FA-58876 / Payroll withholding rules / Open access
Additional Medicare withholding threshold: separately rounded components · case 01
The total Medicare line is off by a cent from the sum of its two printed components.
ROOT CAUSE
The total is recomputed with one combined rounding instead of adding the separately rounded regular and additional amounts.
VERIFIED REPAIR
Restore the contract rule at the separately rounded components step: use `return [base_tax, extra_wages, base_tax + extra]`.
Unsuccessful approach: The attempt still combines the components before rounding and additionally truncates, so the total diverges even more often.
Case contract
Input [ytd_wages, wages] in cents. Regular Medicare is 1.45% of wages rounded half-up. Additional Medicare is 0.9% of the part of this paycheck that pushes year-to-date wages above 200,000.00, rounded half-up separately. Return [medicare, additional_wages, medicare + additional].
Why this case matters
The employer must begin the extra 0.9% exactly with the paycheck that crosses the threshold, and only on the excess portion.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
ytd, wages = x
base_tax = (wages * 145 + 5000) // 10000
over_before = max(0, ytd - 20000000)
over_after = max(0, ytd + wages - 20000000)
extra_wages = over_after - over_before
extra = (extra_wages * 9 + 500) // 1000
return [base_tax, extra_wages, (wages * 145 + extra_wages * 90 + 5000) // 10000]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', [19294581, 2127366], [30847, 1421947, 43645]), ('regression', [20189609, 125208], [1816, 125208, 2943]), ('partial-repair probe', [2439490, 49414], [717, 0, 717]), ('partial-repair probe', [20723172, 31906], [463, 31906, 750]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('boundary control', [19950000, 100000], [1450, 50000, 1900]), ('normal control', [20158685, 407195], [5904, 407195, 9569]), ('normal control', [20518887, 2208012], [32016, 2208012, 51888]), ('normal control', [20000000, 1829965], [26534, 1829965, 43004]), ('normal control', [7554383, 209883], [3043, 0, 3043])], [('regression', [20189609, 125208], [1816, 125208, 2943]), ('regression', [20000000, 13601], [197, 13601, 319]), ('partial-repair probe', [20767841, 19138], [278, 19138, 450]), ('partial-repair probe', [20469014, 260626], [3779, 260626, 6125]), ('boundary control', [0, 0], [0, 0, 0]), ('boundary control', [25000000, 12345], [179, 12345, 290]), ('normal control', [8001356, 2662166], [38601, 0, 38601]), ('normal control', [19681988, 1173456], [17015, 855444, 24714]), ('normal control', [19655408, 1735735], [25168, 1391143, 37688]), ('normal control', [19686537, 15872], [230, 0, 230])], [('regression', [20164631, 554176], [8036, 554176, 13024]), ('regression', [20000000, 13601], [197, 13601, 319]), ('partial-repair probe', [23912137, 659488], [9563, 659488, 15498]), ('partial-repair probe', [21835663, 1842418], [26715, 1842418, 43297]), ('boundary control', [19999999, 1], [0, 0, 0]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('normal control', [3879860, 1040777], [15091, 0, 15091]), ('normal control', [4213397, 2332986], [33828, 0, 33828]), ('normal control', [20000000, 654261], [9487, 654261, 15375]), ('normal control', [20000000, 35595], [516, 35595, 836])], [('regression', [20333577, 41631], [604, 41631, 979]), ('regression', [20290634, 2600150], [37702, 2600150, 61103]), ('partial-repair probe', [19294581, 2127366], [30847, 1421947, 43645]), ('partial-repair probe', [20000000, 1204410], [17464, 1204410, 28304]), ('boundary control', [19950000, 100000], [1450, 50000, 1900]), ('boundary control', [0, 0], [0, 0, 0]), ('normal control', [4705614, 33884], [491, 0, 491]), ('normal control', [4401788, 1347616], [19540, 0, 19540]), ('normal control', [703223, 1018779], [14772, 0, 14772]), ('normal control', [916863, 25193], [365, 0, 365])], [('regression', [20000000, 2376741], [34463, 2376741, 55854]), ('regression', [18969228, 1480792], [21471, 450020, 25521]), ('partial-repair probe', [624582, 1378603], [19990, 0, 19990]), ('partial-repair probe', [19201069, 465833], [6755, 0, 6755]), ('boundary control', [25000000, 12345], [179, 12345, 290]), ('boundary control', [19999999, 1], [0, 0, 0]), ('normal control', [10176860, 61801], [896, 0, 896]), ('normal control', [20000000, 541335], [7849, 541335, 12721]), ('normal control', [20613452, 926054], [13428, 926054, 21762]), ('normal control', [20270374, 43541], [631, 43541, 1023])]]
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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression 0 | [30847, 1421947, 43644] | [30847, 1421947, 43645] | Failed |
| regression 1 | [1816, 125208, 2942] | [1816, 125208, 2943] | Failed |
| partial-repair probe 2 | [717, 0, 717] | [717, 0, 717] | Passed |
| partial-repair probe 3 | [463, 31906, 750] | [463, 31906, 750] | Passed |
| boundary control 4 | [1450, 100000, 2350] | [1450, 100000, 2350] | Passed |
| boundary control 5 | [1450, 50000, 1900] | [1450, 50000, 1900] | Passed |
| normal control 6 | [5904, 407195, 9569] | [5904, 407195, 9569] | Passed |
| normal control 7 | [32016, 2208012, 51888] | [32016, 2208012, 51888] | Passed |
| normal control 8 | [26534, 1829965, 43004] | [26534, 1829965, 43004] | Passed |
| normal control 9 | [3043, 0, 3043] | [3043, 0, 3043] | Passed |
SHA-256 / baa38e7ce62e52e2f7d83eb4e63fdfdcca2ab8330826c3318c62fd1d7c6c7963
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
ytd, wages = x
base_tax = (wages * 145 + 5000) // 10000
over_before = max(0, ytd - 20000000)
over_after = max(0, ytd + wages - 20000000)
extra_wages = over_after - over_before
extra = (extra_wages * 9 + 500) // 1000
return [base_tax, extra_wages, (wages * 145 + extra_wages * 90) // 10000]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', [19294581, 2127366], [30847, 1421947, 43645]), ('regression', [20189609, 125208], [1816, 125208, 2943]), ('partial-repair probe', [2439490, 49414], [717, 0, 717]), ('partial-repair probe', [20723172, 31906], [463, 31906, 750]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('boundary control', [19950000, 100000], [1450, 50000, 1900]), ('normal control', [20158685, 407195], [5904, 407195, 9569]), ('normal control', [20518887, 2208012], [32016, 2208012, 51888]), ('normal control', [20000000, 1829965], [26534, 1829965, 43004]), ('normal control', [7554383, 209883], [3043, 0, 3043])], [('regression', [20189609, 125208], [1816, 125208, 2943]), ('regression', [20000000, 13601], [197, 13601, 319]), ('partial-repair probe', [20767841, 19138], [278, 19138, 450]), ('partial-repair probe', [20469014, 260626], [3779, 260626, 6125]), ('boundary control', [0, 0], [0, 0, 0]), ('boundary control', [25000000, 12345], [179, 12345, 290]), ('normal control', [8001356, 2662166], [38601, 0, 38601]), ('normal control', [19681988, 1173456], [17015, 855444, 24714]), ('normal control', [19655408, 1735735], [25168, 1391143, 37688]), ('normal control', [19686537, 15872], [230, 0, 230])], [('regression', [20164631, 554176], [8036, 554176, 13024]), ('regression', [20000000, 13601], [197, 13601, 319]), ('partial-repair probe', [23912137, 659488], [9563, 659488, 15498]), ('partial-repair probe', [21835663, 1842418], [26715, 1842418, 43297]), ('boundary control', [19999999, 1], [0, 0, 0]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('normal control', [3879860, 1040777], [15091, 0, 15091]), ('normal control', [4213397, 2332986], [33828, 0, 33828]), ('normal control', [20000000, 654261], [9487, 654261, 15375]), ('normal control', [20000000, 35595], [516, 35595, 836])], [('regression', [20333577, 41631], [604, 41631, 979]), ('regression', [20290634, 2600150], [37702, 2600150, 61103]), ('partial-repair probe', [19294581, 2127366], [30847, 1421947, 43645]), ('partial-repair probe', [20000000, 1204410], [17464, 1204410, 28304]), ('boundary control', [19950000, 100000], [1450, 50000, 1900]), ('boundary control', [0, 0], [0, 0, 0]), ('normal control', [4705614, 33884], [491, 0, 491]), ('normal control', [4401788, 1347616], [19540, 0, 19540]), ('normal control', [703223, 1018779], [14772, 0, 14772]), ('normal control', [916863, 25193], [365, 0, 365])], [('regression', [20000000, 2376741], [34463, 2376741, 55854]), ('regression', [18969228, 1480792], [21471, 450020, 25521]), ('partial-repair probe', [624582, 1378603], [19990, 0, 19990]), ('partial-repair probe', [19201069, 465833], [6755, 0, 6755]), ('boundary control', [25000000, 12345], [179, 12345, 290]), ('boundary control', [19999999, 1], [0, 0, 0]), ('normal control', [10176860, 61801], [896, 0, 896]), ('normal control', [20000000, 541335], [7849, 541335, 12721]), ('normal control', [20613452, 926054], [13428, 926054, 21762]), ('normal control', [20270374, 43541], [631, 43541, 1023])]]
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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression 0 | [30847, 1421947, 43644] | [30847, 1421947, 43645] | Failed |
| regression 1 | [1816, 125208, 2942] | [1816, 125208, 2943] | Failed |
| partial-repair probe 2 | [717, 0, 716] | [717, 0, 717] | Failed |
| partial-repair probe 3 | [463, 31906, 749] | [463, 31906, 750] | Failed |
| boundary control 4 | [1450, 100000, 2350] | [1450, 100000, 2350] | Passed |
| boundary control 5 | [1450, 50000, 1900] | [1450, 50000, 1900] | Passed |
| normal control 6 | [5904, 407195, 9569] | [5904, 407195, 9569] | Passed |
| normal control 7 | [32016, 2208012, 51888] | [32016, 2208012, 51888] | Passed |
| normal control 8 | [26534, 1829965, 43004] | [26534, 1829965, 43004] | Passed |
| normal control 9 | [3043, 0, 3043] | [3043, 0, 3043] | Passed |
SHA-256 / dda0f7d5677b1edfe73b2ac5525fa1f4419cc483de415f254222f59b6624d336
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
ytd, wages = x
base_tax = (wages * 145 + 5000) // 10000
over_before = max(0, ytd - 20000000)
over_after = max(0, ytd + wages - 20000000)
extra_wages = over_after - over_before
extra = (extra_wages * 9 + 500) // 1000
return [base_tax, extra_wages, base_tax + extra]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', [19294581, 2127366], [30847, 1421947, 43645]), ('regression', [20189609, 125208], [1816, 125208, 2943]), ('partial-repair probe', [2439490, 49414], [717, 0, 717]), ('partial-repair probe', [20723172, 31906], [463, 31906, 750]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('boundary control', [19950000, 100000], [1450, 50000, 1900]), ('normal control', [20158685, 407195], [5904, 407195, 9569]), ('normal control', [20518887, 2208012], [32016, 2208012, 51888]), ('normal control', [20000000, 1829965], [26534, 1829965, 43004]), ('normal control', [7554383, 209883], [3043, 0, 3043])], [('regression', [20189609, 125208], [1816, 125208, 2943]), ('regression', [20000000, 13601], [197, 13601, 319]), ('partial-repair probe', [20767841, 19138], [278, 19138, 450]), ('partial-repair probe', [20469014, 260626], [3779, 260626, 6125]), ('boundary control', [0, 0], [0, 0, 0]), ('boundary control', [25000000, 12345], [179, 12345, 290]), ('normal control', [8001356, 2662166], [38601, 0, 38601]), ('normal control', [19681988, 1173456], [17015, 855444, 24714]), ('normal control', [19655408, 1735735], [25168, 1391143, 37688]), ('normal control', [19686537, 15872], [230, 0, 230])], [('regression', [20164631, 554176], [8036, 554176, 13024]), ('regression', [20000000, 13601], [197, 13601, 319]), ('partial-repair probe', [23912137, 659488], [9563, 659488, 15498]), ('partial-repair probe', [21835663, 1842418], [26715, 1842418, 43297]), ('boundary control', [19999999, 1], [0, 0, 0]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('normal control', [3879860, 1040777], [15091, 0, 15091]), ('normal control', [4213397, 2332986], [33828, 0, 33828]), ('normal control', [20000000, 654261], [9487, 654261, 15375]), ('normal control', [20000000, 35595], [516, 35595, 836])], [('regression', [20333577, 41631], [604, 41631, 979]), ('regression', [20290634, 2600150], [37702, 2600150, 61103]), ('partial-repair probe', [19294581, 2127366], [30847, 1421947, 43645]), ('partial-repair probe', [20000000, 1204410], [17464, 1204410, 28304]), ('boundary control', [19950000, 100000], [1450, 50000, 1900]), ('boundary control', [0, 0], [0, 0, 0]), ('normal control', [4705614, 33884], [491, 0, 491]), ('normal control', [4401788, 1347616], [19540, 0, 19540]), ('normal control', [703223, 1018779], [14772, 0, 14772]), ('normal control', [916863, 25193], [365, 0, 365])], [('regression', [20000000, 2376741], [34463, 2376741, 55854]), ('regression', [18969228, 1480792], [21471, 450020, 25521]), ('partial-repair probe', [624582, 1378603], [19990, 0, 19990]), ('partial-repair probe', [19201069, 465833], [6755, 0, 6755]), ('boundary control', [25000000, 12345], [179, 12345, 290]), ('boundary control', [19999999, 1], [0, 0, 0]), ('normal control', [10176860, 61801], [896, 0, 896]), ('normal control', [20000000, 541335], [7849, 541335, 12721]), ('normal control', [20613452, 926054], [13428, 926054, 21762]), ('normal control', [20270374, 43541], [631, 43541, 1023])]]
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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression 0 | [30847, 1421947, 43645] | [30847, 1421947, 43645] | Passed |
| regression 1 | [1816, 125208, 2943] | [1816, 125208, 2943] | Passed |
| partial-repair probe 2 | [717, 0, 717] | [717, 0, 717] | Passed |
| partial-repair probe 3 | [463, 31906, 750] | [463, 31906, 750] | Passed |
| boundary control 4 | [1450, 100000, 2350] | [1450, 100000, 2350] | Passed |
| boundary control 5 | [1450, 50000, 1900] | [1450, 50000, 1900] | Passed |
| normal control 6 | [5904, 407195, 9569] | [5904, 407195, 9569] | Passed |
| normal control 7 | [32016, 2208012, 51888] | [32016, 2208012, 51888] | Passed |
| normal control 8 | [26534, 1829965, 43004] | [26534, 1829965, 43004] | Passed |
| normal control 9 | [3043, 0, 3043] | [3043, 0, 3043] | Passed |
SHA-256 / 88ce9a801341cd2ce432485eb3f07f0f09bc90af60d5b62174251bf974876b89
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 2026-09-29T14:46:30.848807+00:00.
Case digest / 7ac5a1765bae65fcd59fbe86ef8becfe4cc8e9cf1104e2c8704e6d787d3ba9ec