{"abstract":"Employees on the cumulative method are withheld as if on the ordinary per-period method.","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 includes year-to-date wages but treats their sum as the annual figure without annualizing.","family":"w2-payroll-withholding-cumulative-wage-method-annualization-base","id":"FA-59181","implementations":{"attempt":{"sha256":"24b976c9fb617c992b292736ea31387dba640aaff4acb09c828b7c0a3d3ceb0e","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'], x['periods'])\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(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': 2182615, 'ytd_wh': 379871, 'wage': 414670, 'period_index': 20, 'periods': 26}, 0), ('partial-repair probe', {'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), ('normal control', {'ytd_wages': 185427, 'ytd_wh': 36091, 'wage': 108159, 'period_index': 2, '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': 2675147, 'ytd_wh': 522064, 'wage': 171429, 'period_index': 26, 'periods': 26}, 0)], [('regression', {'ytd_wages': 9590400, 'ytd_wh': 237513, 'wage': 534789, 'period_index': 22, 'periods': 26}, 1684840), ('regression', {'ytd_wages': 3504142, 'ytd_wh': 423680, 'wage': 219362, 'period_index': 26, 'periods': 26}, 0), ('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': 78474, 'ytd_wh': 12616, 'wage': 2681, 'period_index': 35, 'periods': 52}, 0), ('normal control', {'ytd_wages': 780083, 'ytd_wh': 115357, 'wage': 60520, 'period_index': 12, 'periods': 26}, 0), ('normal control', {'ytd_wages': 30504, 'ytd_wh': 1425, 'wage': 14017, 'period_index': 11, 'periods': 12}, 0), ('normal control', {'ytd_wages': 255421, 'ytd_wh': 47741, 'wage': 37513, 'period_index': 11, 'periods': 12}, 0)], [('regression', {'ytd_wages': 8775450, 'ytd_wh': 1616919, 'wage': 334681, 'period_index': 24, 'periods': 26}, 15666), ('regression', {'ytd_wages': 7060061, 'ytd_wh': 424656, 'wage': 491569, 'period_index': 24, 'periods': 52}, 1110812), ('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': 4101816, 'ytd_wh': 781382, 'wage': 93819, 'period_index': 46, 'periods': 52}, 0), ('normal control', {'ytd_wages': 1734664, 'ytd_wh': 216863, 'wage': 75980, 'period_index': 15, 'periods': 26}, 0), ('normal control', {'ytd_wages': 2864664, 'ytd_wh': 419863, 'wage': 94961, 'period_index': 20, 'periods': 26}, 0), ('normal control', {'ytd_wages': 430759, 'ytd_wh': 55675, 'wage': 54560, 'period_index': 5, 'periods': 12}, 0)], [('regression', {'ytd_wages': 6145936, 'ytd_wh': 219937, 'wage': 315568, 'period_index': 15, 'periods': 52}, 1157747), ('regression', {'ytd_wages': 9590400, 'ytd_wh': 237513, 'wage': 534789, 'period_index': 22, 'periods': 26}, 1684840), ('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': 353147, 'ytd_wh': 9536, 'wage': 96030, 'period_index': 6, 'periods': 12}, 0), ('normal control', {'ytd_wages': 659564, 'ytd_wh': 7849, 'wage': 18236, 'period_index': 20, 'periods': 26}, 0), ('normal control', {'ytd_wages': 2446975, 'ytd_wh': 466368, 'wage': 202023, 'period_index': 12, 'periods': 12}, 0), ('normal control', {'ytd_wages': 152088, 'ytd_wh': 11592, 'wage': 17915, 'period_index': 8, 'periods': 26}, 0)], [('regression', {'ytd_wages': 4585857, 'ytd_wh': 265867, 'wage': 360821, 'period_index': 12, 'periods': 26}, 644413), ('regression', {'ytd_wages': 953768, 'ytd_wh': 32122, 'wage': 67782, 'period_index': 21, 'periods': 26}, 0), ('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': 2303411, 'ytd_wh': 406780, 'wage': 112030, 'period_index': 23, 'periods': 26}, 0), ('normal control', {'ytd_wages': 288287, 'ytd_wh': 41455, 'wage': 26146, 'period_index': 26, 'periods': 26}, 0), ('normal control', {'ytd_wages': 102743, 'ytd_wh': 20507, 'wage': 5626, 'period_index': 12, 'periods': 12}, 0), ('normal control', {'ytd_wages': 1160977, 'ytd_wh': 199709, 'wage': 91537, 'period_index': 11, '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":"15d58b90574151d6611b6583614581977923551c4f18d1c7fe7dbd913cbca943","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(x['wage'] * x['periods'], 1)\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(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': 2182615, 'ytd_wh': 379871, 'wage': 414670, 'period_index': 20, 'periods': 26}, 0), ('partial-repair probe', {'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), ('normal control', {'ytd_wages': 185427, 'ytd_wh': 36091, 'wage': 108159, 'period_index': 2, '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': 2675147, 'ytd_wh': 522064, 'wage': 171429, 'period_index': 26, 'periods': 26}, 0)], [('regression', {'ytd_wages': 9590400, 'ytd_wh': 237513, 'wage': 534789, 'period_index': 22, 'periods': 26}, 1684840), ('regression', {'ytd_wages': 3504142, 'ytd_wh': 423680, 'wage': 219362, 'period_index': 26, 'periods': 26}, 0), ('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': 78474, 'ytd_wh': 12616, 'wage': 2681, 'period_index': 35, 'periods': 52}, 0), ('normal control', {'ytd_wages': 780083, 'ytd_wh': 115357, 'wage': 60520, 'period_index': 12, 'periods': 26}, 0), ('normal control', {'ytd_wages': 30504, 'ytd_wh': 1425, 'wage': 14017, 'period_index': 11, 'periods': 12}, 0), ('normal control', {'ytd_wages': 255421, 'ytd_wh': 47741, 'wage': 37513, 'period_index': 11, 'periods': 12}, 0)], [('regression', {'ytd_wages': 8775450, 'ytd_wh': 1616919, 'wage': 334681, 'period_index': 24, 'periods': 26}, 15666), ('regression', {'ytd_wages': 7060061, 'ytd_wh': 424656, 'wage': 491569, 'period_index': 24, 'periods': 52}, 1110812), ('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': 4101816, 'ytd_wh': 781382, 'wage': 93819, 'period_index': 46, 'periods': 52}, 0), ('normal control', {'ytd_wages': 1734664, 'ytd_wh': 216863, 'wage': 75980, 'period_index': 15, 'periods': 26}, 0), ('normal control', {'ytd_wages': 2864664, 'ytd_wh': 419863, 'wage': 94961, 'period_index': 20, 'periods': 26}, 0), ('normal control', {'ytd_wages': 430759, 'ytd_wh': 55675, 'wage': 54560, 'period_index': 5, 'periods': 12}, 0)], [('regression', {'ytd_wages': 6145936, 'ytd_wh': 219937, 'wage': 315568, 'period_index': 15, 'periods': 52}, 1157747), ('regression', {'ytd_wages': 9590400, 'ytd_wh': 237513, 'wage': 534789, 'period_index': 22, 'periods': 26}, 1684840), ('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': 353147, 'ytd_wh': 9536, 'wage': 96030, 'period_index': 6, 'periods': 12}, 0), ('normal control', {'ytd_wages': 659564, 'ytd_wh': 7849, 'wage': 18236, 'period_index': 20, 'periods': 26}, 0), ('normal control', {'ytd_wages': 2446975, 'ytd_wh': 466368, 'wage': 202023, 'period_index': 12, 'periods': 12}, 0), ('normal control', {'ytd_wages': 152088, 'ytd_wh': 11592, 'wage': 17915, 'period_index': 8, 'periods': 26}, 0)], [('regression', {'ytd_wages': 4585857, 'ytd_wh': 265867, 'wage': 360821, 'period_index': 12, 'periods': 26}, 644413), ('regression', {'ytd_wages': 953768, 'ytd_wh': 32122, 'wage': 67782, 'period_index': 21, 'periods': 26}, 0), ('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': 2303411, 'ytd_wh': 406780, 'wage': 112030, 'period_index': 23, 'periods': 26}, 0), ('normal control', {'ytd_wages': 288287, 'ytd_wh': 41455, 'wage': 26146, 'period_index': 26, 'periods': 26}, 0), ('normal control', {'ytd_wages': 102743, 'ytd_wh': 20507, 'wage': 5626, 'period_index': 12, 'periods': 12}, 0), ('normal control', {'ytd_wages': 1160977, 'ytd_wh': 199709, 'wage': 91537, 'period_index': 11, '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-annualization-base","generated_at":"2026-09-29T14:46:33.814756+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":"Only the current paycheck is annualized, ignoring year-to-date wages and elapsed periods.","sha256":"c18cef584b139279715ba620dc538cdd9bbf1460ea28f7688bb79ecbb354d399","title":"Cumulative wages withholding method: annualization base · 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":44.024,"exit_code":1,"observations":[{"actual":134909,"check":"regression 0","expected":1110812,"passed":false},{"actual":0,"check":"regression 1","expected":0,"passed":true},{"actual":1310987,"check":"partial-repair probe 2","expected":1684840,"passed":false},{"actual":0,"check":"partial-repair probe 3","expected":15666,"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\": 134909, \"expected\": 1110812, \"passed\": false}, {\"check\": \"regression 1\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"partial-repair probe 2\", \"actual\": 1310987, \"expected\": 1684840, \"passed\": false}, {\"check\": \"partial-repair probe 3\", \"actual\": 0, \"expected\": 15666, \"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":46.818,"exit_code":1,"observations":[{"actual":2129858,"check":"regression 0","expected":1110812,"passed":false},{"actual":1149007,"check":"regression 1","expected":0,"passed":false},{"actual":2078481,"check":"partial-repair probe 2","expected":1684840,"passed":false},{"actual":0,"check":"partial-repair probe 3","expected":15666,"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\": 2129858, \"expected\": 1110812, \"passed\": false}, {\"check\": \"regression 1\", \"actual\": 1149007, \"expected\": 0, \"passed\": false}, {\"check\": \"partial-repair probe 2\", \"actual\": 2078481, \"expected\": 1684840, \"passed\": false}, {\"check\": \"partial-repair probe 3\", \"actual\": 0, \"expected\": 15666, \"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."}}