{"abstract":"Withholding jumps discontinuously when income crosses a bracket, taxing all income at the top reached rate.","category":"Payroll withholding rules","checks":9,"contract":"Input {wage, freq, allow, status}. Annualize: wage*periods (weekly 52, biweekly 26, semimonthly 24, monthly 12); subtract 4,300.00 per allowance, floor 0. Marginal brackets over 4,000/15,000/50,000 dollars at 10/12/22% (married thresholds doubled). Annual tax (in cent-percent units) is divided by periods and rounded half-up to cents once.","contract_signature":"x","evaluation_group":"w2-payroll-withholding-annualized-percentage-method","failed_approach":"The attempt accumulates slices but forgets to subtract the bracket floor, taxing from zero in every bracket.","family":"w2-payroll-withholding-annualized-percentage-method-marginal-slice-accumulation","id":"FA-58891","implementations":{"attempt":{"sha256":"28792d7665103d6898e1ada5e12855f542bc4c5a1a054cbd40ab71ac181591cf","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    periods = {'weekly': 52, 'biweekly': 26, 'semimonthly': 24, 'monthly': 12}[x['freq']]\n    annual = x['wage'] * periods\n    adjusted = max(0, annual - x['allow'] * 430000)\n    mult = 2 if x['status'] == 'married' else 1\n    brackets = [(400000 * mult, 10), (1500000 * mult, 12), (5000000 * mult, 22)]\n    tax = 0\n    for i, (lo, rate) in enumerate(brackets):\n        hi = brackets[i + 1][0] if i + 1 < len(brackets) else None\n        if adjusted > lo:\n            top = adjusted if hi is None else min(adjusted, hi)\n            tax += top * rate\n    wh = (tax * 2 + 100 * periods) // (200 * periods)\n    return wh\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression (boundary)', {'wage': 57693, 'freq': 'weekly', 'allow': 0, 'status': 'single'}, 5577), ('regression (boundary)', {'wage': 125000, 'freq': 'semimonthly', 'allow': 1, 'status': 'married'}, 7375), ('partial-repair probe', {'wage': 998152, 'freq': 'semimonthly', 'allow': 1, 'status': 'married'}, 168152), ('partial-repair probe', {'wage': 992194, 'freq': 'weekly', 'allow': 3, 'status': 'married'}, 190902), ('boundary control', {'wage': 0, 'freq': 'weekly', 'allow': 0, 'status': 'single'}, 0), ('normal control', {'wage': 22359, 'freq': 'semimonthly', 'allow': 5, 'status': 'married'}, 0), ('normal control', {'wage': 89742, 'freq': 'monthly', 'allow': 1, 'status': 'married'}, 0), ('normal control', {'wage': 17607, 'freq': 'semimonthly', 'allow': 4, 'status': 'married'}, 0), ('normal control', {'wage': 6134, 'freq': 'semimonthly', 'allow': 0, 'status': 'single'}, 0)], [('regression (boundary)', {'wage': 125000, 'freq': 'semimonthly', 'allow': 1, 'status': 'married'}, 7375), ('regression', {'wage': 998152, 'freq': 'semimonthly', 'allow': 1, 'status': 'married'}, 168152), ('partial-repair probe', {'wage': 992194, 'freq': 'weekly', 'allow': 3, 'status': 'married'}, 190902), ('partial-repair probe', {'wage': 36754, 'freq': 'biweekly', 'allow': 1, 'status': 'single'}, 483), ('boundary control', {'wage': 0, 'freq': 'weekly', 'allow': 0, 'status': 'single'}, 0), ('normal control', {'wage': 52312, 'freq': 'semimonthly', 'allow': 5, 'status': 'single'}, 0), ('normal control', {'wage': 28087, 'freq': 'biweekly', 'allow': 1, 'status': 'single'}, 0), ('normal control', {'wage': 97334, 'freq': 'monthly', 'allow': 6, 'status': 'single'}, 0), ('normal control', {'wage': 18119, 'freq': 'weekly', 'allow': 3, 'status': 'married'}, 0)], [('regression', {'wage': 998152, 'freq': 'semimonthly', 'allow': 1, 'status': 'married'}, 168152), ('regression', {'wage': 992194, 'freq': 'weekly', 'allow': 3, 'status': 'married'}, 190902), ('partial-repair probe', {'wage': 36754, 'freq': 'biweekly', 'allow': 1, 'status': 'single'}, 483), ('partial-repair probe', {'wage': 124657, 'freq': 'semimonthly', 'allow': 4, 'status': 'married'}, 1966), ('boundary control', {'wage': 0, 'freq': 'weekly', 'allow': 0, 'status': 'single'}, 0), ('normal control', {'wage': 10871, 'freq': 'weekly', 'allow': 6, 'status': 'single'}, 0), ('normal control', {'wage': 836, 'freq': 'semimonthly', 'allow': 1, 'status': 'single'}, 0), ('normal control', {'wage': 30453, 'freq': 'biweekly', 'allow': 2, 'status': 'married'}, 0), ('normal control', {'wage': 27188, 'freq': 'semimonthly', 'allow': 4, 'status': 'married'}, 0)], [('regression', {'wage': 992194, 'freq': 'weekly', 'allow': 3, 'status': 'married'}, 190902), ('regression', {'wage': 36754, 'freq': 'biweekly', 'allow': 1, 'status': 'single'}, 483), ('partial-repair probe', {'wage': 157996, 'freq': 'semimonthly', 'allow': 4, 'status': 'married'}, 5300), ('partial-repair probe', {'wage': 1223812, 'freq': 'monthly', 'allow': 5, 'status': 'married'}, 134822), ('boundary control', {'wage': 0, 'freq': 'weekly', 'allow': 0, 'status': 'single'}, 0), ('normal control', {'wage': 23859, 'freq': 'semimonthly', 'allow': 2, 'status': 'married'}, 0), ('normal control', {'wage': 50426, 'freq': 'semimonthly', 'allow': 5, 'status': 'married'}, 0), ('normal control', {'wage': 128102, 'freq': 'monthly', 'allow': 5, 'status': 'married'}, 0), ('normal control', {'wage': 6608, 'freq': 'semimonthly', 'allow': 0, 'status': 'married'}, 0)], [('regression', {'wage': 36754, 'freq': 'biweekly', 'allow': 1, 'status': 'single'}, 483), ('regression', {'wage': 124657, 'freq': 'semimonthly', 'allow': 4, 'status': 'married'}, 1966), ('partial-repair probe', {'wage': 143245, 'freq': 'biweekly', 'allow': 5, 'status': 'married'}, 2978), ('partial-repair probe', {'wage': 475908, 'freq': 'monthly', 'allow': 6, 'status': 'single'}, 25476), ('boundary control', {'wage': 0, 'freq': 'weekly', 'allow': 0, 'status': 'single'}, 0), ('normal control', {'wage': 49359, 'freq': 'weekly', 'allow': 6, 'status': 'single'}, 0), ('normal control', {'wage': 56499, 'freq': 'monthly', 'allow': 4, 'status': 'married'}, 0), ('normal control', {'wage': 6762, 'freq': 'weekly', 'allow': 6, 'status': 'single'}, 0), ('normal control', {'wage': 30428, 'freq': 'monthly', 'allow': 4, 'status': 'married'}, 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":"5993a5d3a0db5c6378a41d6861d720e5c757784c6692ea8137232e6e553d9a48","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    periods = {'weekly': 52, 'biweekly': 26, 'semimonthly': 24, 'monthly': 12}[x['freq']]\n    annual = x['wage'] * periods\n    adjusted = max(0, annual - x['allow'] * 430000)\n    mult = 2 if x['status'] == 'married' else 1\n    brackets = [(400000 * mult, 10), (1500000 * mult, 12), (5000000 * mult, 22)]\n    tax = 0\n    for i, (lo, rate) in enumerate(brackets):\n        hi = brackets[i + 1][0] if i + 1 < len(brackets) else None\n        if adjusted > lo:\n            top = adjusted if hi is None else min(adjusted, hi)\n            tax = adjusted * rate\n    wh = (tax * 2 + 100 * periods) // (200 * periods)\n    return wh\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression (boundary)', {'wage': 57693, 'freq': 'weekly', 'allow': 0, 'status': 'single'}, 5577), ('regression (boundary)', {'wage': 125000, 'freq': 'semimonthly', 'allow': 1, 'status': 'married'}, 7375), ('partial-repair probe', {'wage': 998152, 'freq': 'semimonthly', 'allow': 1, 'status': 'married'}, 168152), ('partial-repair probe', {'wage': 992194, 'freq': 'weekly', 'allow': 3, 'status': 'married'}, 190902), ('boundary control', {'wage': 0, 'freq': 'weekly', 'allow': 0, 'status': 'single'}, 0), ('normal control', {'wage': 22359, 'freq': 'semimonthly', 'allow': 5, 'status': 'married'}, 0), ('normal control', {'wage': 89742, 'freq': 'monthly', 'allow': 1, 'status': 'married'}, 0), ('normal control', {'wage': 17607, 'freq': 'semimonthly', 'allow': 4, 'status': 'married'}, 0), ('normal control', {'wage': 6134, 'freq': 'semimonthly', 'allow': 0, 'status': 'single'}, 0)], [('regression (boundary)', {'wage': 125000, 'freq': 'semimonthly', 'allow': 1, 'status': 'married'}, 7375), ('regression', {'wage': 998152, 'freq': 'semimonthly', 'allow': 1, 'status': 'married'}, 168152), ('partial-repair probe', {'wage': 992194, 'freq': 'weekly', 'allow': 3, 'status': 'married'}, 190902), ('partial-repair probe', {'wage': 36754, 'freq': 'biweekly', 'allow': 1, 'status': 'single'}, 483), ('boundary control', {'wage': 0, 'freq': 'weekly', 'allow': 0, 'status': 'single'}, 0), ('normal control', {'wage': 52312, 'freq': 'semimonthly', 'allow': 5, 'status': 'single'}, 0), ('normal control', {'wage': 28087, 'freq': 'biweekly', 'allow': 1, 'status': 'single'}, 0), ('normal control', {'wage': 97334, 'freq': 'monthly', 'allow': 6, 'status': 'single'}, 0), ('normal control', {'wage': 18119, 'freq': 'weekly', 'allow': 3, 'status': 'married'}, 0)], [('regression', {'wage': 998152, 'freq': 'semimonthly', 'allow': 1, 'status': 'married'}, 168152), ('regression', {'wage': 992194, 'freq': 'weekly', 'allow': 3, 'status': 'married'}, 190902), ('partial-repair probe', {'wage': 36754, 'freq': 'biweekly', 'allow': 1, 'status': 'single'}, 483), ('partial-repair probe', {'wage': 124657, 'freq': 'semimonthly', 'allow': 4, 'status': 'married'}, 1966), ('boundary control', {'wage': 0, 'freq': 'weekly', 'allow': 0, 'status': 'single'}, 0), ('normal control', {'wage': 10871, 'freq': 'weekly', 'allow': 6, 'status': 'single'}, 0), ('normal control', {'wage': 836, 'freq': 'semimonthly', 'allow': 1, 'status': 'single'}, 0), ('normal control', {'wage': 30453, 'freq': 'biweekly', 'allow': 2, 'status': 'married'}, 0), ('normal control', {'wage': 27188, 'freq': 'semimonthly', 'allow': 4, 'status': 'married'}, 0)], [('regression', {'wage': 992194, 'freq': 'weekly', 'allow': 3, 'status': 'married'}, 190902), ('regression', {'wage': 36754, 'freq': 'biweekly', 'allow': 1, 'status': 'single'}, 483), ('partial-repair probe', {'wage': 157996, 'freq': 'semimonthly', 'allow': 4, 'status': 'married'}, 5300), ('partial-repair probe', {'wage': 1223812, 'freq': 'monthly', 'allow': 5, 'status': 'married'}, 134822), ('boundary control', {'wage': 0, 'freq': 'weekly', 'allow': 0, 'status': 'single'}, 0), ('normal control', {'wage': 23859, 'freq': 'semimonthly', 'allow': 2, 'status': 'married'}, 0), ('normal control', {'wage': 50426, 'freq': 'semimonthly', 'allow': 5, 'status': 'married'}, 0), ('normal control', {'wage': 128102, 'freq': 'monthly', 'allow': 5, 'status': 'married'}, 0), ('normal control', {'wage': 6608, 'freq': 'semimonthly', 'allow': 0, 'status': 'married'}, 0)], [('regression', {'wage': 36754, 'freq': 'biweekly', 'allow': 1, 'status': 'single'}, 483), ('regression', {'wage': 124657, 'freq': 'semimonthly', 'allow': 4, 'status': 'married'}, 1966), ('partial-repair probe', {'wage': 143245, 'freq': 'biweekly', 'allow': 5, 'status': 'married'}, 2978), ('partial-repair probe', {'wage': 475908, 'freq': 'monthly', 'allow': 6, 'status': 'single'}, 25476), ('boundary control', {'wage': 0, 'freq': 'weekly', 'allow': 0, 'status': 'single'}, 0), ('normal control', {'wage': 49359, 'freq': 'weekly', 'allow': 6, 'status': 'single'}, 0), ('normal control', {'wage': 56499, 'freq': 'monthly', 'allow': 4, 'status': 'married'}, 0), ('normal control', {'wage': 6762, 'freq': 'weekly', 'allow': 6, 'status': 'single'}, 0), ('normal control', {'wage': 30428, 'freq': 'monthly', 'allow': 4, 'status': 'married'}, 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-annualized-percentage-method-marginal-slice-accumulation","generated_at":"2026-09-29T14:46:30.996873+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Percentage-method withholding depends on marginal bracket slices and on rounding only after de-annualizing.","root_cause":"Each matching bracket overwrites the tax with the flat rate applied to all adjusted income.","sha256":"2fcb76a2dcfa6ff6091f3998f244cbb633c417f80d50cf80a0b8a8590a8b6402","title":"Annualized percentage-method withholding: marginal slice accumulation · 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":38.2,"exit_code":1,"observations":[{"actual":9808,"check":"regression (boundary) 0","expected":5577,"passed":false},{"actual":10708,"check":"regression (boundary) 1","expected":7375,"passed":false},{"actual":278152,"check":"partial-repair probe 2","expected":168152,"passed":false},{"actual":241671,"check":"partial-repair probe 3","expected":190902,"passed":false},{"actual":0,"check":"boundary 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},{"actual":0,"check":"normal control 8","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression (boundary) 0\", \"actual\": 9808, \"expected\": 5577, \"passed\": false}, {\"check\": \"regression (boundary) 1\", \"actual\": 10708, \"expected\": 7375, \"passed\": false}, {\"check\": \"partial-repair probe 2\", \"actual\": 278152, \"expected\": 168152, \"passed\": false}, {\"check\": \"partial-repair probe 3\", \"actual\": 241671, \"expected\": 190902, \"passed\": false}, {\"check\": \"boundary 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}, {\"check\": \"normal control 8\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.786,"exit_code":1,"observations":[{"actual":6923,"check":"regression (boundary) 0","expected":5577,"passed":false},{"actual":10708,"check":"regression (boundary) 1","expected":7375,"passed":false},{"actual":215652,"check":"partial-repair probe 2","expected":168152,"passed":false},{"actual":212825,"check":"partial-repair probe 3","expected":190902,"passed":false},{"actual":0,"check":"boundary 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},{"actual":0,"check":"normal control 8","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression (boundary) 0\", \"actual\": 6923, \"expected\": 5577, \"passed\": false}, {\"check\": \"regression (boundary) 1\", \"actual\": 10708, \"expected\": 7375, \"passed\": false}, {\"check\": \"partial-repair probe 2\", \"actual\": 215652, \"expected\": 168152, \"passed\": false}, {\"check\": \"partial-repair probe 3\", \"actual\": 212825, \"expected\": 190902, \"passed\": false}, {\"check\": \"boundary 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}, {\"check\": \"normal control 8\", \"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."}}