [[31000, '10'], [159000, '10'], [172000, '24'], [193000, '22'], [None, '45']]), 4303815),\n  ('control: single bracket', (777, [[None, '12.5']]), 9713),\n  ('control: three brackets', (50000, [[10000, '10'], [40000, '12'], [None, '22']]), 680000),\n  ('control: at first threshold', (10000, [[10000, '10'], [40000, '12'], [None, '22']]), 100000),\n  ('control: zero', (0, [[10000, '10'], [40000, '12'], [None, '22']]), 0)],\n [('regression open-top-bracket 1',\n   (221539, [[9000, '24'], [72000, '5'], [91000, '33.3'], [101000, '5'], [None, '37']]), 5673643),\n  ('regression open-top-bracket 2', (172773, [[None, '30']]), 5183190),\n  ('control: zero', (0, [[10000, '10'], [40000, '12'], [None, '22']]), 0),\n  ('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),\n  ('control: one over threshold', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022),\n  ('control: fractional rate', (12345, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),\n   126140)]]\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":"3390111d10f109f93b7318c6bb0cc0952fee7a433bfc340984b3c322b7a5f781","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(income, brackets):\n    if not brackets or brackets[-1][0] is not None: return 'ERR:brackets'\n    uppers = [u for u, _ in brackets[:-1]]\n    if any(b <= a for a, b in zip([0] + uppers, uppers)): return 'ERR:brackets'\n    x = max(0, income)\n    tax, lower = Fraction(0), 0\n    for upper, rate in brackets[:-1]:\n        top = x if upper is None else min(x, upper)\n        if top > lower:\n            tax += (top - lower) * Fraction(rate) / 100\n        if upper is None or x <= upper: break\n        lower = upper\n    return int(tax * 100 + Fraction(1, 2))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('regression open-top-bracket 1',\n   (250001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]), 5917183),\n  ('regression open-top-bracket 2', (50000, [[10000, '10'], [40000, '12'], [None, '22']]), 680000),\n  ('control: at first threshold', (10000, [[10000, '10'], [40000, '12'], [None, '22']]), 100000),\n  ('control: zero', (0, [[10000, '10'], [40000, '12'], [None, '22']]), 0),\n  ('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),\n  ('control: one over threshold', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022)],\n [('regression open-top-bracket 1', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022),\n  ('regression open-top-bracket 2', (777, [[None, '12.5']]), 9713),\n  ('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),\n  ('control: fractional rate', (12345, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),\n   126140),\n  ('control: non increasing', (10000, [[10000, '10'], [5000, '20'], [None, '30']]), 'ERR:brackets'),\n  ('control: closed top', (10, [[10000, '10'], [20000, '20']]), 'ERR:brackets')],\n [('regression open-top-bracket 1',\n   (232540, [[34000, '22'], [101000, '15'], [147000, '10'], [184000, '10'], [None, '30']]), 4039200),\n  ('regression open-top-bracket 2', (40000, [[None, '45']]), 1800000),\n  ('control: non increasing', (10000, [[10000, '10'], [5000, '20'], [None, '30']]), 'ERR:brackets'),\n  ('control: closed top', (10, [[10000, '10'], [20000, '20']]), 'ERR:brackets'),\n  ('control: high earner', (250001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),\n   5917183),\n  ('control: single bracket', (777, [[None, '12.5']]), 9713)],\n [('regression open-top-bracket 1', (139460, [[None, '40.5']]), 5648130),\n  ('regression open-top-bracket 2',\n   (236107, [[31000, '10'], [159000, '10'], [172000, '24'], [193000, '22'], [None, '45']]), 4303815),\n  ('control: single bracket', (777, [[None, '12.5']]), 9713),\n  ('control: three brackets', (50000, [[10000, '10'], [40000, '12'], [None, '22']]), 680000),\n  ('control: at first threshold', (10000, [[10000, '10'], [40000, '12'], [None, '22']]), 100000),\n  ('control: zero', (0, [[10000, '10'], [40000, '12'], [None, '22']]), 0)],\n [('regression open-top-bracket 1',\n   (221539, [[9000, '24'], [72000, '5'], [91000, '33.3'], [101000, '5'], [None, '37']]), 5673643),\n  ('regression open-top-bracket 2', (172773, [[None, '30']]), 5183190),\n  ('control: zero', (0, [[10000, '10'], [40000, '12'], [None, '22']]), 0),\n  ('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),\n  ('control: one over threshold', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022),\n  ('control: fractional rate', (12345, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),\n   126140)]]\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":"61d141b524b830050dba721acfd893b7dc0147e15090a93ee5aec81242983f79","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(income, brackets):\n    if not brackets or brackets[-1][0] is not None: return 'ERR:brackets'\n    uppers = [u for u, _ in brackets[:-1]]\n    if any(b <= a for a, b in zip([0] + uppers, uppers)): return 'ERR:brackets'\n    x = max(0, income)\n    tax, lower = Fraction(0), 0\n    for upper, rate in brackets:\n        top = x if upper is None else min(x, upper)\n        if top > lower:\n            tax += (top - lower) * Fraction(rate) / 100\n        if upper is None or x <= upper: break\n        lower = upper\n    return int(tax * 100 + Fraction(1, 2))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('regression open-top-bracket 1',\n   (250001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]), 5917183),\n  ('regression open-top-bracket 2', (50000, [[10000, '10'], [40000, '12'], [None, '22']]), 680000),\n  ('control: at first threshold', (10000, [[10000, '10'], [40000, '12'], [None, '22']]), 100000),\n  ('control: zero', (0, [[10000, '10'], [40000, '12'], [None, '22']]), 0),\n  ('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),\n  ('control: one over threshold', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022)],\n [('regression open-top-bracket 1', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022),\n  ('regression open-top-bracket 2', (777, [[None, '12.5']]), 9713),\n  ('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),\n  ('control: fractional rate', (12345, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),\n   126140),\n  ('control: non increasing', (10000, [[10000, '10'], [5000, '20'], [None, '30']]), 'ERR:brackets'),\n  ('control: closed top', (10, [[10000, '10'], [20000, '20']]), 'ERR:brackets')],\n [('regression open-top-bracket 1',\n   (232540, [[34000, '22'], [101000, '15'], [147000, '10'], [184000, '10'], [None, '30']]), 4039200),\n  ('regression open-top-bracket 2', (40000, [[None, '45']]), 1800000),\n  ('control: non increasing', (10000, [[10000, '10'], [5000, '20'], [None, '30']]), 'ERR:brackets'),\n  ('control: closed top', (10, [[10000, '10'], [20000, '20']]), 'ERR:brackets'),\n  ('control: high earner', (250001, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),\n   5917183),\n  ('control: single bracket', (777, [[None, '12.5']]), 9713)],\n [('regression open-top-bracket 1', (139460, [[None, '40.5']]), 5648130),\n  ('regression open-top-bracket 2',\n   (236107, [[31000, '10'], [159000, '10'], [172000, '24'], [193000, '22'], [None, '45']]), 4303815),\n  ('control: single bracket', (777, [[None, '12.5']]), 9713),\n  ('control: three brackets', (50000, [[10000, '10'], [40000, '12'], [None, '22']]), 680000),\n  ('control: at first threshold', (10000, [[10000, '10'], [40000, '12'], [None, '22']]), 100000),\n  ('control: zero', (0, [[10000, '10'], [40000, '12'], [None, '22']]), 0)],\n [('regression open-top-bracket 1',\n   (221539, [[9000, '24'], [72000, '5'], [91000, '33.3'], [101000, '5'], [None, '37']]), 5673643),\n  ('regression open-top-bracket 2', (172773, [[None, '30']]), 5183190),\n  ('control: zero', (0, [[10000, '10'], [40000, '12'], [None, '22']]), 0),\n  ('control: negative', (-5, [[10000, '10'], [40000, '12'], [None, '22']]), 0),\n  ('control: one over threshold', (40001, [[10000, '10'], [40000, '12'], [None, '22']]), 460022),\n  ('control: fractional rate', (12345, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]),\n   126140)]]\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-progressive-marginal-slices-open-top-bracket","generated_at":"2026-09-29T14:47:03.985243+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":"Apply the final rate to all income above the last threshold.","root_cause":"The loop skips the open-ended final bracket.","sha256":"c47028d45dd4e648f7208b4e4e856c5d4bd9e3f9ce8edadb092c2af463f1c4eb","title":"Income above the last threshold escapes tax · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.419,"exit_code":1,"observations":[{"actual":5340024,"check":"regression open-top-bracket 1","expected":5917183,"passed":false},{"actual":580000,"check":"regression open-top-bracket 2","expected":680000,"passed":false},{"actual":100000,"check":"control: at first threshold","expected":100000,"passed":true},{"actual":0,"check":"control: zero","expected":0,"passed":true},{"actual":0,"check":"control: negative","expected":0,"passed":true},{"actual":460012,"check":"control: one over threshold","expected":460022,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression open-top-bracket 1\", \"actual\": 5340024, \"expected\": 5917183, \"passed\": false}, {\"check\": \"regression open-top-bracket 2\", \"actual\": 580000, \"expected\": 680000, \"passed\": false}, {\"check\": \"control: at first threshold\", \"actual\": 100000, \"expected\": 100000, \"passed\": true}, {\"check\": \"control: zero\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"control: negative\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"control: one over threshold\", \"actual\": 460012, \"expected\": 460022, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.879,"exit_code":1,"observations":[{"actual":3710400,"check":"regression open-top-bracket 1","expected":5917183,"passed":false},{"actual":460000,"check":"regression open-top-bracket 2","expected":680000,"passed":false},{"actual":100000,"check":"control: at first threshold","expected":100000,"passed":true},{"actual":0,"check":"control: zero","expected":0,"passed":true},{"actual":0,"check":"control: negative","expected":0,"passed":true},{"actual":460000,"check":"control: one over threshold","expected":460022,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression open-top-bracket 1\", \"actual\": 3710400, \"expected\": 5917183, \"passed\": false}, {\"check\": \"regression open-top-bracket 2\", \"actual\": 460000, \"expected\": 680000, \"passed\": false}, {\"check\": \"control: at first threshold\", \"actual\": 100000, \"expected\": 100000, \"passed\": true}, {\"check\": \"control: zero\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"control: negative\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"control: one over threshold\", \"actual\": 460000, \"expected\": 460022, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":40.035,"exit_code":0,"observations":[{"actual":5917183,"check":"regression open-top-bracket 1","expected":5917183,"passed":true},{"actual":680000,"check":"regression open-top-bracket 2","expected":680000,"passed":true},{"actual":100000,"check":"control: at first threshold","expected":100000,"passed":true},{"actual":0,"check":"control: zero","expected":0,"passed":true},{"actual":0,"check":"control: negative","expected":0,"passed":true},{"actual":460022,"check":"control: one over threshold","expected":460022,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression open-top-bracket 1\", \"actual\": 5917183, \"expected\": 5917183, \"passed\": true}, {\"check\": \"regression open-top-bracket 2\", \"actual\": 680000, \"expected\": 680000, \"passed\": true}, {\"check\": \"control: at first threshold\", \"actual\": 100000, \"expected\": 100000, \"passed\": true}, {\"check\": \"control: zero\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"control: negative\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"control: one over threshold\", \"actual\": 460022, \"expected\": 460022, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}