FA-59111 / Payroll withholding rules / Open access
Group-term life imputed income: age band boundary · case 01
Employees exactly at a band's starting age are charged the younger band's rate.
ROOT CAUSE
Band upper limits are treated as inclusive, keeping boundary ages in the lower band.
VERIFIED REPAIR
Restore the contract rule at the age band boundary step: use `if x['age'] < upper:`.
Unsuccessful approach: The attempt uses age at next birthday, moving employees into the older band a year early.
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 = 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': 23127161, 'age': 70, 'months': 4, 'employee_paid': 0}, 149368), ('regression', {'coverage': 16856564, 'age': 70, 'months': 8, 'employee_paid': 0}, 195396), ('partial-repair probe', {'coverage': 31951582, 'age': 24, 'months': 2, 'employee_paid': 0}, 2695), ('partial-repair probe', {'coverage': 26680167, 'age': 24, 'months': 8, 'employee_paid': 0}, 8672), ('normal control', {'coverage': 5000000, 'age': 30, 'months': 6, 'employee_paid': 0}, 0), ('normal control', {'coverage': 7307633, 'age': 24, 'months': 3, 'employee_paid': 19462}, 0), ('normal control', {'coverage': 5000000, 'age': 64, 'months': 3, 'employee_paid': 0}, 0), ('normal control', {'coverage': 5000000, 'age': 24, 'months': 10, 'employee_paid': 0}, 0)], [('regression', {'coverage': 16856564, 'age': 70, 'months': 8, 'employee_paid': 0}, 195396), ('regression', {'coverage': 9181727, 'age': 25, 'months': 6, 'employee_paid': 0}, 1505), ('partial-repair probe', {'coverage': 20685038, 'age': 29, 'months': 4, 'employee_paid': 4881}, 0), ('partial-repair probe', {'coverage': 20847001, 'age': 64, 'months': 8, 'employee_paid': 0}, 83672), ('normal control', {'coverage': 4843457, 'age': 30, 'months': 9, 'employee_paid': 37040}, 0), ('normal control', {'coverage': 19400395, 'age': 25, 'months': 7, 'employee_paid': 36789}, 0), ('normal control', {'coverage': 5000000, 'age': 25, 'months': 6, 'employee_paid': 0}, 0), ('normal control', {'coverage': 5000000, 'age': 65, 'months': 8, 'employee_paid': 12759}, 0)], [('regression', {'coverage': 9181727, 'age': 25, 'months': 6, 'employee_paid': 0}, 1505), ('regression', {'coverage': 15762067, 'age': 70, 'months': 10, 'employee_paid': 0}, 221699), ('partial-repair probe', {'coverage': 6128065, 'age': 64, 'months': 12, 'employee_paid': 8257}, 677), ('partial-repair probe', {'coverage': 25191576, 'age': 24, 'months': 5, 'employee_paid': 4142}, 906), ('normal control', {'coverage': 5000000, 'age': 61, 'months': 12, 'employee_paid': 2761}, 0), ('normal control', {'coverage': 22529249, 'age': 29, 'months': 1, 'employee_paid': 38785}, 0), ('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': 15762067, 'age': 70, 'months': 10, 'employee_paid': 0}, 221699), ('regression', {'coverage': 45748038, 'age': 25, 'months': 3, 'employee_paid': 2480}, 4855), ('partial-repair probe', {'coverage': 18671520, 'age': 24, 'months': 12, 'employee_paid': 0}, 8203), ('partial-repair probe', {'coverage': 27955665, 'age': 24, 'months': 10, 'employee_paid': 5575}, 5903), ('normal control', {'coverage': 9261111, 'age': 29, 'months': 1, 'employee_paid': 24425}, 0), ('normal control', {'coverage': 20304981, 'age': 29, 'months': 10, 'employee_paid': 12373}, 0), ('normal control', {'coverage': 5000000, 'age': 64, 'months': 12, 'employee_paid': 0}, 0), ('normal control', {'coverage': 5000000, 'age': 27, 'months': 10, 'employee_paid': 0}, 0)], [('regression', {'coverage': 45748038, 'age': 25, 'months': 3, 'employee_paid': 2480}, 4855), ('regression', {'coverage': 46403884, 'age': 30, 'months': 4, 'employee_paid': 0}, 13249), ('partial-repair probe', {'coverage': 9682341, 'age': 49, 'months': 2, 'employee_paid': 0}, 1405), ('partial-repair probe', {'coverage': 11740179, 'age': 64, 'months': 10, 'employee_paid': 0}, 44485), ('normal control', {'coverage': 635952, 'age': 25, 'months': 4, 'employee_paid': 16597}, 0), ('normal control', {'coverage': 22006788, 'age': 66, 'months': 9, 'employee_paid': 6358}, 188030), ('normal control', {'coverage': 5000000, 'age': 29, 'months': 2, 'employee_paid': 22644}, 0), ('normal control', {'coverage': 15550480, 'age': 24, 'months': 6, 'employee_paid': 26462}, 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 | 92086 | 149368 | Failed |
| regression 1 | 120463 | 195396 | Failed |
| partial-repair probe 2 | 2695 | 2695 | Passed |
| partial-repair probe 3 | 8672 | 8672 | Passed |
| normal control 4 | 0 | 0 | Passed |
| normal control 5 | 0 | 0 | Passed |
| normal control 6 | 0 | 0 | Passed |
| normal control 7 | 0 | 0 | Passed |
SHA-256 / 57a7abf1b4a0199a131fdba7bd7ee7a5f89eda20006f4e3867cf7fb0cca18132
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'] + 1 < 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': 23127161, 'age': 70, 'months': 4, 'employee_paid': 0}, 149368), ('regression', {'coverage': 16856564, 'age': 70, 'months': 8, 'employee_paid': 0}, 195396), ('partial-repair probe', {'coverage': 31951582, 'age': 24, 'months': 2, 'employee_paid': 0}, 2695), ('partial-repair probe', {'coverage': 26680167, 'age': 24, 'months': 8, 'employee_paid': 0}, 8672), ('normal control', {'coverage': 5000000, 'age': 30, 'months': 6, 'employee_paid': 0}, 0), ('normal control', {'coverage': 7307633, 'age': 24, 'months': 3, 'employee_paid': 19462}, 0), ('normal control', {'coverage': 5000000, 'age': 64, 'months': 3, 'employee_paid': 0}, 0), ('normal control', {'coverage': 5000000, 'age': 24, 'months': 10, 'employee_paid': 0}, 0)], [('regression', {'coverage': 16856564, 'age': 70, 'months': 8, 'employee_paid': 0}, 195396), ('regression', {'coverage': 9181727, 'age': 25, 'months': 6, 'employee_paid': 0}, 1505), ('partial-repair probe', {'coverage': 20685038, 'age': 29, 'months': 4, 'employee_paid': 4881}, 0), ('partial-repair probe', {'coverage': 20847001, 'age': 64, 'months': 8, 'employee_paid': 0}, 83672), ('normal control', {'coverage': 4843457, 'age': 30, 'months': 9, 'employee_paid': 37040}, 0), ('normal control', {'coverage': 19400395, 'age': 25, 'months': 7, 'employee_paid': 36789}, 0), ('normal control', {'coverage': 5000000, 'age': 25, 'months': 6, 'employee_paid': 0}, 0), ('normal control', {'coverage': 5000000, 'age': 65, 'months': 8, 'employee_paid': 12759}, 0)], [('regression', {'coverage': 9181727, 'age': 25, 'months': 6, 'employee_paid': 0}, 1505), ('regression', {'coverage': 15762067, 'age': 70, 'months': 10, 'employee_paid': 0}, 221699), ('partial-repair probe', {'coverage': 6128065, 'age': 64, 'months': 12, 'employee_paid': 8257}, 677), ('partial-repair probe', {'coverage': 25191576, 'age': 24, 'months': 5, 'employee_paid': 4142}, 906), ('normal control', {'coverage': 5000000, 'age': 61, 'months': 12, 'employee_paid': 2761}, 0), ('normal control', {'coverage': 22529249, 'age': 29, 'months': 1, 'employee_paid': 38785}, 0), ('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': 15762067, 'age': 70, 'months': 10, 'employee_paid': 0}, 221699), ('regression', {'coverage': 45748038, 'age': 25, 'months': 3, 'employee_paid': 2480}, 4855), ('partial-repair probe', {'coverage': 18671520, 'age': 24, 'months': 12, 'employee_paid': 0}, 8203), ('partial-repair probe', {'coverage': 27955665, 'age': 24, 'months': 10, 'employee_paid': 5575}, 5903), ('normal control', {'coverage': 9261111, 'age': 29, 'months': 1, 'employee_paid': 24425}, 0), ('normal control', {'coverage': 20304981, 'age': 29, 'months': 10, 'employee_paid': 12373}, 0), ('normal control', {'coverage': 5000000, 'age': 64, 'months': 12, 'employee_paid': 0}, 0), ('normal control', {'coverage': 5000000, 'age': 27, 'months': 10, 'employee_paid': 0}, 0)], [('regression', {'coverage': 45748038, 'age': 25, 'months': 3, 'employee_paid': 2480}, 4855), ('regression', {'coverage': 46403884, 'age': 30, 'months': 4, 'employee_paid': 0}, 13249), ('partial-repair probe', {'coverage': 9682341, 'age': 49, 'months': 2, 'employee_paid': 0}, 1405), ('partial-repair probe', {'coverage': 11740179, 'age': 64, 'months': 10, 'employee_paid': 0}, 44485), ('normal control', {'coverage': 635952, 'age': 25, 'months': 4, 'employee_paid': 16597}, 0), ('normal control', {'coverage': 22006788, 'age': 66, 'months': 9, 'employee_paid': 6358}, 188030), ('normal control', {'coverage': 5000000, 'age': 29, 'months': 2, 'employee_paid': 22644}, 0), ('normal control', {'coverage': 15550480, 'age': 24, 'months': 6, 'employee_paid': 26462}, 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 | 149368 | 149368 | Passed |
| regression 1 | 195396 | 195396 | Passed |
| partial-repair probe 2 | 3234 | 2695 | Failed |
| partial-repair probe 3 | 10406 | 8672 | Failed |
| normal control 4 | 0 | 0 | Passed |
| normal control 5 | 0 | 0 | Passed |
| normal control 6 | 0 | 0 | Passed |
| normal control 7 | 0 | 0 | Passed |
SHA-256 / 96ac9ac80bc31b98e6eaca7f374cbe5cbe4bec16f5a60c61934fad5fb920d100
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': 23127161, 'age': 70, 'months': 4, 'employee_paid': 0}, 149368), ('regression', {'coverage': 16856564, 'age': 70, 'months': 8, 'employee_paid': 0}, 195396), ('partial-repair probe', {'coverage': 31951582, 'age': 24, 'months': 2, 'employee_paid': 0}, 2695), ('partial-repair probe', {'coverage': 26680167, 'age': 24, 'months': 8, 'employee_paid': 0}, 8672), ('normal control', {'coverage': 5000000, 'age': 30, 'months': 6, 'employee_paid': 0}, 0), ('normal control', {'coverage': 7307633, 'age': 24, 'months': 3, 'employee_paid': 19462}, 0), ('normal control', {'coverage': 5000000, 'age': 64, 'months': 3, 'employee_paid': 0}, 0), ('normal control', {'coverage': 5000000, 'age': 24, 'months': 10, 'employee_paid': 0}, 0)], [('regression', {'coverage': 16856564, 'age': 70, 'months': 8, 'employee_paid': 0}, 195396), ('regression', {'coverage': 9181727, 'age': 25, 'months': 6, 'employee_paid': 0}, 1505), ('partial-repair probe', {'coverage': 20685038, 'age': 29, 'months': 4, 'employee_paid': 4881}, 0), ('partial-repair probe', {'coverage': 20847001, 'age': 64, 'months': 8, 'employee_paid': 0}, 83672), ('normal control', {'coverage': 4843457, 'age': 30, 'months': 9, 'employee_paid': 37040}, 0), ('normal control', {'coverage': 19400395, 'age': 25, 'months': 7, 'employee_paid': 36789}, 0), ('normal control', {'coverage': 5000000, 'age': 25, 'months': 6, 'employee_paid': 0}, 0), ('normal control', {'coverage': 5000000, 'age': 65, 'months': 8, 'employee_paid': 12759}, 0)], [('regression', {'coverage': 9181727, 'age': 25, 'months': 6, 'employee_paid': 0}, 1505), ('regression', {'coverage': 15762067, 'age': 70, 'months': 10, 'employee_paid': 0}, 221699), ('partial-repair probe', {'coverage': 6128065, 'age': 64, 'months': 12, 'employee_paid': 8257}, 677), ('partial-repair probe', {'coverage': 25191576, 'age': 24, 'months': 5, 'employee_paid': 4142}, 906), ('normal control', {'coverage': 5000000, 'age': 61, 'months': 12, 'employee_paid': 2761}, 0), ('normal control', {'coverage': 22529249, 'age': 29, 'months': 1, 'employee_paid': 38785}, 0), ('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': 15762067, 'age': 70, 'months': 10, 'employee_paid': 0}, 221699), ('regression', {'coverage': 45748038, 'age': 25, 'months': 3, 'employee_paid': 2480}, 4855), ('partial-repair probe', {'coverage': 18671520, 'age': 24, 'months': 12, 'employee_paid': 0}, 8203), ('partial-repair probe', {'coverage': 27955665, 'age': 24, 'months': 10, 'employee_paid': 5575}, 5903), ('normal control', {'coverage': 9261111, 'age': 29, 'months': 1, 'employee_paid': 24425}, 0), ('normal control', {'coverage': 20304981, 'age': 29, 'months': 10, 'employee_paid': 12373}, 0), ('normal control', {'coverage': 5000000, 'age': 64, 'months': 12, 'employee_paid': 0}, 0), ('normal control', {'coverage': 5000000, 'age': 27, 'months': 10, 'employee_paid': 0}, 0)], [('regression', {'coverage': 45748038, 'age': 25, 'months': 3, 'employee_paid': 2480}, 4855), ('regression', {'coverage': 46403884, 'age': 30, 'months': 4, 'employee_paid': 0}, 13249), ('partial-repair probe', {'coverage': 9682341, 'age': 49, 'months': 2, 'employee_paid': 0}, 1405), ('partial-repair probe', {'coverage': 11740179, 'age': 64, 'months': 10, 'employee_paid': 0}, 44485), ('normal control', {'coverage': 635952, 'age': 25, 'months': 4, 'employee_paid': 16597}, 0), ('normal control', {'coverage': 22006788, 'age': 66, 'months': 9, 'employee_paid': 6358}, 188030), ('normal control', {'coverage': 5000000, 'age': 29, 'months': 2, 'employee_paid': 22644}, 0), ('normal control', {'coverage': 15550480, 'age': 24, 'months': 6, 'employee_paid': 26462}, 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 | 149368 | 149368 | Passed |
| regression 1 | 195396 | 195396 | Passed |
| partial-repair probe 2 | 2695 | 2695 | Passed |
| partial-repair probe 3 | 8672 | 8672 | Passed |
| normal control 4 | 0 | 0 | Passed |
| normal control 5 | 0 | 0 | Passed |
| normal control 6 | 0 | 0 | Passed |
| normal control 7 | 0 | 0 | Passed |
SHA-256 / 4e66eaab393e837c05276952af8c83413f7f901ec737ab232e02154cba1ad553
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 2026-09-29T14:46:33.098021+00:00.
Case digest / 941c0e6dd92f3e0a78524ffabaa9f580303b1cad2914622f3caa93ce9fdfbe2b