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FA-58861 / Payroll withholding rules / Open access

Social security wage-base withholding: cent rounding of tax · case 01

Withholding is a cent short whenever 6.2% of taxable wages has a fractional cent of one half or more.

Verified by executionVariant 1 · 10 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The tax truncates fractional cents instead of rounding half-up as the contract requires.

VERIFIED REPAIR

Restore the contract rule at the cent rounding of tax step: use `tax = (taxable * 62 + 500) // 1000`.

Unsuccessful approach: The attempt rounds every fractional cent up (ceiling), over-withholding by a cent when the fraction is below one half.

Case contract

Input {ytd, lines:[[kind, cents]], base, exempt}. Social security wages are reg+ot+bonus+tips minus sec125 (401k deferrals do not reduce them), floored at 0. Exempt employees owe nothing ([0,0]). Taxable = min(wages, max(0, base-ytd)); tax = 6.2% rounded half-up to the cent. Return [taxable, tax].

Why this case matters

Employee social security withholding must stop exactly at the annual wage base and use the FICA wage definition, not the income-tax one.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    lines = x['lines']
    fica = 0
    for kind, amt in lines:
        if kind in ('reg', 'ot', 'bonus', 'tips'):
            fica += amt
        elif kind == 'sec125':
            fica -= amt
    fica = max(0, fica)
    if x['exempt']:
        return [0, 0]
    room = max(0, x['base'] - x['ytd'])
    taxable = min(fica, room)
    tax = taxable * 62 // 1000
    return [taxable, tax]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'ytd': 16856079, 'lines': [['ot', 1416], ['401k', 15045]], 'base': 16860000, 'exempt': False}, [1416, 88]), ('regression', {'ytd': 888135, 'lines': [['reg', 4773]], 'base': 1000000, 'exempt': False}, [4773, 296]), ('partial-repair probe', {'ytd': 8981578, 'lines': [['sec125', 35], ['ot', 4702], ['sec125', 74887], ['tips', 226998]], 'base': 17610000, 'exempt': False}, [156778, 9720]), ('partial-repair probe', {'ytd': 6205542, 'lines': [['ot', 2254], ['reg', 6550], ['tips', 10665], ['sec125', 2193]], 'base': 17610000, 'exempt': False}, [17276, 1071]), ('boundary control', {'ytd': 16860000, 'lines': [['reg', 100000]], 'base': 16860000, 'exempt': False}, [0, 0]), ('boundary control', {'ytd': 16800000, 'lines': [['reg', 100000], ['401k', 5000]], 'base': 16860000, 'exempt': False}, [60000, 3720]), ('normal control', {'ytd': 1002361, 'lines': [['bonus', 5955]], 'base': 1000000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 16598376, 'lines': [['401k', 17815], ['sec125', 6865]], 'base': 16860000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 17473948, 'lines': [['sec125', 1367], ['sec125', 805]], 'base': 17610000, 'exempt': True}, [0, 0]), ('normal control', {'ytd': 16862120, 'lines': [['401k', 4852]], 'base': 16860000, 'exempt': False}, [0, 0])], [('regression', {'ytd': 888135, 'lines': [['reg', 4773]], 'base': 1000000, 'exempt': False}, [4773, 296]), ('regression', {'ytd': 3381968, 'lines': [['401k', 4345], ['ot', 6225]], 'base': 17610000, 'exempt': False}, [6225, 386]), ('partial-repair probe', {'ytd': 16617084, 'lines': [['reg', 4712], ['reg', 365692], ['sec125', 340208]], 'base': 16860000, 'exempt': False}, [30196, 1872]), ('partial-repair probe', {'ytd': 17543362, 'lines': [['401k', 1330], ['ot', 1995], ['bonus', 366]], 'base': 17610000, 'exempt': False}, [2361, 146]), ('boundary control', {'ytd': 0, 'lines': [['sec125', 10000], ['reg', 5000]], 'base': 16860000, 'exempt': False}, [0, 0]), ('boundary control', {'ytd': 0, 'lines': [['reg', 12345]], 'base': 16860000, 'exempt': True}, [0, 0]), ('normal control', {'ytd': 17429873, 'lines': [['reg', 14135], ['sec125', 260961], ['ot', 187839]], 'base': 17610000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 17365173, 'lines': [['401k', 1322]], 'base': 17610000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 1004946, 'lines': [['bonus', 48], ['ot', 3255]], 'base': 1000000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 16863463, 'lines': [['sec125', 37799], ['reg', 9785]], 'base': 16860000, 'exempt': False}, [0, 0])], [('regression', {'ytd': 3381968, 'lines': [['401k', 4345], ['ot', 6225]], 'base': 17610000, 'exempt': False}, [6225, 386]), ('regression', {'ytd': 4027320, 'lines': [['tips', 88262], ['bonus', 963], ['sec125', 1621], ['ot', 9375]], 'base': 17610000, 'exempt': False}, [96979, 6013]), ('partial-repair probe', {'ytd': 16573248, 'lines': [['401k', 19585], ['sec125', 2886], ['bonus', 129728]], 'base': 16860000, 'exempt': False}, [126842, 7864]), ('partial-repair probe', {'ytd': 459688, 'lines': [['tips', 299844], ['reg', 213642]], 'base': 1000000, 'exempt': False}, [513486, 31836]), ('boundary control', {'ytd': 16860000, 'lines': [['reg', 100000]], 'base': 16860000, 'exempt': False}, [0, 0]), ('boundary control', {'ytd': 16800000, 'lines': [['reg', 100000], ['401k', 5000]], 'base': 16860000, 'exempt': False}, [60000, 3720]), ('normal control', {'ytd': 17613197, 'lines': [['sec125', 92109], ['ot', 11145], ['401k', 6145], ['tips', 1513]], 'base': 17610000, 'exempt': True}, [0, 0]), ('normal control', {'ytd': 1000562, 'lines': [['ot', 19155], ['sec125', 716], ['bonus', 9555], ['ot', 607]], 'base': 1000000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 1007445, 'lines': [['reg', 945], ['ot', 220313], ['reg', 6015], ['reg', 18815]], 'base': 1000000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 16860733, 'lines': [['401k', 16515], ['bonus', 563], ['ot', 10025]], 'base': 16860000, 'exempt': False}, [0, 0])], [('regression', {'ytd': 4027320, 'lines': [['tips', 88262], ['bonus', 963], ['sec125', 1621], ['ot', 9375]], 'base': 17610000, 'exempt': False}, [96979, 6013]), ('regression', {'ytd': 789375, 'lines': [['tips', 9625], ['bonus', 237249]], 'base': 1000000, 'exempt': False}, [210625, 13059]), ('partial-repair probe', {'ytd': 13755339, 'lines': [['tips', 7370], ['sec125', 287]], 'base': 17610000, 'exempt': False}, [7083, 439]), ('partial-repair probe', {'ytd': 786397, 'lines': [['reg', 9355], ['ot', 292], ['ot', 1195]], 'base': 1000000, 'exempt': False}, [10842, 672]), ('boundary control', {'ytd': 0, 'lines': [['sec125', 10000], ['reg', 5000]], 'base': 16860000, 'exempt': False}, [0, 0]), ('boundary control', {'ytd': 0, 'lines': [['reg', 12345]], 'base': 16860000, 'exempt': True}, [0, 0]), ('normal control', {'ytd': 1003495, 'lines': [['tips', 16185], ['bonus', 19575]], 'base': 1000000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 17386310, 'lines': [['401k', 2353]], 'base': 17610000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 16860000, 'lines': [['reg', 7465], ['reg', 3855], ['401k', 4387], ['bonus', 5805]], 'base': 16860000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 17612007, 'lines': [['reg', 4615], ['ot', 12255]], 'base': 17610000, 'exempt': False}, [0, 0])], [('regression', {'ytd': 789375, 'lines': [['tips', 9625], ['bonus', 237249]], 'base': 1000000, 'exempt': False}, [210625, 13059]), ('regression', {'ytd': 781798, 'lines': [['bonus', 12386]], 'base': 1000000, 'exempt': False}, [12386, 768]), ('partial-repair probe', {'ytd': 12285212, 'lines': [['reg', 19765], ['bonus', 19865], ['bonus', 153], ['ot', 16705]], 'base': 17610000, 'exempt': False}, [56488, 3502]), ('partial-repair probe', {'ytd': 12812610, 'lines': [['401k', 2454], ['ot', 3955]], 'base': 16860000, 'exempt': False}, [3955, 245]), ('boundary control', {'ytd': 16860000, 'lines': [['reg', 100000]], 'base': 16860000, 'exempt': False}, [0, 0]), ('boundary control', {'ytd': 16800000, 'lines': [['reg', 100000], ['401k', 5000]], 'base': 16860000, 'exempt': False}, [60000, 3720]), ('normal control', {'ytd': 1000000, 'lines': [['tips', 285990], ['bonus', 1566], ['401k', 16295]], 'base': 1000000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 16863311, 'lines': [['tips', 19505]], 'base': 16860000, 'exempt': True}, [0, 0]), ('normal control', {'ytd': 17612457, 'lines': [['tips', 6928], ['401k', 1357], ['tips', 4125], ['bonus', 143712]], 'base': 17610000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 4871884, 'lines': [['401k', 9525]], 'base': 17610000, 'exempt': False}, [0, 0])]]
for i, (label, args, expected) in enumerate(fixtures[N-1]):
    check("%s %d" % (label, i), solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression 0[1416, 87][1416, 88]Failed
regression 1[4773, 295][4773, 296]Failed
partial-repair probe 2[156778, 9720][156778, 9720]Passed
partial-repair probe 3[17276, 1071][17276, 1071]Passed
boundary control 4[0, 0][0, 0]Passed
boundary control 5[60000, 3720][60000, 3720]Passed
normal control 6[0, 0][0, 0]Passed
normal control 7[0, 0][0, 0]Passed
normal control 8[0, 0][0, 0]Passed
normal control 9[0, 0][0, 0]Passed

SHA-256 / b6a576fe81be504a59b3f1ab445f496ba6ca1a019cd2ae457ea233120689f112

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    lines = x['lines']
    fica = 0
    for kind, amt in lines:
        if kind in ('reg', 'ot', 'bonus', 'tips'):
            fica += amt
        elif kind == 'sec125':
            fica -= amt
    fica = max(0, fica)
    if x['exempt']:
        return [0, 0]
    room = max(0, x['base'] - x['ytd'])
    taxable = min(fica, room)
    tax = (taxable * 62 + 999) // 1000
    return [taxable, tax]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'ytd': 16856079, 'lines': [['ot', 1416], ['401k', 15045]], 'base': 16860000, 'exempt': False}, [1416, 88]), ('regression', {'ytd': 888135, 'lines': [['reg', 4773]], 'base': 1000000, 'exempt': False}, [4773, 296]), ('partial-repair probe', {'ytd': 8981578, 'lines': [['sec125', 35], ['ot', 4702], ['sec125', 74887], ['tips', 226998]], 'base': 17610000, 'exempt': False}, [156778, 9720]), ('partial-repair probe', {'ytd': 6205542, 'lines': [['ot', 2254], ['reg', 6550], ['tips', 10665], ['sec125', 2193]], 'base': 17610000, 'exempt': False}, [17276, 1071]), ('boundary control', {'ytd': 16860000, 'lines': [['reg', 100000]], 'base': 16860000, 'exempt': False}, [0, 0]), ('boundary control', {'ytd': 16800000, 'lines': [['reg', 100000], ['401k', 5000]], 'base': 16860000, 'exempt': False}, [60000, 3720]), ('normal control', {'ytd': 1002361, 'lines': [['bonus', 5955]], 'base': 1000000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 16598376, 'lines': [['401k', 17815], ['sec125', 6865]], 'base': 16860000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 17473948, 'lines': [['sec125', 1367], ['sec125', 805]], 'base': 17610000, 'exempt': True}, [0, 0]), ('normal control', {'ytd': 16862120, 'lines': [['401k', 4852]], 'base': 16860000, 'exempt': False}, [0, 0])], [('regression', {'ytd': 888135, 'lines': [['reg', 4773]], 'base': 1000000, 'exempt': False}, [4773, 296]), ('regression', {'ytd': 3381968, 'lines': [['401k', 4345], ['ot', 6225]], 'base': 17610000, 'exempt': False}, [6225, 386]), ('partial-repair probe', {'ytd': 16617084, 'lines': [['reg', 4712], ['reg', 365692], ['sec125', 340208]], 'base': 16860000, 'exempt': False}, [30196, 1872]), ('partial-repair probe', {'ytd': 17543362, 'lines': [['401k', 1330], ['ot', 1995], ['bonus', 366]], 'base': 17610000, 'exempt': False}, [2361, 146]), ('boundary control', {'ytd': 0, 'lines': [['sec125', 10000], ['reg', 5000]], 'base': 16860000, 'exempt': False}, [0, 0]), ('boundary control', {'ytd': 0, 'lines': [['reg', 12345]], 'base': 16860000, 'exempt': True}, [0, 0]), ('normal control', {'ytd': 17429873, 'lines': [['reg', 14135], ['sec125', 260961], ['ot', 187839]], 'base': 17610000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 17365173, 'lines': [['401k', 1322]], 'base': 17610000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 1004946, 'lines': [['bonus', 48], ['ot', 3255]], 'base': 1000000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 16863463, 'lines': [['sec125', 37799], ['reg', 9785]], 'base': 16860000, 'exempt': False}, [0, 0])], [('regression', {'ytd': 3381968, 'lines': [['401k', 4345], ['ot', 6225]], 'base': 17610000, 'exempt': False}, [6225, 386]), ('regression', {'ytd': 4027320, 'lines': [['tips', 88262], ['bonus', 963], ['sec125', 1621], ['ot', 9375]], 'base': 17610000, 'exempt': False}, [96979, 6013]), ('partial-repair probe', {'ytd': 16573248, 'lines': [['401k', 19585], ['sec125', 2886], ['bonus', 129728]], 'base': 16860000, 'exempt': False}, [126842, 7864]), ('partial-repair probe', {'ytd': 459688, 'lines': [['tips', 299844], ['reg', 213642]], 'base': 1000000, 'exempt': False}, [513486, 31836]), ('boundary control', {'ytd': 16860000, 'lines': [['reg', 100000]], 'base': 16860000, 'exempt': False}, [0, 0]), ('boundary control', {'ytd': 16800000, 'lines': [['reg', 100000], ['401k', 5000]], 'base': 16860000, 'exempt': False}, [60000, 3720]), ('normal control', {'ytd': 17613197, 'lines': [['sec125', 92109], ['ot', 11145], ['401k', 6145], ['tips', 1513]], 'base': 17610000, 'exempt': True}, [0, 0]), ('normal control', {'ytd': 1000562, 'lines': [['ot', 19155], ['sec125', 716], ['bonus', 9555], ['ot', 607]], 'base': 1000000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 1007445, 'lines': [['reg', 945], ['ot', 220313], ['reg', 6015], ['reg', 18815]], 'base': 1000000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 16860733, 'lines': [['401k', 16515], ['bonus', 563], ['ot', 10025]], 'base': 16860000, 'exempt': False}, [0, 0])], [('regression', {'ytd': 4027320, 'lines': [['tips', 88262], ['bonus', 963], ['sec125', 1621], ['ot', 9375]], 'base': 17610000, 'exempt': False}, [96979, 6013]), ('regression', {'ytd': 789375, 'lines': [['tips', 9625], ['bonus', 237249]], 'base': 1000000, 'exempt': False}, [210625, 13059]), ('partial-repair probe', {'ytd': 13755339, 'lines': [['tips', 7370], ['sec125', 287]], 'base': 17610000, 'exempt': False}, [7083, 439]), ('partial-repair probe', {'ytd': 786397, 'lines': [['reg', 9355], ['ot', 292], ['ot', 1195]], 'base': 1000000, 'exempt': False}, [10842, 672]), ('boundary control', {'ytd': 0, 'lines': [['sec125', 10000], ['reg', 5000]], 'base': 16860000, 'exempt': False}, [0, 0]), ('boundary control', {'ytd': 0, 'lines': [['reg', 12345]], 'base': 16860000, 'exempt': True}, [0, 0]), ('normal control', {'ytd': 1003495, 'lines': [['tips', 16185], ['bonus', 19575]], 'base': 1000000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 17386310, 'lines': [['401k', 2353]], 'base': 17610000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 16860000, 'lines': [['reg', 7465], ['reg', 3855], ['401k', 4387], ['bonus', 5805]], 'base': 16860000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 17612007, 'lines': [['reg', 4615], ['ot', 12255]], 'base': 17610000, 'exempt': False}, [0, 0])], [('regression', {'ytd': 789375, 'lines': [['tips', 9625], ['bonus', 237249]], 'base': 1000000, 'exempt': False}, [210625, 13059]), ('regression', {'ytd': 781798, 'lines': [['bonus', 12386]], 'base': 1000000, 'exempt': False}, [12386, 768]), ('partial-repair probe', {'ytd': 12285212, 'lines': [['reg', 19765], ['bonus', 19865], ['bonus', 153], ['ot', 16705]], 'base': 17610000, 'exempt': False}, [56488, 3502]), ('partial-repair probe', {'ytd': 12812610, 'lines': [['401k', 2454], ['ot', 3955]], 'base': 16860000, 'exempt': False}, [3955, 245]), ('boundary control', {'ytd': 16860000, 'lines': [['reg', 100000]], 'base': 16860000, 'exempt': False}, [0, 0]), ('boundary control', {'ytd': 16800000, 'lines': [['reg', 100000], ['401k', 5000]], 'base': 16860000, 'exempt': False}, [60000, 3720]), ('normal control', {'ytd': 1000000, 'lines': [['tips', 285990], ['bonus', 1566], ['401k', 16295]], 'base': 1000000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 16863311, 'lines': [['tips', 19505]], 'base': 16860000, 'exempt': True}, [0, 0]), ('normal control', {'ytd': 17612457, 'lines': [['tips', 6928], ['401k', 1357], ['tips', 4125], ['bonus', 143712]], 'base': 17610000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 4871884, 'lines': [['401k', 9525]], 'base': 17610000, 'exempt': False}, [0, 0])]]
for i, (label, args, expected) in enumerate(fixtures[N-1]):
    check("%s %d" % (label, i), solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression 0[1416, 88][1416, 88]Passed
regression 1[4773, 296][4773, 296]Passed
partial-repair probe 2[156778, 9721][156778, 9720]Failed
partial-repair probe 3[17276, 1072][17276, 1071]Failed
boundary control 4[0, 0][0, 0]Passed
boundary control 5[60000, 3720][60000, 3720]Passed
normal control 6[0, 0][0, 0]Passed
normal control 7[0, 0][0, 0]Passed
normal control 8[0, 0][0, 0]Passed
normal control 9[0, 0][0, 0]Passed

SHA-256 / 9fb983700d94d8b39d5d2258f718d85bcc5ba627ddb8f242404cabddee52fa6b

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    lines = x['lines']
    fica = 0
    for kind, amt in lines:
        if kind in ('reg', 'ot', 'bonus', 'tips'):
            fica += amt
        elif kind == 'sec125':
            fica -= amt
    fica = max(0, fica)
    if x['exempt']:
        return [0, 0]
    room = max(0, x['base'] - x['ytd'])
    taxable = min(fica, room)
    tax = (taxable * 62 + 500) // 1000
    return [taxable, tax]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'ytd': 16856079, 'lines': [['ot', 1416], ['401k', 15045]], 'base': 16860000, 'exempt': False}, [1416, 88]), ('regression', {'ytd': 888135, 'lines': [['reg', 4773]], 'base': 1000000, 'exempt': False}, [4773, 296]), ('partial-repair probe', {'ytd': 8981578, 'lines': [['sec125', 35], ['ot', 4702], ['sec125', 74887], ['tips', 226998]], 'base': 17610000, 'exempt': False}, [156778, 9720]), ('partial-repair probe', {'ytd': 6205542, 'lines': [['ot', 2254], ['reg', 6550], ['tips', 10665], ['sec125', 2193]], 'base': 17610000, 'exempt': False}, [17276, 1071]), ('boundary control', {'ytd': 16860000, 'lines': [['reg', 100000]], 'base': 16860000, 'exempt': False}, [0, 0]), ('boundary control', {'ytd': 16800000, 'lines': [['reg', 100000], ['401k', 5000]], 'base': 16860000, 'exempt': False}, [60000, 3720]), ('normal control', {'ytd': 1002361, 'lines': [['bonus', 5955]], 'base': 1000000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 16598376, 'lines': [['401k', 17815], ['sec125', 6865]], 'base': 16860000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 17473948, 'lines': [['sec125', 1367], ['sec125', 805]], 'base': 17610000, 'exempt': True}, [0, 0]), ('normal control', {'ytd': 16862120, 'lines': [['401k', 4852]], 'base': 16860000, 'exempt': False}, [0, 0])], [('regression', {'ytd': 888135, 'lines': [['reg', 4773]], 'base': 1000000, 'exempt': False}, [4773, 296]), ('regression', {'ytd': 3381968, 'lines': [['401k', 4345], ['ot', 6225]], 'base': 17610000, 'exempt': False}, [6225, 386]), ('partial-repair probe', {'ytd': 16617084, 'lines': [['reg', 4712], ['reg', 365692], ['sec125', 340208]], 'base': 16860000, 'exempt': False}, [30196, 1872]), ('partial-repair probe', {'ytd': 17543362, 'lines': [['401k', 1330], ['ot', 1995], ['bonus', 366]], 'base': 17610000, 'exempt': False}, [2361, 146]), ('boundary control', {'ytd': 0, 'lines': [['sec125', 10000], ['reg', 5000]], 'base': 16860000, 'exempt': False}, [0, 0]), ('boundary control', {'ytd': 0, 'lines': [['reg', 12345]], 'base': 16860000, 'exempt': True}, [0, 0]), ('normal control', {'ytd': 17429873, 'lines': [['reg', 14135], ['sec125', 260961], ['ot', 187839]], 'base': 17610000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 17365173, 'lines': [['401k', 1322]], 'base': 17610000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 1004946, 'lines': [['bonus', 48], ['ot', 3255]], 'base': 1000000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 16863463, 'lines': [['sec125', 37799], ['reg', 9785]], 'base': 16860000, 'exempt': False}, [0, 0])], [('regression', {'ytd': 3381968, 'lines': [['401k', 4345], ['ot', 6225]], 'base': 17610000, 'exempt': False}, [6225, 386]), ('regression', {'ytd': 4027320, 'lines': [['tips', 88262], ['bonus', 963], ['sec125', 1621], ['ot', 9375]], 'base': 17610000, 'exempt': False}, [96979, 6013]), ('partial-repair probe', {'ytd': 16573248, 'lines': [['401k', 19585], ['sec125', 2886], ['bonus', 129728]], 'base': 16860000, 'exempt': False}, [126842, 7864]), ('partial-repair probe', {'ytd': 459688, 'lines': [['tips', 299844], ['reg', 213642]], 'base': 1000000, 'exempt': False}, [513486, 31836]), ('boundary control', {'ytd': 16860000, 'lines': [['reg', 100000]], 'base': 16860000, 'exempt': False}, [0, 0]), ('boundary control', {'ytd': 16800000, 'lines': [['reg', 100000], ['401k', 5000]], 'base': 16860000, 'exempt': False}, [60000, 3720]), ('normal control', {'ytd': 17613197, 'lines': [['sec125', 92109], ['ot', 11145], ['401k', 6145], ['tips', 1513]], 'base': 17610000, 'exempt': True}, [0, 0]), ('normal control', {'ytd': 1000562, 'lines': [['ot', 19155], ['sec125', 716], ['bonus', 9555], ['ot', 607]], 'base': 1000000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 1007445, 'lines': [['reg', 945], ['ot', 220313], ['reg', 6015], ['reg', 18815]], 'base': 1000000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 16860733, 'lines': [['401k', 16515], ['bonus', 563], ['ot', 10025]], 'base': 16860000, 'exempt': False}, [0, 0])], [('regression', {'ytd': 4027320, 'lines': [['tips', 88262], ['bonus', 963], ['sec125', 1621], ['ot', 9375]], 'base': 17610000, 'exempt': False}, [96979, 6013]), ('regression', {'ytd': 789375, 'lines': [['tips', 9625], ['bonus', 237249]], 'base': 1000000, 'exempt': False}, [210625, 13059]), ('partial-repair probe', {'ytd': 13755339, 'lines': [['tips', 7370], ['sec125', 287]], 'base': 17610000, 'exempt': False}, [7083, 439]), ('partial-repair probe', {'ytd': 786397, 'lines': [['reg', 9355], ['ot', 292], ['ot', 1195]], 'base': 1000000, 'exempt': False}, [10842, 672]), ('boundary control', {'ytd': 0, 'lines': [['sec125', 10000], ['reg', 5000]], 'base': 16860000, 'exempt': False}, [0, 0]), ('boundary control', {'ytd': 0, 'lines': [['reg', 12345]], 'base': 16860000, 'exempt': True}, [0, 0]), ('normal control', {'ytd': 1003495, 'lines': [['tips', 16185], ['bonus', 19575]], 'base': 1000000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 17386310, 'lines': [['401k', 2353]], 'base': 17610000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 16860000, 'lines': [['reg', 7465], ['reg', 3855], ['401k', 4387], ['bonus', 5805]], 'base': 16860000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 17612007, 'lines': [['reg', 4615], ['ot', 12255]], 'base': 17610000, 'exempt': False}, [0, 0])], [('regression', {'ytd': 789375, 'lines': [['tips', 9625], ['bonus', 237249]], 'base': 1000000, 'exempt': False}, [210625, 13059]), ('regression', {'ytd': 781798, 'lines': [['bonus', 12386]], 'base': 1000000, 'exempt': False}, [12386, 768]), ('partial-repair probe', {'ytd': 12285212, 'lines': [['reg', 19765], ['bonus', 19865], ['bonus', 153], ['ot', 16705]], 'base': 17610000, 'exempt': False}, [56488, 3502]), ('partial-repair probe', {'ytd': 12812610, 'lines': [['401k', 2454], ['ot', 3955]], 'base': 16860000, 'exempt': False}, [3955, 245]), ('boundary control', {'ytd': 16860000, 'lines': [['reg', 100000]], 'base': 16860000, 'exempt': False}, [0, 0]), ('boundary control', {'ytd': 16800000, 'lines': [['reg', 100000], ['401k', 5000]], 'base': 16860000, 'exempt': False}, [60000, 3720]), ('normal control', {'ytd': 1000000, 'lines': [['tips', 285990], ['bonus', 1566], ['401k', 16295]], 'base': 1000000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 16863311, 'lines': [['tips', 19505]], 'base': 16860000, 'exempt': True}, [0, 0]), ('normal control', {'ytd': 17612457, 'lines': [['tips', 6928], ['401k', 1357], ['tips', 4125], ['bonus', 143712]], 'base': 17610000, 'exempt': False}, [0, 0]), ('normal control', {'ytd': 4871884, 'lines': [['401k', 9525]], 'base': 17610000, 'exempt': False}, [0, 0])]]
for i, (label, args, expected) in enumerate(fixtures[N-1]):
    check("%s %d" % (label, i), solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression 0[1416, 88][1416, 88]Passed
regression 1[4773, 296][4773, 296]Passed
partial-repair probe 2[156778, 9720][156778, 9720]Passed
partial-repair probe 3[17276, 1071][17276, 1071]Passed
boundary control 4[0, 0][0, 0]Passed
boundary control 5[60000, 3720][60000, 3720]Passed
normal control 6[0, 0][0, 0]Passed
normal control 7[0, 0][0, 0]Passed
normal control 8[0, 0][0, 0]Passed
normal control 9[0, 0][0, 0]Passed

SHA-256 / 15cbc0097170ad3ea20028bf4688301afc56ec7c44bc3a78ea2003f02117a556

Verification & scope

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.

Observations recorded using Python 3.12.14 at 2026-09-29T14:46:30.759320+00:00.

Case digest / a3caf943ee84a1e488afd2bbedfe9064be3f1eee9f2a0a88493dd521147ead29