FA-59121 / Payroll withholding rules / Open access
Group-term life imputed income: employee payment offset · case 01
Employees paying part of the premium after tax still see the full imputed cost.
ROOT CAUSE
After-tax employee payments are not subtracted from the imputed cost.
VERIFIED REPAIR
Restore the contract rule at the employee payment offset step: use `imputed = max(0, cost - x['employee_paid'])`.
Unsuccessful approach: The attempt subtracts payments after the floor, producing negative imputed income.
Case contract
Input {coverage cents, age, months, employee_paid}. Monthly cost per 1,000.00 of coverage by age band (<25:5, <30:6, <35:8, <40:9, <45:10, <50:15, <55:23, <60:43, <65:66, <70:127, else 206 cents). Excess = max(0, coverage - 50,000.00). Imputed = max(0, excess/100000*rate*months - employee_paid), half-up. Return imputed cents.
Why this case matters
Imputed income for employer-paid life insurance depends on age bands, the 50,000 exclusion and after-tax employee payments.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
import math
N = 1
observations = []
def solve(x):
bands = [(25, 5), (30, 6), (35, 8), (40, 9), (45, 10), (50, 15), (55, 23), (60, 43), (65, 66), (70, 127)]
rate = 206
for upper, r in bands:
if x['age'] < upper:
rate = r
break
excess = max(0, x['coverage'] - 5000000)
cost = Fraction(excess * rate * x['months'], 100000)
imputed = cost
return math.floor(imputed + Fraction(1, 2))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'coverage': 7307633, 'age': 24, 'months': 3, 'employee_paid': 19462}, 0), ('regression', {'coverage': 20685038, 'age': 29, 'months': 4, 'employee_paid': 4881}, 0), ('partial-repair probe', {'coverage': 4843457, 'age': 30, 'months': 9, 'employee_paid': 37040}, 0), ('partial-repair probe', {'coverage': 19400395, 'age': 25, 'months': 7, 'employee_paid': 36789}, 0), ('normal control', {'coverage': 31951582, 'age': 24, 'months': 2, 'employee_paid': 0}, 2695), ('normal control', {'coverage': 5000000, 'age': 30, 'months': 6, 'employee_paid': 0}, 0), ('normal control', {'coverage': 5000000, 'age': 64, 'months': 3, 'employee_paid': 0}, 0), ('normal control', {'coverage': 23127161, 'age': 70, 'months': 4, 'employee_paid': 0}, 149368)], [('regression', {'coverage': 20685038, 'age': 29, 'months': 4, 'employee_paid': 4881}, 0), ('regression', {'coverage': 45748038, 'age': 25, 'months': 3, 'employee_paid': 2480}, 4855), ('partial-repair probe', {'coverage': 4843457, 'age': 30, 'months': 9, 'employee_paid': 37040}, 0), ('partial-repair probe', {'coverage': 19400395, 'age': 25, 'months': 7, 'employee_paid': 36789}, 0), ('normal control', {'coverage': 5000000, 'age': 24, 'months': 10, 'employee_paid': 0}, 0), ('normal control', {'coverage': 26680167, 'age': 24, 'months': 8, 'employee_paid': 0}, 8672), ('normal control', {'coverage': 16856564, 'age': 70, 'months': 8, 'employee_paid': 0}, 195396), ('normal control', {'coverage': 9181727, 'age': 25, 'months': 6, 'employee_paid': 0}, 1505)], [('regression', {'coverage': 19400395, 'age': 25, 'months': 7, 'employee_paid': 36789}, 0), ('regression', {'coverage': 45748038, 'age': 25, 'months': 3, 'employee_paid': 2480}, 4855), ('partial-repair probe', {'coverage': 5000000, 'age': 65, 'months': 8, 'employee_paid': 12759}, 0), ('partial-repair probe', {'coverage': 5000000, 'age': 61, 'months': 12, 'employee_paid': 2761}, 0), ('normal control', {'coverage': 15762067, 'age': 70, 'months': 10, 'employee_paid': 0}, 221699), ('normal control', {'coverage': 5000000, 'age': 25, 'months': 6, 'employee_paid': 0}, 0), ('normal control', {'coverage': 46403884, 'age': 30, 'months': 4, 'employee_paid': 0}, 13249), ('normal control', {'coverage': 5153794, 'age': 25, 'months': 6, 'employee_paid': 0}, 55)], [('regression', {'coverage': 22529249, 'age': 29, 'months': 1, 'employee_paid': 38785}, 0), ('regression', {'coverage': 19400395, 'age': 25, 'months': 7, 'employee_paid': 36789}, 0), ('partial-repair probe', {'coverage': 9261111, 'age': 29, 'months': 1, 'employee_paid': 24425}, 0), ('partial-repair probe', {'coverage': 20304981, 'age': 29, 'months': 10, 'employee_paid': 12373}, 0), ('normal control', {'coverage': 44993212, 'age': 70, 'months': 2, 'employee_paid': 0}, 164772), ('normal control', {'coverage': 20847001, 'age': 64, 'months': 8, 'employee_paid': 0}, 83672), ('normal control', {'coverage': 15471033, 'age': 66, 'months': 5, 'employee_paid': 0}, 66491), ('normal control', {'coverage': 5000000, 'age': 50, 'months': 9, 'employee_paid': 0}, 0)], [('regression', {'coverage': 9261111, 'age': 29, 'months': 1, 'employee_paid': 24425}, 0), ('regression', {'coverage': 22529249, 'age': 29, 'months': 1, 'employee_paid': 38785}, 0), ('partial-repair probe', {'coverage': 20304981, 'age': 29, 'months': 10, 'employee_paid': 12373}, 0), ('partial-repair probe', {'coverage': 635952, 'age': 25, 'months': 4, 'employee_paid': 16597}, 0), ('normal control', {'coverage': 17670130, 'age': 50, 'months': 11, 'employee_paid': 0}, 32055), ('normal control', {'coverage': 40943559, 'age': 30, 'months': 6, 'employee_paid': 0}, 17253), ('normal control', {'coverage': 5000000, 'age': 64, 'months': 12, 'employee_paid': 0}, 0), ('normal control', {'coverage': 5000000, 'age': 27, 'months': 10, 'employee_paid': 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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression 0 | 346 | 0 | Failed |
| regression 1 | 3764 | 0 | Failed |
| partial-repair probe 2 | 0 | 0 | Passed |
| partial-repair probe 3 | 6048 | 0 | Failed |
| normal control 4 | 2695 | 2695 | Passed |
| normal control 5 | 0 | 0 | Passed |
| normal control 6 | 0 | 0 | Passed |
| normal control 7 | 149368 | 149368 | Passed |
SHA-256 / 9f2888aca3c1358eac59135b270215f243ef6c9b21b2369a382439ffd0e0e108
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
import math
N = 1
observations = []
def solve(x):
bands = [(25, 5), (30, 6), (35, 8), (40, 9), (45, 10), (50, 15), (55, 23), (60, 43), (65, 66), (70, 127)]
rate = 206
for upper, r in bands:
if x['age'] < upper:
rate = r
break
excess = max(0, x['coverage'] - 5000000)
cost = Fraction(excess * rate * x['months'], 100000)
imputed = max(0, cost) - x['employee_paid']
return math.floor(imputed + Fraction(1, 2))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'coverage': 7307633, 'age': 24, 'months': 3, 'employee_paid': 19462}, 0), ('regression', {'coverage': 20685038, 'age': 29, 'months': 4, 'employee_paid': 4881}, 0), ('partial-repair probe', {'coverage': 4843457, 'age': 30, 'months': 9, 'employee_paid': 37040}, 0), ('partial-repair probe', {'coverage': 19400395, 'age': 25, 'months': 7, 'employee_paid': 36789}, 0), ('normal control', {'coverage': 31951582, 'age': 24, 'months': 2, 'employee_paid': 0}, 2695), ('normal control', {'coverage': 5000000, 'age': 30, 'months': 6, 'employee_paid': 0}, 0), ('normal control', {'coverage': 5000000, 'age': 64, 'months': 3, 'employee_paid': 0}, 0), ('normal control', {'coverage': 23127161, 'age': 70, 'months': 4, 'employee_paid': 0}, 149368)], [('regression', {'coverage': 20685038, 'age': 29, 'months': 4, 'employee_paid': 4881}, 0), ('regression', {'coverage': 45748038, 'age': 25, 'months': 3, 'employee_paid': 2480}, 4855), ('partial-repair probe', {'coverage': 4843457, 'age': 30, 'months': 9, 'employee_paid': 37040}, 0), ('partial-repair probe', {'coverage': 19400395, 'age': 25, 'months': 7, 'employee_paid': 36789}, 0), ('normal control', {'coverage': 5000000, 'age': 24, 'months': 10, 'employee_paid': 0}, 0), ('normal control', {'coverage': 26680167, 'age': 24, 'months': 8, 'employee_paid': 0}, 8672), ('normal control', {'coverage': 16856564, 'age': 70, 'months': 8, 'employee_paid': 0}, 195396), ('normal control', {'coverage': 9181727, 'age': 25, 'months': 6, 'employee_paid': 0}, 1505)], [('regression', {'coverage': 19400395, 'age': 25, 'months': 7, 'employee_paid': 36789}, 0), ('regression', {'coverage': 45748038, 'age': 25, 'months': 3, 'employee_paid': 2480}, 4855), ('partial-repair probe', {'coverage': 5000000, 'age': 65, 'months': 8, 'employee_paid': 12759}, 0), ('partial-repair probe', {'coverage': 5000000, 'age': 61, 'months': 12, 'employee_paid': 2761}, 0), ('normal control', {'coverage': 15762067, 'age': 70, 'months': 10, 'employee_paid': 0}, 221699), ('normal control', {'coverage': 5000000, 'age': 25, 'months': 6, 'employee_paid': 0}, 0), ('normal control', {'coverage': 46403884, 'age': 30, 'months': 4, 'employee_paid': 0}, 13249), ('normal control', {'coverage': 5153794, 'age': 25, 'months': 6, 'employee_paid': 0}, 55)], [('regression', {'coverage': 22529249, 'age': 29, 'months': 1, 'employee_paid': 38785}, 0), ('regression', {'coverage': 19400395, 'age': 25, 'months': 7, 'employee_paid': 36789}, 0), ('partial-repair probe', {'coverage': 9261111, 'age': 29, 'months': 1, 'employee_paid': 24425}, 0), ('partial-repair probe', {'coverage': 20304981, 'age': 29, 'months': 10, 'employee_paid': 12373}, 0), ('normal control', {'coverage': 44993212, 'age': 70, 'months': 2, 'employee_paid': 0}, 164772), ('normal control', {'coverage': 20847001, 'age': 64, 'months': 8, 'employee_paid': 0}, 83672), ('normal control', {'coverage': 15471033, 'age': 66, 'months': 5, 'employee_paid': 0}, 66491), ('normal control', {'coverage': 5000000, 'age': 50, 'months': 9, 'employee_paid': 0}, 0)], [('regression', {'coverage': 9261111, 'age': 29, 'months': 1, 'employee_paid': 24425}, 0), ('regression', {'coverage': 22529249, 'age': 29, 'months': 1, 'employee_paid': 38785}, 0), ('partial-repair probe', {'coverage': 20304981, 'age': 29, 'months': 10, 'employee_paid': 12373}, 0), ('partial-repair probe', {'coverage': 635952, 'age': 25, 'months': 4, 'employee_paid': 16597}, 0), ('normal control', {'coverage': 17670130, 'age': 50, 'months': 11, 'employee_paid': 0}, 32055), ('normal control', {'coverage': 40943559, 'age': 30, 'months': 6, 'employee_paid': 0}, 17253), ('normal control', {'coverage': 5000000, 'age': 64, 'months': 12, 'employee_paid': 0}, 0), ('normal control', {'coverage': 5000000, 'age': 27, 'months': 10, 'employee_paid': 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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression 0 | -19116 | 0 | Failed |
| regression 1 | -1117 | 0 | Failed |
| partial-repair probe 2 | -37040 | 0 | Failed |
| partial-repair probe 3 | -30741 | 0 | Failed |
| normal control 4 | 2695 | 2695 | Passed |
| normal control 5 | 0 | 0 | Passed |
| normal control 6 | 0 | 0 | Passed |
| normal control 7 | 149368 | 149368 | Passed |
SHA-256 / ef78e0f016094f69d3278b58e55a4164b6656296c5461978783396e8a424773f
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
import math
N = 1
observations = []
def solve(x):
bands = [(25, 5), (30, 6), (35, 8), (40, 9), (45, 10), (50, 15), (55, 23), (60, 43), (65, 66), (70, 127)]
rate = 206
for upper, r in bands:
if x['age'] < upper:
rate = r
break
excess = max(0, x['coverage'] - 5000000)
cost = Fraction(excess * rate * x['months'], 100000)
imputed = max(0, cost - x['employee_paid'])
return math.floor(imputed + Fraction(1, 2))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'coverage': 7307633, 'age': 24, 'months': 3, 'employee_paid': 19462}, 0), ('regression', {'coverage': 20685038, 'age': 29, 'months': 4, 'employee_paid': 4881}, 0), ('partial-repair probe', {'coverage': 4843457, 'age': 30, 'months': 9, 'employee_paid': 37040}, 0), ('partial-repair probe', {'coverage': 19400395, 'age': 25, 'months': 7, 'employee_paid': 36789}, 0), ('normal control', {'coverage': 31951582, 'age': 24, 'months': 2, 'employee_paid': 0}, 2695), ('normal control', {'coverage': 5000000, 'age': 30, 'months': 6, 'employee_paid': 0}, 0), ('normal control', {'coverage': 5000000, 'age': 64, 'months': 3, 'employee_paid': 0}, 0), ('normal control', {'coverage': 23127161, 'age': 70, 'months': 4, 'employee_paid': 0}, 149368)], [('regression', {'coverage': 20685038, 'age': 29, 'months': 4, 'employee_paid': 4881}, 0), ('regression', {'coverage': 45748038, 'age': 25, 'months': 3, 'employee_paid': 2480}, 4855), ('partial-repair probe', {'coverage': 4843457, 'age': 30, 'months': 9, 'employee_paid': 37040}, 0), ('partial-repair probe', {'coverage': 19400395, 'age': 25, 'months': 7, 'employee_paid': 36789}, 0), ('normal control', {'coverage': 5000000, 'age': 24, 'months': 10, 'employee_paid': 0}, 0), ('normal control', {'coverage': 26680167, 'age': 24, 'months': 8, 'employee_paid': 0}, 8672), ('normal control', {'coverage': 16856564, 'age': 70, 'months': 8, 'employee_paid': 0}, 195396), ('normal control', {'coverage': 9181727, 'age': 25, 'months': 6, 'employee_paid': 0}, 1505)], [('regression', {'coverage': 19400395, 'age': 25, 'months': 7, 'employee_paid': 36789}, 0), ('regression', {'coverage': 45748038, 'age': 25, 'months': 3, 'employee_paid': 2480}, 4855), ('partial-repair probe', {'coverage': 5000000, 'age': 65, 'months': 8, 'employee_paid': 12759}, 0), ('partial-repair probe', {'coverage': 5000000, 'age': 61, 'months': 12, 'employee_paid': 2761}, 0), ('normal control', {'coverage': 15762067, 'age': 70, 'months': 10, 'employee_paid': 0}, 221699), ('normal control', {'coverage': 5000000, 'age': 25, 'months': 6, 'employee_paid': 0}, 0), ('normal control', {'coverage': 46403884, 'age': 30, 'months': 4, 'employee_paid': 0}, 13249), ('normal control', {'coverage': 5153794, 'age': 25, 'months': 6, 'employee_paid': 0}, 55)], [('regression', {'coverage': 22529249, 'age': 29, 'months': 1, 'employee_paid': 38785}, 0), ('regression', {'coverage': 19400395, 'age': 25, 'months': 7, 'employee_paid': 36789}, 0), ('partial-repair probe', {'coverage': 9261111, 'age': 29, 'months': 1, 'employee_paid': 24425}, 0), ('partial-repair probe', {'coverage': 20304981, 'age': 29, 'months': 10, 'employee_paid': 12373}, 0), ('normal control', {'coverage': 44993212, 'age': 70, 'months': 2, 'employee_paid': 0}, 164772), ('normal control', {'coverage': 20847001, 'age': 64, 'months': 8, 'employee_paid': 0}, 83672), ('normal control', {'coverage': 15471033, 'age': 66, 'months': 5, 'employee_paid': 0}, 66491), ('normal control', {'coverage': 5000000, 'age': 50, 'months': 9, 'employee_paid': 0}, 0)], [('regression', {'coverage': 9261111, 'age': 29, 'months': 1, 'employee_paid': 24425}, 0), ('regression', {'coverage': 22529249, 'age': 29, 'months': 1, 'employee_paid': 38785}, 0), ('partial-repair probe', {'coverage': 20304981, 'age': 29, 'months': 10, 'employee_paid': 12373}, 0), ('partial-repair probe', {'coverage': 635952, 'age': 25, 'months': 4, 'employee_paid': 16597}, 0), ('normal control', {'coverage': 17670130, 'age': 50, 'months': 11, 'employee_paid': 0}, 32055), ('normal control', {'coverage': 40943559, 'age': 30, 'months': 6, 'employee_paid': 0}, 17253), ('normal control', {'coverage': 5000000, 'age': 64, 'months': 12, 'employee_paid': 0}, 0), ('normal control', {'coverage': 5000000, 'age': 27, 'months': 10, 'employee_paid': 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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression 0 | 0 | 0 | Passed |
| regression 1 | 0 | 0 | Passed |
| partial-repair probe 2 | 0 | 0 | Passed |
| partial-repair probe 3 | 0 | 0 | Passed |
| normal control 4 | 2695 | 2695 | Passed |
| normal control 5 | 0 | 0 | Passed |
| normal control 6 | 0 | 0 | Passed |
| normal control 7 | 149368 | 149368 | Passed |
SHA-256 / 7c0f06d30892b4fa3dc196f37004286812e69519078e0ad787a0f16ff0dd33e4
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 2026-09-29T14:46:33.131242+00:00.
Case digest / fe8ba393efc0ae9bcb77367d54e5b4836585d557db9a17df9412d0f5330151f0