{"abstract":"Someone with taxable income exactly 40000 is told their marginal rate is 22%.","category":"Tax bracket computation","checks":6,"contract":"solve(gross, deduction, brackets): taxable = max(0, gross - deduction); tax uses the progressive slices. The marginal rate is the rate of the bracket containing taxable income with (lower, upper] semantics (income exactly at a threshold is in the lower bracket), and is '0' when gross < deduction (unused deduction absorbs the next dollar; at gross == deduction the next dollar is taxed at the first rate). The effective rate is tax / gross in basis points rounded half-up (0 when gross <= 0). Return [marginal_rate_string, effective_bps].","contract_signature":"gross, deduction, brackets","evaluation_group":"w2-tax_bracket_computation-marginal-and-effective-rate","failed_approach":"Special-casing zero income does not repair membership at other thresholds.","family":"w2-tax_bracket_computation-marginal-and-effective-rate-threshold-membership","id":"FA-62491","implementations":{"attempt":{"sha256":"c47f800597d9e92bf4b6d47cce98f0b7070b34cba4d4fa45e664da53711daceb","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(gross, deduction, brackets):\n    def prog(x, br):\n        tax, lower = Fraction(0), 0\n        for upper, rate in br:\n            top = x if upper is None else min(x, upper)\n            if top > lower: tax += (top - lower) * Fraction(rate) / 100\n            if upper is None or x <= upper: break\n            lower = upper\n        return tax\n    def cents(v):\n        v = v * 100\n        return int(v + Fraction(1, 2)) if v >= 0 else -int(-v + Fraction(1, 2))\n    \n    taxable = max(0, gross - deduction)\n    tax = prog(taxable, brackets)\n    if gross < deduction:\n        marginal = '0'\n    else:\n        marginal = next(rate for upper, rate in brackets if upper is None or taxable < upper or taxable == 0)\n    eff = cents(tax * 100 / gross) if gross > 0 else 0\n    return [marginal, eff]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('regression threshold-membership 1', (54600, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['12', 842]),\n  ('regression threshold-membership 2', (10000, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 1000]),\n  ('control: top bracket', (50000, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['22', 1360]),\n  ('control: deduction not exhausted', (10000, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['0', 0]),\n  ('control: deduction exactly used', (14600, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 0]),\n  ('control: five brackets',\n   (123456, 14600, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]), ['24', 1582])],\n [('regression threshold-membership 1', (13000, 3000, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 769]),\n  ('regression threshold-membership 2', (40000, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['12', 1150]),\n  ('control: deduction not exhausted', (10000, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['0', 0]),\n  ('control: deduction exactly used', (14600, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 0]),\n  ('control: five brackets',\n   (123456, 14600, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]), ['24', 1582]),\n  ('control: zero gross', (0, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 0])],\n [('regression threshold-membership 1', (54600, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['12', 842]),\n  ('regression threshold-membership 2', (10000, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 1000]),\n  ('control: zero gross', (0, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 0]),\n  ('control: one above threshold', (10001, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['12', 1000]),\n  ('control: top bracket', (50000, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['22', 1360]),\n  ('control: deduction not exhausted', (10000, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['0', 0])],\n [('regression threshold-membership 1', (13000, 3000, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 769]),\n  ('regression threshold-membership 2', (40000, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['12', 1150]),\n  ('control: top bracket', (50000, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['22', 1360]),\n  ('control: exact first threshold', (10000, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 1000]),\n  ('control: deduction not exhausted', (10000, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['0', 0]),\n  ('control: deduction exactly used', (14600, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 0])],\n [('regression threshold-membership 1', (54600, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['12', 842]),\n  ('regression threshold-membership 2', (10000, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 1000]),\n  ('control: deduction exactly used', (14600, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 0]),\n  ('control: five brackets',\n   (123456, 14600, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]), ['24', 1582]),\n  ('control: zero gross', (0, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 0]),\n  ('control: one above threshold', (10001, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['12', 1000])]]\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":"7de3e737aea6d7a6c4a03afbd78de910a64fb6214d760a264d11c7c1fbfc5fcc","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(gross, deduction, brackets):\n    def prog(x, br):\n        tax, lower = Fraction(0), 0\n        for upper, rate in br:\n            top = x if upper is None else min(x, upper)\n            if top > lower: tax += (top - lower) * Fraction(rate) / 100\n            if upper is None or x <= upper: break\n            lower = upper\n        return tax\n    def cents(v):\n        v = v * 100\n        return int(v + Fraction(1, 2)) if v >= 0 else -int(-v + Fraction(1, 2))\n    \n    taxable = max(0, gross - deduction)\n    tax = prog(taxable, brackets)\n    if gross < deduction:\n        marginal = '0'\n    else:\n        marginal = next(rate for upper, rate in brackets if upper is None or taxable < upper)\n    eff = cents(tax * 100 / gross) if gross > 0 else 0\n    return [marginal, eff]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[('regression threshold-membership 1', (54600, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['12', 842]),\n  ('regression threshold-membership 2', (10000, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 1000]),\n  ('control: top bracket', (50000, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['22', 1360]),\n  ('control: deduction not exhausted', (10000, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['0', 0]),\n  ('control: deduction exactly used', (14600, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 0]),\n  ('control: five brackets',\n   (123456, 14600, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]), ['24', 1582])],\n [('regression threshold-membership 1', (13000, 3000, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 769]),\n  ('regression threshold-membership 2', (40000, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['12', 1150]),\n  ('control: deduction not exhausted', (10000, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['0', 0]),\n  ('control: deduction exactly used', (14600, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 0]),\n  ('control: five brackets',\n   (123456, 14600, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]), ['24', 1582]),\n  ('control: zero gross', (0, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 0])],\n [('regression threshold-membership 1', (54600, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['12', 842]),\n  ('regression threshold-membership 2', (10000, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 1000]),\n  ('control: zero gross', (0, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 0]),\n  ('control: one above threshold', (10001, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['12', 1000]),\n  ('control: top bracket', (50000, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['22', 1360]),\n  ('control: deduction not exhausted', (10000, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['0', 0])],\n [('regression threshold-membership 1', (13000, 3000, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 769]),\n  ('regression threshold-membership 2', (40000, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['12', 1150]),\n  ('control: top bracket', (50000, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['22', 1360]),\n  ('control: exact first threshold', (10000, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 1000]),\n  ('control: deduction not exhausted', (10000, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['0', 0]),\n  ('control: deduction exactly used', (14600, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 0])],\n [('regression threshold-membership 1', (54600, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['12', 842]),\n  ('regression threshold-membership 2', (10000, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 1000]),\n  ('control: deduction exactly used', (14600, 14600, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 0]),\n  ('control: five brackets',\n   (123456, 14600, [[11000, '10'], [44725, '12'], [95375, '22'], [182100, '24'], [None, '32.5']]), ['24', 1582]),\n  ('control: zero gross', (0, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['10', 0]),\n  ('control: one above threshold', (10001, 0, [[10000, '10'], [40000, '12'], [None, '22']]), ['12', 1000])]]\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-marginal-and-effective-rate-threshold-membership","generated_at":"2026-09-29T14:47:05.155689+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.","root_cause":"The containing bracket uses taxable < upper.","sha256":"80b302c4f8e9831f944aad9cce9274b4d3f6701cdb9334a838c698c6e7a3cf57","title":"Income exactly at a threshold is assigned to the higher bracket · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":42.602,"exit_code":1,"observations":[{"actual":["22",842],"check":"regression threshold-membership 1","expected":["12",842],"passed":false},{"actual":["12",1000],"check":"regression threshold-membership 2","expected":["10",1000],"passed":false},{"actual":["22",1360],"check":"control: top bracket","expected":["22",1360],"passed":true},{"actual":["0",0],"check":"control: deduction not exhausted","expected":["0",0],"passed":true},{"actual":["10",0],"check":"control: deduction exactly used","expected":["10",0],"passed":true},{"actual":["24",1582],"check":"control: five brackets","expected":["24",1582],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression threshold-membership 1\", \"actual\": [\"22\", 842], \"expected\": [\"12\", 842], \"passed\": false}, {\"check\": \"regression threshold-membership 2\", \"actual\": [\"12\", 1000], \"expected\": [\"10\", 1000], \"passed\": false}, {\"check\": \"control: top bracket\", \"actual\": [\"22\", 1360], \"expected\": [\"22\", 1360], \"passed\": true}, {\"check\": \"control: deduction not exhausted\", \"actual\": [\"0\", 0], \"expected\": [\"0\", 0], \"passed\": true}, {\"check\": \"control: deduction exactly used\", \"actual\": [\"10\", 0], \"expected\": [\"10\", 0], \"passed\": true}, {\"check\": \"control: five brackets\", \"actual\": [\"24\", 1582], \"expected\": [\"24\", 1582], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.085,"exit_code":1,"observations":[{"actual":["22",842],"check":"regression threshold-membership 1","expected":["12",842],"passed":false},{"actual":["12",1000],"check":"regression threshold-membership 2","expected":["10",1000],"passed":false},{"actual":["22",1360],"check":"control: top bracket","expected":["22",1360],"passed":true},{"actual":["0",0],"check":"control: deduction not exhausted","expected":["0",0],"passed":true},{"actual":["10",0],"check":"control: deduction exactly used","expected":["10",0],"passed":true},{"actual":["24",1582],"check":"control: five brackets","expected":["24",1582],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression threshold-membership 1\", \"actual\": [\"22\", 842], \"expected\": [\"12\", 842], \"passed\": false}, {\"check\": \"regression threshold-membership 2\", \"actual\": [\"12\", 1000], \"expected\": [\"10\", 1000], \"passed\": false}, {\"check\": \"control: top bracket\", \"actual\": [\"22\", 1360], \"expected\": [\"22\", 1360], \"passed\": true}, {\"check\": \"control: deduction not exhausted\", \"actual\": [\"0\", 0], \"expected\": [\"0\", 0], \"passed\": true}, {\"check\": \"control: deduction exactly used\", \"actual\": [\"10\", 0], \"expected\": [\"10\", 0], \"passed\": true}, {\"check\": \"control: five brackets\", \"actual\": [\"24\", 1582], \"expected\": [\"24\", 1582], \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}