FA-59061 / Payroll withholding rules / Open access

HSA payroll contribution limit by coverage month: employer contributions count · case 01

Employees whose employer also funds the HSA are allowed to exceed the combined limit.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Employer contributions are ignored when computing the remaining room.

VERIFIED REPAIR

Restore the contract rule at the employer contributions count step: use `limit - x['employer_ytd'] - x['employee_ytd']`.

Unsuccessful approach: The attempt subtracts employer money but forgets the employee's own prior contributions.

Case contract

Input {coverage: 12 monthly entries None|self|family, age, employer_ytd, employee_ytd, request}. If December is covered, every month is treated as having December's tier (last-month rule). Limit = sum of monthly limits (self 358.00, family 712.50). Age 55+ adds 1,000.00 * covered months // 12. Allowed payroll contribution = min(request, max(0, limit - employer_ytd - employee_ytd)). Return [limit, allowed].

Why this case matters

HSA payroll contributions must be stopped at a limit that depends on month-by-month coverage, the last-month rule and employer money.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(x):
    cov = x['coverage']
    monthly = {'self': 35800, 'family': 71250}
    if cov[11] is not None:
        months = [cov[11]] * 12
    else:
        months = cov
    limit = sum(monthly[m] for m in months if m is not None)
    covered = sum(1 for m in months if m is not None)
    if x['age'] >= 55:
        limit += 100000 * covered // 12
    room = max(0, limit - x['employee_ytd'])
    allowed = min(x['request'], room)
    return [limit, allowed]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'coverage': ['self', 'self', 'family', 'family', 'family', None, 'self', 'family', None, None, 'family', None], 'age': 41, 'employer_ytd': 182987, 'employee_ytd': 284378, 'request': 281989}, [463650, 0]), ('regression', {'coverage': [None, None, None, None, None, None, 'self', None, None, None, None, None], 'age': 55, 'employer_ytd': 115762, 'employee_ytd': 24574, 'request': 286981}, [44133, 0]), ('partial-repair probe', {'coverage': [None, 'self', 'family', 'self', 'self', None, 'family', None, 'self', 'family', 'family', None], 'age': 40, 'employer_ytd': 225872, 'employee_ytd': 144016, 'request': 380678}, [428200, 58312]), ('partial-repair probe', {'coverage': ['self', None, 'self', 'family', 'family', None, None, None, None, 'family', None, 'self'], 'age': 48, 'employer_ytd': 141642, 'employee_ytd': 558877, 'request': 321776}, [429600, 0]), ('normal control', {'coverage': [None, None, None, None, None, None, None, 'family', 'family', 'family', 'family', 'family'], 'age': 55, 'employer_ytd': 0, 'employee_ytd': 238336, 'request': 135874}, [955000, 135874]), ('normal control', {'coverage': [None, None, 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self'], 'age': 55, 'employer_ytd': 0, 'employee_ytd': 456065, 'request': 36894}, [529600, 36894]), ('normal control', {'coverage': [None, 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 40, 'employer_ytd': 0, 'employee_ytd': 74724, 'request': 118780}, [855000, 118780]), ('normal control', {'coverage': [None, 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 40, 'employer_ytd': 0, 'employee_ytd': 164388, 'request': 96773}, [855000, 96773])], [('regression', {'coverage': [None, 'self', 'family', 'self', 'self', None, 'family', None, 'self', 'family', 'family', None], 'age': 40, 'employer_ytd': 225872, 'employee_ytd': 144016, 'request': 380678}, [428200, 58312]), ('regression', {'coverage': ['self', 'self', 'family', 'family', 'family', None, 'self', 'family', None, None, 'family', None], 'age': 41, 'employer_ytd': 182987, 'employee_ytd': 284378, 'request': 281989}, [463650, 0]), ('partial-repair probe', {'coverage': ['self', None, 'self', 'family', 'family', None, None, None, None, 'family', None, 'self'], 'age': 48, 'employer_ytd': 141642, 'employee_ytd': 558877, 'request': 321776}, [429600, 0]), ('partial-repair probe', {'coverage': ['family', 'family', 'family', None, 'self', 'self', None, 'family', 'family', 'family', None, 'self'], 'age': 55, 'employer_ytd': 0, 'employee_ytd': 380378, 'request': 301438}, [529600, 149222]), ('normal control', {'coverage': [None, None, None, None, None, None, None, 'family', 'family', 'family', 'family', 'family'], 'age': 56, 'employer_ytd': 0, 'employee_ytd': 506616, 'request': 122643}, [955000, 122643]), ('normal control', {'coverage': [None, 'family', None, None, None, None, 'family', None, 'self', 'self', None, 'family'], 'age': 36, 'employer_ytd': 0, 'employee_ytd': 317677, 'request': 360183}, [855000, 360183]), ('normal control', {'coverage': [None, None, None, None, None, None, None, None, None, None, None, 'family'], 'age': 56, 'employer_ytd': 72944, 'employee_ytd': 287033, 'request': 147965}, [955000, 147965]), ('normal control', {'coverage': ['self', 'family', None, None, 'family', 'family', 'family', 'family', None, None, 'self', 'family'], 'age': 56, 'employer_ytd': 0, 'employee_ytd': 12981, 'request': 364571}, [955000, 364571])], [('regression', {'coverage': [None, None, None, None, None, None, None, 'self', 'self', 'self', 'self', 'self'], 'age': 25, 'employer_ytd': 28613, 'employee_ytd': 65322, 'request': 390696}, [429600, 335665]), ('regression', {'coverage': [None, 'self', 'family', 'self', 'self', None, 'family', None, 'self', 'family', 'family', None], 'age': 40, 'employer_ytd': 225872, 'employee_ytd': 144016, 'request': 380678}, [428200, 58312]), ('partial-repair probe', {'coverage': [None, 'family', None, None, 'family', 'self', 'family', 'self', None, 'self', None, None], 'age': 40, 'employer_ytd': 0, 'employee_ytd': 423473, 'request': 127772}, [321150, 0]), ('partial-repair probe', {'coverage': ['self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self'], 'age': 54, 'employer_ytd': 0, 'employee_ytd': 551908, 'request': 166115}, [429600, 0]), ('normal control', {'coverage': [None, None, None, None, None, None, 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 55, 'employer_ytd': 102233, 'employee_ytd': 513881, 'request': 171346}, [955000, 171346]), ('normal control', {'coverage': [None, None, None, None, None, None, None, None, 'family', 'family', 'family', 'family'], 'age': 30, 'employer_ytd': 0, 'employee_ytd': 594908, 'request': 135782}, [855000, 135782]), ('normal control', {'coverage': ['family', 'self', None, 'self', None, 'self', 'family', 'family', 'self', 'family', None, 'family'], 'age': 65, 'employer_ytd': 119262, 'employee_ytd': 404161, 'request': 137517}, [955000, 137517]), ('normal control', {'coverage': ['self', None, None, None, None, 'family', None, None, None, 'self', None, 'family'], 'age': 35, 'employer_ytd': 0, 'employee_ytd': 316436, 'request': 299379}, [855000, 299379])], [('regression', {'coverage': ['family', None, 'self', 'family', 'family', 'self', 'self', 'self', 'self', 'self', 'family', 'self'], 'age': 40, 'employer_ytd': 209919, 'employee_ytd': 194888, 'request': 252834}, [429600, 24793]), ('regression', {'coverage': [None, None, None, None, None, None, None, 'family', 'family', None, None, None], 'age': 37, 'employer_ytd': 208148, 'employee_ytd': 1425, 'request': 155636}, [142500, 0]), ('partial-repair probe', {'coverage': ['self', 'self', 'self', None, 'family', 'self', None, None, 'self', None, 'family', None], 'age': 55, 'employer_ytd': 286268, 'employee_ytd': 434159, 'request': 197484}, [379833, 0]), ('partial-repair probe', {'coverage': [None, None, None, None, None, None, None, None, None, 'self', 'self', None], 'age': 40, 'employer_ytd': 0, 'employee_ytd': 243944, 'request': 352402}, [71600, 0]), ('normal control', {'coverage': [None, None, None, None, None, None, None, None, 'family', 'family', 'family', 'family'], 'age': 55, 'employer_ytd': 0, 'employee_ytd': 112368, 'request': 180107}, [955000, 180107]), ('normal control', {'coverage': [None, None, None, None, None, None, 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 44, 'employer_ytd': 0, 'employee_ytd': 292931, 'request': 211494}, [855000, 211494]), ('normal control', {'coverage': [None, None, None, None, None, None, 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 40, 'employer_ytd': 0, 'employee_ytd': 141822, 'request': 189175}, [855000, 189175]), ('normal control', {'coverage': [None, None, None, None, None, None, 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 56, 'employer_ytd': 256678, 'employee_ytd': 281811, 'request': 361142}, [955000, 361142])], [('regression', {'coverage': [None, 'self', 'family', 'family', None, 'family', 'self', 'family', 'family', 'self', None, 'self'], 'age': 54, 'employer_ytd': 250670, 'employee_ytd': 128042, 'request': 333278}, [429600, 50888]), ('regression', {'coverage': [None, None, None, None, None, None, None, 'self', 'self', 'self', 'self', 'self'], 'age': 25, 'employer_ytd': 28613, 'employee_ytd': 65322, 'request': 390696}, [429600, 335665]), ('partial-repair probe', {'coverage': [None, None, None, None, None, None, None, None, None, None, None, 'self'], 'age': 56, 'employer_ytd': 0, 'employee_ytd': 524863, 'request': 386331}, [529600, 4737]), ('partial-repair probe', {'coverage': [None, None, 'self', 'self', 'family', None, 'family', None, None, 'family', None, None], 'age': 56, 'employer_ytd': 180971, 'employee_ytd': 345821, 'request': 207004}, [327016, 0]), ('normal control', {'coverage': [None, None, None, None, None, None, None, None, None, None, 'family', 'family'], 'age': 56, 'employer_ytd': 104769, 'employee_ytd': 270158, 'request': 236626}, [955000, 236626]), ('normal control', {'coverage': [None, 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self'], 'age': 56, 'employer_ytd': 0, 'employee_ytd': 81281, 'request': 140013}, [529600, 140013]), ('normal control', {'coverage': [None, None, None, None, None, None, None, None, None, None, None, 'family'], 'age': 55, 'employer_ytd': 0, 'employee_ytd': 57407, 'request': 185458}, [955000, 185458]), ('normal control', {'coverage': [None, None, None, None, 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 30, 'employer_ytd': 173842, 'employee_ytd': 330283, 'request': 54863}, [855000, 54863])]]
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	`[463650, 179272]`	`[463650, 0]`	Failed
regression 1	`[44133, 19559]`	`[44133, 0]`	Failed
partial-repair probe 2	`[428200, 284184]`	`[428200, 58312]`	Failed
partial-repair probe 3	`[429600, 0]`	`[429600, 0]`	Passed
normal control 4	`[955000, 135874]`	`[955000, 135874]`	Passed
normal control 5	`[529600, 36894]`	`[529600, 36894]`	Passed
normal control 6	`[855000, 118780]`	`[855000, 118780]`	Passed
normal control 7	`[855000, 96773]`	`[855000, 96773]`	Passed

SHA-256 / fff7c9464ee8c90a1933a23ca1555d24f47db33e573a77c90901a10a7a2b38be

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(x):
    cov = x['coverage']
    monthly = {'self': 35800, 'family': 71250}
    if cov[11] is not None:
        months = [cov[11]] * 12
    else:
        months = cov
    limit = sum(monthly[m] for m in months if m is not None)
    covered = sum(1 for m in months if m is not None)
    if x['age'] >= 55:
        limit += 100000 * covered // 12
    room = max(0, limit - x['employer_ytd'])
    allowed = min(x['request'], room)
    return [limit, allowed]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'coverage': ['self', 'self', 'family', 'family', 'family', None, 'self', 'family', None, None, 'family', None], 'age': 41, 'employer_ytd': 182987, 'employee_ytd': 284378, 'request': 281989}, [463650, 0]), ('regression', {'coverage': [None, None, None, None, None, None, 'self', None, None, None, None, None], 'age': 55, 'employer_ytd': 115762, 'employee_ytd': 24574, 'request': 286981}, [44133, 0]), ('partial-repair probe', {'coverage': [None, 'self', 'family', 'self', 'self', None, 'family', None, 'self', 'family', 'family', None], 'age': 40, 'employer_ytd': 225872, 'employee_ytd': 144016, 'request': 380678}, [428200, 58312]), ('partial-repair probe', {'coverage': ['self', None, 'self', 'family', 'family', None, None, None, None, 'family', None, 'self'], 'age': 48, 'employer_ytd': 141642, 'employee_ytd': 558877, 'request': 321776}, [429600, 0]), ('normal control', {'coverage': [None, None, None, None, None, None, None, 'family', 'family', 'family', 'family', 'family'], 'age': 55, 'employer_ytd': 0, 'employee_ytd': 238336, 'request': 135874}, [955000, 135874]), ('normal control', {'coverage': [None, None, 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self'], 'age': 55, 'employer_ytd': 0, 'employee_ytd': 456065, 'request': 36894}, [529600, 36894]), ('normal control', {'coverage': [None, 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 40, 'employer_ytd': 0, 'employee_ytd': 74724, 'request': 118780}, [855000, 118780]), ('normal control', {'coverage': [None, 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 40, 'employer_ytd': 0, 'employee_ytd': 164388, 'request': 96773}, [855000, 96773])], [('regression', {'coverage': [None, 'self', 'family', 'self', 'self', None, 'family', None, 'self', 'family', 'family', None], 'age': 40, 'employer_ytd': 225872, 'employee_ytd': 144016, 'request': 380678}, [428200, 58312]), ('regression', {'coverage': ['self', 'self', 'family', 'family', 'family', None, 'self', 'family', None, None, 'family', None], 'age': 41, 'employer_ytd': 182987, 'employee_ytd': 284378, 'request': 281989}, [463650, 0]), ('partial-repair probe', {'coverage': ['self', None, 'self', 'family', 'family', None, None, None, None, 'family', None, 'self'], 'age': 48, 'employer_ytd': 141642, 'employee_ytd': 558877, 'request': 321776}, [429600, 0]), ('partial-repair probe', {'coverage': ['family', 'family', 'family', None, 'self', 'self', None, 'family', 'family', 'family', None, 'self'], 'age': 55, 'employer_ytd': 0, 'employee_ytd': 380378, 'request': 301438}, [529600, 149222]), ('normal control', {'coverage': [None, None, None, None, None, None, None, 'family', 'family', 'family', 'family', 'family'], 'age': 56, 'employer_ytd': 0, 'employee_ytd': 506616, 'request': 122643}, [955000, 122643]), ('normal control', {'coverage': [None, 'family', None, None, None, None, 'family', None, 'self', 'self', None, 'family'], 'age': 36, 'employer_ytd': 0, 'employee_ytd': 317677, 'request': 360183}, [855000, 360183]), ('normal control', {'coverage': [None, None, None, None, None, None, None, None, None, None, None, 'family'], 'age': 56, 'employer_ytd': 72944, 'employee_ytd': 287033, 'request': 147965}, [955000, 147965]), ('normal control', {'coverage': ['self', 'family', None, None, 'family', 'family', 'family', 'family', None, None, 'self', 'family'], 'age': 56, 'employer_ytd': 0, 'employee_ytd': 12981, 'request': 364571}, [955000, 364571])], [('regression', {'coverage': [None, None, None, None, None, None, None, 'self', 'self', 'self', 'self', 'self'], 'age': 25, 'employer_ytd': 28613, 'employee_ytd': 65322, 'request': 390696}, [429600, 335665]), ('regression', {'coverage': [None, 'self', 'family', 'self', 'self', None, 'family', None, 'self', 'family', 'family', None], 'age': 40, 'employer_ytd': 225872, 'employee_ytd': 144016, 'request': 380678}, [428200, 58312]), ('partial-repair probe', {'coverage': [None, 'family', None, None, 'family', 'self', 'family', 'self', None, 'self', None, None], 'age': 40, 'employer_ytd': 0, 'employee_ytd': 423473, 'request': 127772}, [321150, 0]), ('partial-repair probe', {'coverage': ['self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self'], 'age': 54, 'employer_ytd': 0, 'employee_ytd': 551908, 'request': 166115}, [429600, 0]), ('normal control', {'coverage': [None, None, None, None, None, None, 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 55, 'employer_ytd': 102233, 'employee_ytd': 513881, 'request': 171346}, [955000, 171346]), ('normal control', {'coverage': [None, None, None, None, None, None, None, None, 'family', 'family', 'family', 'family'], 'age': 30, 'employer_ytd': 0, 'employee_ytd': 594908, 'request': 135782}, [855000, 135782]), ('normal control', {'coverage': ['family', 'self', None, 'self', None, 'self', 'family', 'family', 'self', 'family', None, 'family'], 'age': 65, 'employer_ytd': 119262, 'employee_ytd': 404161, 'request': 137517}, [955000, 137517]), ('normal control', {'coverage': ['self', None, None, None, None, 'family', None, None, None, 'self', None, 'family'], 'age': 35, 'employer_ytd': 0, 'employee_ytd': 316436, 'request': 299379}, [855000, 299379])], [('regression', {'coverage': ['family', None, 'self', 'family', 'family', 'self', 'self', 'self', 'self', 'self', 'family', 'self'], 'age': 40, 'employer_ytd': 209919, 'employee_ytd': 194888, 'request': 252834}, [429600, 24793]), ('regression', {'coverage': [None, None, None, None, None, None, None, 'family', 'family', None, None, None], 'age': 37, 'employer_ytd': 208148, 'employee_ytd': 1425, 'request': 155636}, [142500, 0]), ('partial-repair probe', {'coverage': ['self', 'self', 'self', None, 'family', 'self', None, None, 'self', None, 'family', None], 'age': 55, 'employer_ytd': 286268, 'employee_ytd': 434159, 'request': 197484}, [379833, 0]), ('partial-repair probe', {'coverage': [None, None, None, None, None, None, None, None, None, 'self', 'self', None], 'age': 40, 'employer_ytd': 0, 'employee_ytd': 243944, 'request': 352402}, [71600, 0]), ('normal control', {'coverage': [None, None, None, None, None, None, None, None, 'family', 'family', 'family', 'family'], 'age': 55, 'employer_ytd': 0, 'employee_ytd': 112368, 'request': 180107}, [955000, 180107]), ('normal control', {'coverage': [None, None, None, None, None, None, 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 44, 'employer_ytd': 0, 'employee_ytd': 292931, 'request': 211494}, [855000, 211494]), ('normal control', {'coverage': [None, None, None, None, None, None, 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 40, 'employer_ytd': 0, 'employee_ytd': 141822, 'request': 189175}, [855000, 189175]), ('normal control', {'coverage': [None, None, None, None, None, None, 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 56, 'employer_ytd': 256678, 'employee_ytd': 281811, 'request': 361142}, [955000, 361142])], [('regression', {'coverage': [None, 'self', 'family', 'family', None, 'family', 'self', 'family', 'family', 'self', None, 'self'], 'age': 54, 'employer_ytd': 250670, 'employee_ytd': 128042, 'request': 333278}, [429600, 50888]), ('regression', {'coverage': [None, None, None, None, None, None, None, 'self', 'self', 'self', 'self', 'self'], 'age': 25, 'employer_ytd': 28613, 'employee_ytd': 65322, 'request': 390696}, [429600, 335665]), ('partial-repair probe', {'coverage': [None, None, None, None, None, None, None, None, None, None, None, 'self'], 'age': 56, 'employer_ytd': 0, 'employee_ytd': 524863, 'request': 386331}, [529600, 4737]), ('partial-repair probe', {'coverage': [None, None, 'self', 'self', 'family', None, 'family', None, None, 'family', None, None], 'age': 56, 'employer_ytd': 180971, 'employee_ytd': 345821, 'request': 207004}, [327016, 0]), ('normal control', {'coverage': [None, None, None, None, None, None, None, None, None, None, 'family', 'family'], 'age': 56, 'employer_ytd': 104769, 'employee_ytd': 270158, 'request': 236626}, [955000, 236626]), ('normal control', {'coverage': [None, 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self'], 'age': 56, 'employer_ytd': 0, 'employee_ytd': 81281, 'request': 140013}, [529600, 140013]), ('normal control', {'coverage': [None, None, None, None, None, None, None, None, None, None, None, 'family'], 'age': 55, 'employer_ytd': 0, 'employee_ytd': 57407, 'request': 185458}, [955000, 185458]), ('normal control', {'coverage': [None, None, None, None, 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 30, 'employer_ytd': 173842, 'employee_ytd': 330283, 'request': 54863}, [855000, 54863])]]
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	`[463650, 280663]`	`[463650, 0]`	Failed
regression 1	`[44133, 0]`	`[44133, 0]`	Passed
partial-repair probe 2	`[428200, 202328]`	`[428200, 58312]`	Failed
partial-repair probe 3	`[429600, 287958]`	`[429600, 0]`	Failed
normal control 4	`[955000, 135874]`	`[955000, 135874]`	Passed
normal control 5	`[529600, 36894]`	`[529600, 36894]`	Passed
normal control 6	`[855000, 118780]`	`[855000, 118780]`	Passed
normal control 7	`[855000, 96773]`	`[855000, 96773]`	Passed

SHA-256 / 9affbf6b26d4adf4fd68fa6a829f903d84ea668ba53e362116b4a79625f0218a

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(x):
    cov = x['coverage']
    monthly = {'self': 35800, 'family': 71250}
    if cov[11] is not None:
        months = [cov[11]] * 12
    else:
        months = cov
    limit = sum(monthly[m] for m in months if m is not None)
    covered = sum(1 for m in months if m is not None)
    if x['age'] >= 55:
        limit += 100000 * covered // 12
    room = max(0, limit - x['employer_ytd'] - x['employee_ytd'])
    allowed = min(x['request'], room)
    return [limit, allowed]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'coverage': ['self', 'self', 'family', 'family', 'family', None, 'self', 'family', None, None, 'family', None], 'age': 41, 'employer_ytd': 182987, 'employee_ytd': 284378, 'request': 281989}, [463650, 0]), ('regression', {'coverage': [None, None, None, None, None, None, 'self', None, None, None, None, None], 'age': 55, 'employer_ytd': 115762, 'employee_ytd': 24574, 'request': 286981}, [44133, 0]), ('partial-repair probe', {'coverage': [None, 'self', 'family', 'self', 'self', None, 'family', None, 'self', 'family', 'family', None], 'age': 40, 'employer_ytd': 225872, 'employee_ytd': 144016, 'request': 380678}, [428200, 58312]), ('partial-repair probe', {'coverage': ['self', None, 'self', 'family', 'family', None, None, None, None, 'family', None, 'self'], 'age': 48, 'employer_ytd': 141642, 'employee_ytd': 558877, 'request': 321776}, [429600, 0]), ('normal control', {'coverage': [None, None, None, None, None, None, None, 'family', 'family', 'family', 'family', 'family'], 'age': 55, 'employer_ytd': 0, 'employee_ytd': 238336, 'request': 135874}, [955000, 135874]), ('normal control', {'coverage': [None, None, 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self'], 'age': 55, 'employer_ytd': 0, 'employee_ytd': 456065, 'request': 36894}, [529600, 36894]), ('normal control', {'coverage': [None, 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 40, 'employer_ytd': 0, 'employee_ytd': 74724, 'request': 118780}, [855000, 118780]), ('normal control', {'coverage': [None, 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 40, 'employer_ytd': 0, 'employee_ytd': 164388, 'request': 96773}, [855000, 96773])], [('regression', {'coverage': [None, 'self', 'family', 'self', 'self', None, 'family', None, 'self', 'family', 'family', None], 'age': 40, 'employer_ytd': 225872, 'employee_ytd': 144016, 'request': 380678}, [428200, 58312]), ('regression', {'coverage': ['self', 'self', 'family', 'family', 'family', None, 'self', 'family', None, None, 'family', None], 'age': 41, 'employer_ytd': 182987, 'employee_ytd': 284378, 'request': 281989}, [463650, 0]), ('partial-repair probe', {'coverage': ['self', None, 'self', 'family', 'family', None, None, None, None, 'family', None, 'self'], 'age': 48, 'employer_ytd': 141642, 'employee_ytd': 558877, 'request': 321776}, [429600, 0]), ('partial-repair probe', {'coverage': ['family', 'family', 'family', None, 'self', 'self', None, 'family', 'family', 'family', None, 'self'], 'age': 55, 'employer_ytd': 0, 'employee_ytd': 380378, 'request': 301438}, [529600, 149222]), ('normal control', {'coverage': [None, None, None, None, None, None, None, 'family', 'family', 'family', 'family', 'family'], 'age': 56, 'employer_ytd': 0, 'employee_ytd': 506616, 'request': 122643}, [955000, 122643]), ('normal control', {'coverage': [None, 'family', None, None, None, None, 'family', None, 'self', 'self', None, 'family'], 'age': 36, 'employer_ytd': 0, 'employee_ytd': 317677, 'request': 360183}, [855000, 360183]), ('normal control', {'coverage': [None, None, None, None, None, None, None, None, None, None, None, 'family'], 'age': 56, 'employer_ytd': 72944, 'employee_ytd': 287033, 'request': 147965}, [955000, 147965]), ('normal control', {'coverage': ['self', 'family', None, None, 'family', 'family', 'family', 'family', None, None, 'self', 'family'], 'age': 56, 'employer_ytd': 0, 'employee_ytd': 12981, 'request': 364571}, [955000, 364571])], [('regression', {'coverage': [None, None, None, None, None, None, None, 'self', 'self', 'self', 'self', 'self'], 'age': 25, 'employer_ytd': 28613, 'employee_ytd': 65322, 'request': 390696}, [429600, 335665]), ('regression', {'coverage': [None, 'self', 'family', 'self', 'self', None, 'family', None, 'self', 'family', 'family', None], 'age': 40, 'employer_ytd': 225872, 'employee_ytd': 144016, 'request': 380678}, [428200, 58312]), ('partial-repair probe', {'coverage': [None, 'family', None, None, 'family', 'self', 'family', 'self', None, 'self', None, None], 'age': 40, 'employer_ytd': 0, 'employee_ytd': 423473, 'request': 127772}, [321150, 0]), ('partial-repair probe', {'coverage': ['self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self'], 'age': 54, 'employer_ytd': 0, 'employee_ytd': 551908, 'request': 166115}, [429600, 0]), ('normal control', {'coverage': [None, None, None, None, None, None, 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 55, 'employer_ytd': 102233, 'employee_ytd': 513881, 'request': 171346}, [955000, 171346]), ('normal control', {'coverage': [None, None, None, None, None, None, None, None, 'family', 'family', 'family', 'family'], 'age': 30, 'employer_ytd': 0, 'employee_ytd': 594908, 'request': 135782}, [855000, 135782]), ('normal control', {'coverage': ['family', 'self', None, 'self', None, 'self', 'family', 'family', 'self', 'family', None, 'family'], 'age': 65, 'employer_ytd': 119262, 'employee_ytd': 404161, 'request': 137517}, [955000, 137517]), ('normal control', {'coverage': ['self', None, None, None, None, 'family', None, None, None, 'self', None, 'family'], 'age': 35, 'employer_ytd': 0, 'employee_ytd': 316436, 'request': 299379}, [855000, 299379])], [('regression', {'coverage': ['family', None, 'self', 'family', 'family', 'self', 'self', 'self', 'self', 'self', 'family', 'self'], 'age': 40, 'employer_ytd': 209919, 'employee_ytd': 194888, 'request': 252834}, [429600, 24793]), ('regression', {'coverage': [None, None, None, None, None, None, None, 'family', 'family', None, None, None], 'age': 37, 'employer_ytd': 208148, 'employee_ytd': 1425, 'request': 155636}, [142500, 0]), ('partial-repair probe', {'coverage': ['self', 'self', 'self', None, 'family', 'self', None, None, 'self', None, 'family', None], 'age': 55, 'employer_ytd': 286268, 'employee_ytd': 434159, 'request': 197484}, [379833, 0]), ('partial-repair probe', {'coverage': [None, None, None, None, None, None, None, None, None, 'self', 'self', None], 'age': 40, 'employer_ytd': 0, 'employee_ytd': 243944, 'request': 352402}, [71600, 0]), ('normal control', {'coverage': [None, None, None, None, None, None, None, None, 'family', 'family', 'family', 'family'], 'age': 55, 'employer_ytd': 0, 'employee_ytd': 112368, 'request': 180107}, [955000, 180107]), ('normal control', {'coverage': [None, None, None, None, None, None, 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 44, 'employer_ytd': 0, 'employee_ytd': 292931, 'request': 211494}, [855000, 211494]), ('normal control', {'coverage': [None, None, None, None, None, None, 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 40, 'employer_ytd': 0, 'employee_ytd': 141822, 'request': 189175}, [855000, 189175]), ('normal control', {'coverage': [None, None, None, None, None, None, 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 56, 'employer_ytd': 256678, 'employee_ytd': 281811, 'request': 361142}, [955000, 361142])], [('regression', {'coverage': [None, 'self', 'family', 'family', None, 'family', 'self', 'family', 'family', 'self', None, 'self'], 'age': 54, 'employer_ytd': 250670, 'employee_ytd': 128042, 'request': 333278}, [429600, 50888]), ('regression', {'coverage': [None, None, None, None, None, None, None, 'self', 'self', 'self', 'self', 'self'], 'age': 25, 'employer_ytd': 28613, 'employee_ytd': 65322, 'request': 390696}, [429600, 335665]), ('partial-repair probe', {'coverage': [None, None, None, None, None, None, None, None, None, None, None, 'self'], 'age': 56, 'employer_ytd': 0, 'employee_ytd': 524863, 'request': 386331}, [529600, 4737]), ('partial-repair probe', {'coverage': [None, None, 'self', 'self', 'family', None, 'family', None, None, 'family', None, None], 'age': 56, 'employer_ytd': 180971, 'employee_ytd': 345821, 'request': 207004}, [327016, 0]), ('normal control', {'coverage': [None, None, None, None, None, None, None, None, None, None, 'family', 'family'], 'age': 56, 'employer_ytd': 104769, 'employee_ytd': 270158, 'request': 236626}, [955000, 236626]), ('normal control', {'coverage': [None, 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self', 'self'], 'age': 56, 'employer_ytd': 0, 'employee_ytd': 81281, 'request': 140013}, [529600, 140013]), ('normal control', {'coverage': [None, None, None, None, None, None, None, None, None, None, None, 'family'], 'age': 55, 'employer_ytd': 0, 'employee_ytd': 57407, 'request': 185458}, [955000, 185458]), ('normal control', {'coverage': [None, None, None, None, 'family', 'family', 'family', 'family', 'family', 'family', 'family', 'family'], 'age': 30, 'employer_ytd': 173842, 'employee_ytd': 330283, 'request': 54863}, [855000, 54863])]]
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	`[463650, 0]`	`[463650, 0]`	Passed
regression 1	`[44133, 0]`	`[44133, 0]`	Passed
partial-repair probe 2	`[428200, 58312]`	`[428200, 58312]`	Passed
partial-repair probe 3	`[429600, 0]`	`[429600, 0]`	Passed
normal control 4	`[955000, 135874]`	`[955000, 135874]`	Passed
normal control 5	`[529600, 36894]`	`[529600, 36894]`	Passed
normal control 6	`[855000, 118780]`	`[855000, 118780]`	Passed
normal control 7	`[855000, 96773]`	`[855000, 96773]`	Passed

SHA-256 / 63e646a0a347afa86888387b97f02ad946b17311073cdb067f437af0d5eb7641

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 2026-09-29T14:46:32.742507+00:00.

Case digest / 49cc200bcc91b0d89f6d566dc2eb111e729a054e2967caec133ff8389966d936