FA-58871 / Payroll withholding rules / Open access
Additional Medicare withholding threshold: prior excess measurement · case 01
Employees below the threshold get additional Medicare wages larger than the paycheck itself.
ROOT CAUSE
The excess before this paycheck is not floored at zero, so a negative prior excess inflates the difference.
VERIFIED REPAIR
Restore the contract rule at the prior excess measurement step: use `over_before = max(0, ytd - 20000000)`.
Unsuccessful approach: The attempt floors the prior excess but subtracts the current paycheck from year-to-date as if it were already included, double-counting the crossing paycheck.
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 = 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 (boundary)', [19950000, 100000], [1450, 50000, 1900]), ('regression (boundary)', [0, 0], [0, 0, 0]), ('partial-repair probe (boundary)', [25000000, 12345], [179, 12345, 290]), ('partial-repair probe', [20158685, 407195], [5904, 407195, 9569]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('normal control', [20000000, 1829965], [26534, 1829965, 43004]), ('normal control', [20000000, 654261], [9487, 654261, 15375]), ('normal control', [20000000, 1204410], [17464, 1204410, 28304]), ('normal control', [20000000, 35595], [516, 35595, 836])], [('regression (boundary)', [0, 0], [0, 0, 0]), ('regression (boundary)', [19999999, 1], [0, 0, 0]), ('partial-repair probe', [20518887, 2208012], [32016, 2208012, 51888]), ('partial-repair probe', [20723172, 31906], [463, 31906, 750]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('normal control', [20000000, 13601], [197, 13601, 319]), ('normal control', [20000000, 211218], [3063, 211218, 4964]), ('normal control', [20000000, 541335], [7849, 541335, 12721]), ('normal control', [20000000, 14262], [207, 14262, 335])], [('regression (boundary)', [19999999, 1], [0, 0, 0]), ('regression', [7554383, 209883], [3043, 0, 3043]), ('partial-repair probe', [20767841, 19138], [278, 19138, 450]), ('partial-repair probe', [20469014, 260626], [3779, 260626, 6125]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('normal control', [20000000, 15560], [226, 15560, 366]), ('normal control', [20000000, 46156], [669, 46156, 1084]), ('normal control', [20000000, 8435], [122, 8435, 198]), ('normal control', [20000000, 12860], [186, 12860, 302])], [('regression', [7554383, 209883], [3043, 0, 3043]), ('regression', [8001356, 2662166], [38601, 0, 38601]), ('partial-repair probe', [23912137, 659488], [9563, 659488, 15498]), ('partial-repair probe', [21835663, 1842418], [26715, 1842418, 43297]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('normal control', [20000000, 2376741], [34463, 2376741, 55854]), ('normal control', [20000000, 808350], [11721, 808350, 18996]), ('normal control', [20000000, 9624], [140, 9624, 227]), ('normal control', [20000000, 1041041], [15095, 1041041, 24464])], [('regression', [8001356, 2662166], [38601, 0, 38601]), ('regression', [2439490, 49414], [717, 0, 717]), ('partial-repair probe', [20631534, 41656], [604, 41656, 979]), ('partial-repair probe', [20609547, 21397], [310, 21397, 503]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('normal control', [20000000, 325488], [4720, 325488, 7649]), ('normal control', [20000000, 229558], [3329, 229558, 5395]), ('normal control', [20000000, 2962928], [42962, 2962928, 69628]), ('normal control', [20000000, 1917303], [27801, 1917303, 45057])]]
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 (boundary) 0 | [1450, 100000, 2350] | [1450, 50000, 1900] | Failed |
| regression (boundary) 1 | [0, 20000000, 180000] | [0, 0, 0] | Failed |
| partial-repair probe (boundary) 2 | [179, 12345, 290] | [179, 12345, 290] | Passed |
| partial-repair probe 3 | [5904, 407195, 9569] | [5904, 407195, 9569] | Passed |
| boundary control 4 | [1450, 100000, 2350] | [1450, 100000, 2350] | Passed |
| normal control 5 | [26534, 1829965, 43004] | [26534, 1829965, 43004] | Passed |
| normal control 6 | [9487, 654261, 15375] | [9487, 654261, 15375] | Passed |
| normal control 7 | [17464, 1204410, 28304] | [17464, 1204410, 28304] | Passed |
| normal control 8 | [516, 35595, 836] | [516, 35595, 836] | Passed |
SHA-256 / d240e780094e98d6d762b5b1e1c3538bbd429f5335ad4c7b22f5b84e8021f42a
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 - wages - 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 (boundary)', [19950000, 100000], [1450, 50000, 1900]), ('regression (boundary)', [0, 0], [0, 0, 0]), ('partial-repair probe (boundary)', [25000000, 12345], [179, 12345, 290]), ('partial-repair probe', [20158685, 407195], [5904, 407195, 9569]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('normal control', [20000000, 1829965], [26534, 1829965, 43004]), ('normal control', [20000000, 654261], [9487, 654261, 15375]), ('normal control', [20000000, 1204410], [17464, 1204410, 28304]), ('normal control', [20000000, 35595], [516, 35595, 836])], [('regression (boundary)', [0, 0], [0, 0, 0]), ('regression (boundary)', [19999999, 1], [0, 0, 0]), ('partial-repair probe', [20518887, 2208012], [32016, 2208012, 51888]), ('partial-repair probe', [20723172, 31906], [463, 31906, 750]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('normal control', [20000000, 13601], [197, 13601, 319]), ('normal control', [20000000, 211218], [3063, 211218, 4964]), ('normal control', [20000000, 541335], [7849, 541335, 12721]), ('normal control', [20000000, 14262], [207, 14262, 335])], [('regression (boundary)', [19999999, 1], [0, 0, 0]), ('regression', [7554383, 209883], [3043, 0, 3043]), ('partial-repair probe', [20767841, 19138], [278, 19138, 450]), ('partial-repair probe', [20469014, 260626], [3779, 260626, 6125]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('normal control', [20000000, 15560], [226, 15560, 366]), ('normal control', [20000000, 46156], [669, 46156, 1084]), ('normal control', [20000000, 8435], [122, 8435, 198]), ('normal control', [20000000, 12860], [186, 12860, 302])], [('regression', [7554383, 209883], [3043, 0, 3043]), ('regression', [8001356, 2662166], [38601, 0, 38601]), ('partial-repair probe', [23912137, 659488], [9563, 659488, 15498]), ('partial-repair probe', [21835663, 1842418], [26715, 1842418, 43297]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('normal control', [20000000, 2376741], [34463, 2376741, 55854]), ('normal control', [20000000, 808350], [11721, 808350, 18996]), ('normal control', [20000000, 9624], [140, 9624, 227]), ('normal control', [20000000, 1041041], [15095, 1041041, 24464])], [('regression', [8001356, 2662166], [38601, 0, 38601]), ('regression', [2439490, 49414], [717, 0, 717]), ('partial-repair probe', [20631534, 41656], [604, 41656, 979]), ('partial-repair probe', [20609547, 21397], [310, 21397, 503]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('normal control', [20000000, 325488], [4720, 325488, 7649]), ('normal control', [20000000, 229558], [3329, 229558, 5395]), ('normal control', [20000000, 2962928], [42962, 2962928, 69628]), ('normal control', [20000000, 1917303], [27801, 1917303, 45057])]]
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 (boundary) 0 | [1450, 50000, 1900] | [1450, 50000, 1900] | Passed |
| regression (boundary) 1 | [0, 0, 0] | [0, 0, 0] | Passed |
| partial-repair probe (boundary) 2 | [179, 24690, 401] | [179, 12345, 290] | Failed |
| partial-repair probe 3 | [5904, 565880, 10997] | [5904, 407195, 9569] | Failed |
| boundary control 4 | [1450, 100000, 2350] | [1450, 100000, 2350] | Passed |
| normal control 5 | [26534, 1829965, 43004] | [26534, 1829965, 43004] | Passed |
| normal control 6 | [9487, 654261, 15375] | [9487, 654261, 15375] | Passed |
| normal control 7 | [17464, 1204410, 28304] | [17464, 1204410, 28304] | Passed |
| normal control 8 | [516, 35595, 836] | [516, 35595, 836] | Passed |
SHA-256 / 20542187388bf68e4501330b1dce819991e5f8ebbb2809d682a1f1ac64c91cde
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 (boundary)', [19950000, 100000], [1450, 50000, 1900]), ('regression (boundary)', [0, 0], [0, 0, 0]), ('partial-repair probe (boundary)', [25000000, 12345], [179, 12345, 290]), ('partial-repair probe', [20158685, 407195], [5904, 407195, 9569]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('normal control', [20000000, 1829965], [26534, 1829965, 43004]), ('normal control', [20000000, 654261], [9487, 654261, 15375]), ('normal control', [20000000, 1204410], [17464, 1204410, 28304]), ('normal control', [20000000, 35595], [516, 35595, 836])], [('regression (boundary)', [0, 0], [0, 0, 0]), ('regression (boundary)', [19999999, 1], [0, 0, 0]), ('partial-repair probe', [20518887, 2208012], [32016, 2208012, 51888]), ('partial-repair probe', [20723172, 31906], [463, 31906, 750]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('normal control', [20000000, 13601], [197, 13601, 319]), ('normal control', [20000000, 211218], [3063, 211218, 4964]), ('normal control', [20000000, 541335], [7849, 541335, 12721]), ('normal control', [20000000, 14262], [207, 14262, 335])], [('regression (boundary)', [19999999, 1], [0, 0, 0]), ('regression', [7554383, 209883], [3043, 0, 3043]), ('partial-repair probe', [20767841, 19138], [278, 19138, 450]), ('partial-repair probe', [20469014, 260626], [3779, 260626, 6125]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('normal control', [20000000, 15560], [226, 15560, 366]), ('normal control', [20000000, 46156], [669, 46156, 1084]), ('normal control', [20000000, 8435], [122, 8435, 198]), ('normal control', [20000000, 12860], [186, 12860, 302])], [('regression', [7554383, 209883], [3043, 0, 3043]), ('regression', [8001356, 2662166], [38601, 0, 38601]), ('partial-repair probe', [23912137, 659488], [9563, 659488, 15498]), ('partial-repair probe', [21835663, 1842418], [26715, 1842418, 43297]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('normal control', [20000000, 2376741], [34463, 2376741, 55854]), ('normal control', [20000000, 808350], [11721, 808350, 18996]), ('normal control', [20000000, 9624], [140, 9624, 227]), ('normal control', [20000000, 1041041], [15095, 1041041, 24464])], [('regression', [8001356, 2662166], [38601, 0, 38601]), ('regression', [2439490, 49414], [717, 0, 717]), ('partial-repair probe', [20631534, 41656], [604, 41656, 979]), ('partial-repair probe', [20609547, 21397], [310, 21397, 503]), ('boundary control', [20000000, 100000], [1450, 100000, 2350]), ('normal control', [20000000, 325488], [4720, 325488, 7649]), ('normal control', [20000000, 229558], [3329, 229558, 5395]), ('normal control', [20000000, 2962928], [42962, 2962928, 69628]), ('normal control', [20000000, 1917303], [27801, 1917303, 45057])]]
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 (boundary) 0 | [1450, 50000, 1900] | [1450, 50000, 1900] | Passed |
| regression (boundary) 1 | [0, 0, 0] | [0, 0, 0] | Passed |
| partial-repair probe (boundary) 2 | [179, 12345, 290] | [179, 12345, 290] | Passed |
| partial-repair probe 3 | [5904, 407195, 9569] | [5904, 407195, 9569] | Passed |
| boundary control 4 | [1450, 100000, 2350] | [1450, 100000, 2350] | Passed |
| normal control 5 | [26534, 1829965, 43004] | [26534, 1829965, 43004] | Passed |
| normal control 6 | [9487, 654261, 15375] | [9487, 654261, 15375] | Passed |
| normal control 7 | [17464, 1204410, 28304] | [17464, 1204410, 28304] | Passed |
| normal control 8 | [516, 35595, 836] | [516, 35595, 836] | Passed |
SHA-256 / 6518578a9f724417a447afd7a663d57fb1c1facfccf024d5b82b94e6478a7d79
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 2026-09-29T14:46:30.829820+00:00.
Case digest / e449439b2b0b858c310138f60671bf0072708c628fe2be1d83e0beeea6a502ff