{"abstract":"High earners are withheld far more than the bracket schedule implies.","category":"Payroll withholding rules","checks":8,"contract":"Input {ytd_wages, ytd_wh, wage, period_index k (1-based, includes this period), periods}. Annualized = (ytd_wages + wage)*periods/k exactly. Annual tax: 0% to 10,000.00, 12% to 40,000.00, 24% above. Tax to date = annual tax * k/periods. Withholding = max(0, tax_to_date - ytd_wh) rounded half-up at the end.","contract_signature":"x","evaluation_group":"w2-payroll-withholding-cumulative-wage-method","failed_approach":"The attempt uses the right slice but the middle bracket rate.","family":"w2-payroll-withholding-cumulative-wage-method-bracket-upper-tier","id":"FA-59191","implementations":{"attempt":{"sha256":"ae551262cfe946cf6bd785c8b354ad57a7ba60b1b02e52f39e07dab26d1b8e88","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    k = x['period_index']\n    total = x['ytd_wages'] + x['wage']\n    annual = Fraction(total * x['periods'], k)\n    def tax(a):\n        t = Fraction(0)\n        if a > 1000000:\n            t += (min(a, 4000000) - 1000000) * Fraction(12, 100)\n        if a > 4000000:\n            t += (a - 4000000) * Fraction(12, 100)\n        return t\n    due = tax(annual) * k / x['periods']\n    wh = max(0, due - x['ytd_wh'])\n    return math.floor(wh + Fraction(1, 2))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression', {'ytd_wages': 7060061, 'ytd_wh': 424656, 'wage': 491569, 'period_index': 24, 'periods': 52}, 1110812), ('regression', {'ytd_wages': 9590400, 'ytd_wh': 237513, 'wage': 534789, 'period_index': 22, 'periods': 26}, 1684840), ('partial-repair probe', {'ytd_wages': 8775450, 'ytd_wh': 1616919, 'wage': 334681, 'period_index': 24, 'periods': 26}, 15666), ('partial-repair probe', {'ytd_wages': 6145936, 'ytd_wh': 219937, 'wage': 315568, 'period_index': 15, 'periods': 52}, 1157747), ('normal control', {'ytd_wages': 2182615, 'ytd_wh': 379871, 'wage': 414670, 'period_index': 20, 'periods': 26}, 0), ('normal control', {'ytd_wages': 3504142, 'ytd_wh': 423680, 'wage': 219362, 'period_index': 26, 'periods': 26}, 0), ('normal control', {'ytd_wages': 953768, 'ytd_wh': 32122, 'wage': 67782, 'period_index': 21, 'periods': 26}, 0), ('normal control', {'ytd_wages': 185427, 'ytd_wh': 36091, 'wage': 108159, 'period_index': 2, 'periods': 12}, 0)], [('regression', {'ytd_wages': 9590400, 'ytd_wh': 237513, 'wage': 534789, 'period_index': 22, 'periods': 26}, 1684840), ('regression', {'ytd_wages': 8775450, 'ytd_wh': 1616919, 'wage': 334681, 'period_index': 24, 'periods': 26}, 15666), ('partial-repair probe', {'ytd_wages': 6145936, 'ytd_wh': 219937, 'wage': 315568, 'period_index': 15, 'periods': 52}, 1157747), ('partial-repair probe', {'ytd_wages': 0, 'ytd_wh': 1, 'wage': 366567, 'period_index': 1, 'periods': 12}, 37975), ('normal control', {'ytd_wages': 2268722, 'ytd_wh': 255963, 'wage': 370037, 'period_index': 8, 'periods': 12}, 0), ('normal control', {'ytd_wages': 141603, 'ytd_wh': 11497, 'wage': 15563, 'period_index': 7, 'periods': 12}, 0), ('normal control', {'ytd_wages': 29165, 'ytd_wh': 3348, 'wage': 5167, 'period_index': 8, 'periods': 52}, 0), ('normal control', {'ytd_wages': 32735, 'ytd_wh': 3167, 'wage': 155253, 'period_index': 2, 'periods': 12}, 0)], [('regression', {'ytd_wages': 8775450, 'ytd_wh': 1616919, 'wage': 334681, 'period_index': 24, 'periods': 26}, 15666), ('regression', {'ytd_wages': 6145936, 'ytd_wh': 219937, 'wage': 315568, 'period_index': 15, 'periods': 52}, 1157747), ('partial-repair probe', {'ytd_wages': 0, 'ytd_wh': 1, 'wage': 366567, 'period_index': 1, 'periods': 12}, 37975), ('partial-repair probe', {'ytd_wages': 4585857, 'ytd_wh': 265867, 'wage': 360821, 'period_index': 12, 'periods': 26}, 644413), ('normal control', {'ytd_wages': 507467, 'ytd_wh': 39498, 'wage': 384392, 'period_index': 10, 'periods': 12}, 0), ('normal control', {'ytd_wages': 2675147, 'ytd_wh': 522064, 'wage': 171429, 'period_index': 26, 'periods': 26}, 0), ('normal control', {'ytd_wages': 3055036, 'ytd_wh': 132701, 'wage': 516493, 'period_index': 12, 'periods': 12}, 175882), ('normal control', {'ytd_wages': 36870, 'ytd_wh': 6321, 'wage': 487926, 'period_index': 2, 'periods': 12}, 36655)], [('regression', {'ytd_wages': 6145936, 'ytd_wh': 219937, 'wage': 315568, 'period_index': 15, 'periods': 52}, 1157747), ('regression', {'ytd_wages': 0, 'ytd_wh': 1, 'wage': 366567, 'period_index': 1, 'periods': 12}, 37975), ('partial-repair probe', {'ytd_wages': 2724662, 'ytd_wh': 86701, 'wage': 332622, 'period_index': 7, 'periods': 52}, 566278), ('partial-repair probe', {'ytd_wages': 1665992, 'ytd_wh': 58323, 'wage': 387492, 'period_index': 4, 'periods': 12}, 234513), ('normal control', {'ytd_wages': 1078164, 'ytd_wh': 161049, 'wage': 458540, 'period_index': 6, 'periods': 12}, 0), ('normal control', {'ytd_wages': 978329, 'ytd_wh': 122337, 'wage': 298469, 'period_index': 9, 'periods': 26}, 0), ('normal control', {'ytd_wages': 81196, 'ytd_wh': 9361, 'wage': 306786, 'period_index': 2, 'periods': 12}, 17197), ('normal control', {'ytd_wages': 78474, 'ytd_wh': 12616, 'wage': 2681, 'period_index': 35, 'periods': 52}, 0)], [('regression', {'ytd_wages': 0, 'ytd_wh': 1, 'wage': 366567, 'period_index': 1, 'periods': 12}, 37975), ('regression', {'ytd_wages': 4585857, 'ytd_wh': 265867, 'wage': 360821, 'period_index': 12, 'periods': 26}, 644413), ('partial-repair probe', {'ytd_wages': 17382079, 'ytd_wh': 703861, 'wage': 564605, 'period_index': 25, 'periods': 52}, 3314882), ('partial-repair probe', {'ytd_wages': 7572146, 'ytd_wh': 1352041, 'wage': 228907, 'period_index': 18, 'periods': 52}, 312519), ('normal control', {'ytd_wages': 1412754, 'ytd_wh': 40526, 'wage': 95617, 'period_index': 11, 'periods': 12}, 30479), ('normal control', {'ytd_wages': 867698, 'ytd_wh': 9315, 'wage': 86343, 'period_index': 8, 'periods': 12}, 25170), ('normal control', {'ytd_wages': 179570, 'ytd_wh': 6855, 'wage': 84088, 'period_index': 5, 'periods': 52}, 13245), ('normal control', {'ytd_wages': 780083, 'ytd_wh': 115357, 'wage': 60520, 'period_index': 12, 'periods': 26}, 0)]]\nfor i, (label, args, expected) in enumerate(fixtures[N-1]):\n    check(\"%s %d\" % (label, i), 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":"9ec32133817fe212151c396066303fd372dadcd3d989c2bf07c30c0bc672285a","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    k = x['period_index']\n    total = x['ytd_wages'] + x['wage']\n    annual = Fraction(total * x['periods'], k)\n    def tax(a):\n        t = Fraction(0)\n        if a > 1000000:\n            t += (min(a, 4000000) - 1000000) * Fraction(12, 100)\n        if a > 4000000:\n            t += (a - 1000000) * Fraction(24, 100)\n        return t\n    due = tax(annual) * k / x['periods']\n    wh = max(0, due - x['ytd_wh'])\n    return math.floor(wh + Fraction(1, 2))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression', {'ytd_wages': 7060061, 'ytd_wh': 424656, 'wage': 491569, 'period_index': 24, 'periods': 52}, 1110812), ('regression', {'ytd_wages': 9590400, 'ytd_wh': 237513, 'wage': 534789, 'period_index': 22, 'periods': 26}, 1684840), ('partial-repair probe', {'ytd_wages': 8775450, 'ytd_wh': 1616919, 'wage': 334681, 'period_index': 24, 'periods': 26}, 15666), ('partial-repair probe', {'ytd_wages': 6145936, 'ytd_wh': 219937, 'wage': 315568, 'period_index': 15, 'periods': 52}, 1157747), ('normal control', {'ytd_wages': 2182615, 'ytd_wh': 379871, 'wage': 414670, 'period_index': 20, 'periods': 26}, 0), ('normal control', {'ytd_wages': 3504142, 'ytd_wh': 423680, 'wage': 219362, 'period_index': 26, 'periods': 26}, 0), ('normal control', {'ytd_wages': 953768, 'ytd_wh': 32122, 'wage': 67782, 'period_index': 21, 'periods': 26}, 0), ('normal control', {'ytd_wages': 185427, 'ytd_wh': 36091, 'wage': 108159, 'period_index': 2, 'periods': 12}, 0)], [('regression', {'ytd_wages': 9590400, 'ytd_wh': 237513, 'wage': 534789, 'period_index': 22, 'periods': 26}, 1684840), ('regression', {'ytd_wages': 8775450, 'ytd_wh': 1616919, 'wage': 334681, 'period_index': 24, 'periods': 26}, 15666), ('partial-repair probe', {'ytd_wages': 6145936, 'ytd_wh': 219937, 'wage': 315568, 'period_index': 15, 'periods': 52}, 1157747), ('partial-repair probe', {'ytd_wages': 0, 'ytd_wh': 1, 'wage': 366567, 'period_index': 1, 'periods': 12}, 37975), ('normal control', {'ytd_wages': 2268722, 'ytd_wh': 255963, 'wage': 370037, 'period_index': 8, 'periods': 12}, 0), ('normal control', {'ytd_wages': 141603, 'ytd_wh': 11497, 'wage': 15563, 'period_index': 7, 'periods': 12}, 0), ('normal control', {'ytd_wages': 29165, 'ytd_wh': 3348, 'wage': 5167, 'period_index': 8, 'periods': 52}, 0), ('normal control', {'ytd_wages': 32735, 'ytd_wh': 3167, 'wage': 155253, 'period_index': 2, 'periods': 12}, 0)], [('regression', {'ytd_wages': 8775450, 'ytd_wh': 1616919, 'wage': 334681, 'period_index': 24, 'periods': 26}, 15666), ('regression', {'ytd_wages': 6145936, 'ytd_wh': 219937, 'wage': 315568, 'period_index': 15, 'periods': 52}, 1157747), ('partial-repair probe', {'ytd_wages': 0, 'ytd_wh': 1, 'wage': 366567, 'period_index': 1, 'periods': 12}, 37975), ('partial-repair probe', {'ytd_wages': 4585857, 'ytd_wh': 265867, 'wage': 360821, 'period_index': 12, 'periods': 26}, 644413), ('normal control', {'ytd_wages': 507467, 'ytd_wh': 39498, 'wage': 384392, 'period_index': 10, 'periods': 12}, 0), ('normal control', {'ytd_wages': 2675147, 'ytd_wh': 522064, 'wage': 171429, 'period_index': 26, 'periods': 26}, 0), ('normal control', {'ytd_wages': 3055036, 'ytd_wh': 132701, 'wage': 516493, 'period_index': 12, 'periods': 12}, 175882), ('normal control', {'ytd_wages': 36870, 'ytd_wh': 6321, 'wage': 487926, 'period_index': 2, 'periods': 12}, 36655)], [('regression', {'ytd_wages': 6145936, 'ytd_wh': 219937, 'wage': 315568, 'period_index': 15, 'periods': 52}, 1157747), ('regression', {'ytd_wages': 0, 'ytd_wh': 1, 'wage': 366567, 'period_index': 1, 'periods': 12}, 37975), ('partial-repair probe', {'ytd_wages': 2724662, 'ytd_wh': 86701, 'wage': 332622, 'period_index': 7, 'periods': 52}, 566278), ('partial-repair probe', {'ytd_wages': 1665992, 'ytd_wh': 58323, 'wage': 387492, 'period_index': 4, 'periods': 12}, 234513), ('normal control', {'ytd_wages': 1078164, 'ytd_wh': 161049, 'wage': 458540, 'period_index': 6, 'periods': 12}, 0), ('normal control', {'ytd_wages': 978329, 'ytd_wh': 122337, 'wage': 298469, 'period_index': 9, 'periods': 26}, 0), ('normal control', {'ytd_wages': 81196, 'ytd_wh': 9361, 'wage': 306786, 'period_index': 2, 'periods': 12}, 17197), ('normal control', {'ytd_wages': 78474, 'ytd_wh': 12616, 'wage': 2681, 'period_index': 35, 'periods': 52}, 0)], [('regression', {'ytd_wages': 0, 'ytd_wh': 1, 'wage': 366567, 'period_index': 1, 'periods': 12}, 37975), ('regression', {'ytd_wages': 4585857, 'ytd_wh': 265867, 'wage': 360821, 'period_index': 12, 'periods': 26}, 644413), ('partial-repair probe', {'ytd_wages': 17382079, 'ytd_wh': 703861, 'wage': 564605, 'period_index': 25, 'periods': 52}, 3314882), ('partial-repair probe', {'ytd_wages': 7572146, 'ytd_wh': 1352041, 'wage': 228907, 'period_index': 18, 'periods': 52}, 312519), ('normal control', {'ytd_wages': 1412754, 'ytd_wh': 40526, 'wage': 95617, 'period_index': 11, 'periods': 12}, 30479), ('normal control', {'ytd_wages': 867698, 'ytd_wh': 9315, 'wage': 86343, 'period_index': 8, 'periods': 12}, 25170), ('normal control', {'ytd_wages': 179570, 'ytd_wh': 6855, 'wage': 84088, 'period_index': 5, 'periods': 52}, 13245), ('normal control', {'ytd_wages': 780083, 'ytd_wh': 115357, 'wage': 60520, 'period_index': 12, 'periods': 26}, 0)]]\nfor i, (label, args, expected) in enumerate(fixtures[N-1]):\n    check(\"%s %d\" % (label, i), 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 teaching model of a stipulated payroll rule with toy thresholds and rates. It makes no claim of conformance to any tax authority, statute or jurisdiction and is not payroll software. 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-payroll-withholding-cumulative-wage-method-bracket-upper-tier","generated_at":"2026-09-29T14:46:33.871824+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"The cumulative method spreads irregular pay across elapsed periods and trues up against prior withholding.","root_cause":"The top bracket slice starts at the first threshold, double taxing the middle slice.","sha256":"80b4c45c31c34513f2f0508c5cd79eaf1be1a780f694d83a3cfa34bf488cd764","title":"Cumulative wages withholding method: bracket upper tier · 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":46.588,"exit_code":1,"observations":[{"actual":426155,"check":"regression 0","expected":1110812,"passed":false},{"actual":875971,"check":"regression 1","expected":1684840,"passed":false},{"actual":0,"check":"partial-repair probe 2","expected":15666,"passed":false},{"actual":520828,"check":"partial-repair probe 3","expected":1157747,"passed":false},{"actual":0,"check":"normal control 4","expected":0,"passed":true},{"actual":0,"check":"normal control 5","expected":0,"passed":true},{"actual":0,"check":"normal control 6","expected":0,"passed":true},{"actual":0,"check":"normal control 7","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 0\", \"actual\": 426155, \"expected\": 1110812, \"passed\": false}, {\"check\": \"regression 1\", \"actual\": 875971, \"expected\": 1684840, \"passed\": false}, {\"check\": \"partial-repair probe 2\", \"actual\": 0, \"expected\": 15666, \"passed\": false}, {\"check\": \"partial-repair probe 3\", \"actual\": 520828, \"expected\": 1157747, \"passed\": false}, {\"check\": \"normal control 4\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"normal control 5\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"normal control 6\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"normal control 7\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":46.017,"exit_code":1,"observations":[{"actual":1443120,"check":"regression 0","expected":1110812,"passed":false},{"actual":2294071,"check":"regression 1","expected":1684840,"passed":false},{"actual":680282,"check":"partial-repair probe 2","expected":15666,"passed":false},{"actual":1365439,"check":"partial-repair probe 3","expected":1157747,"passed":false},{"actual":0,"check":"normal control 4","expected":0,"passed":true},{"actual":0,"check":"normal control 5","expected":0,"passed":true},{"actual":0,"check":"normal control 6","expected":0,"passed":true},{"actual":0,"check":"normal control 7","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 0\", \"actual\": 1443120, \"expected\": 1110812, \"passed\": false}, {\"check\": \"regression 1\", \"actual\": 2294071, \"expected\": 1684840, \"passed\": false}, {\"check\": \"partial-repair probe 2\", \"actual\": 680282, \"expected\": 15666, \"passed\": false}, {\"check\": \"partial-repair probe 3\", \"actual\": 1365439, \"expected\": 1157747, \"passed\": false}, {\"check\": \"normal control 4\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"normal control 5\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"normal control 6\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"normal control 7\", \"actual\": 0, \"expected\": 0, \"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."}}