FAILURE MAP
← Case archive

FA-59201 / Payroll withholding rules / Open access

Multi-state wage allocation by work days: remainder ranking · case 01

Leftover cents go to the states with the most days instead of the largest fractional shares.

Verified by executionVariant 1 · 10 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Remainder cents follow the base day ordering and ignore fractional remainders.

THE FAILURE

Remainder cents follow the base day ordering and ignore fractional remainders.

Unsuccessful approach: The attempt ranks remainders ascending, favouring the smallest fractions.

Case contract

Input {wage, days: {state: work days}, resident}. With zero total days all wages go to the resident state. Otherwise each state gets floor(wage*days/total); leftover cents go one each to states ranked by largest fractional remainder, ties by the base order (days descending, then state name). States allocated 0 cents are omitted. Return {state: cents}.

Why this case matters

State wage allocation must sum exactly to the paycheck with a deterministic remainder rule.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    days = x['days']
    total = sum(days.values())
    if total == 0:
        return {x['resident']: x['wage']}
    order = sorted(days, key=lambda s: (-days[s], s))
    alloc = {s: x['wage'] * days[s] // total for s in order}
    rema = order
    left = x['wage'] - sum(alloc.values())
    for s in rema[:left]:
        alloc[s] += 1
    return {s: v for s, v in alloc.items() if v}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'wage': 17, 'days': {'NJ': 1, 'PA': 3, 'NY': 3}, 'resident': 'NY'}, {'NY': 7, 'PA': 7, 'NJ': 3}), ('regression', {'wage': 179374, 'days': {'PA': 20, 'NJ': 2, 'MA': 0}, 'resident': 'NY'}, {'PA': 163067, 'NJ': 16307}), ('partial-repair probe', {'wage': 315271, 'days': {'PA': 2, 'NY': 3, 'CT': 1}, 'resident': 'NJ'}, {'NY': 157636, 'PA': 105090, 'CT': 52545}), ('partial-repair probe', {'wage': 273177, 'days': {'PA': 0, 'NY': 1, 'NJ': 3}, 'resident': 'NJ'}, {'NJ': 204883, 'NY': 68294}), ('boundary control', {'wage': 100, 'days': {'NY': 1, 'NJ': 1, 'CT': 1}, 'resident': 'NJ'}, {'CT': 34, 'NJ': 33, 'NY': 33}), ('boundary control', {'wage': 5000, 'days': {'NY': 0, 'NJ': 0}, 'resident': 'NJ'}, {'NJ': 5000}), ('normal control', {'wage': 410311, 'days': {'PA': 10}, 'resident': 'CT'}, {'PA': 410311}), ('normal control', {'wage': 9, 'days': {'PA': 1, 'CT': 8}, 'resident': 'NY'}, {'CT': 8, 'PA': 1}), ('normal control', {'wage': 61318, 'days': {'CT': 0, 'MA': 0, 'PA': 12, 'NJ': 19}, 'resident': 'NY'}, {'NJ': 37582, 'PA': 23736}), ('normal control', {'wage': 22, 'days': {'CT': 0}, 'resident': 'NY'}, {'NY': 22})], [('regression', {'wage': 179374, 'days': {'PA': 20, 'NJ': 2, 'MA': 0}, 'resident': 'NY'}, {'PA': 163067, 'NJ': 16307}), ('regression', {'wage': 172162, 'days': {'MA': 6, 'CT': 3, 'PA': 11}, 'resident': 'NJ'}, {'PA': 94689, 'MA': 51649, 'CT': 25824}), ('partial-repair probe', {'wage': 273177, 'days': {'PA': 0, 'NY': 1, 'NJ': 3}, 'resident': 'NJ'}, {'NJ': 204883, 'NY': 68294}), ('partial-repair probe', {'wage': 525270, 'days': {'MA': 2, 'PA': 11, 'NJ': 22}, 'resident': 'NJ'}, {'NJ': 330170, 'PA': 165085, 'MA': 30015}), ('boundary control', {'wage': 100, 'days': {'NY': 1, 'NJ': 1, 'CT': 1}, 'resident': 'NJ'}, {'CT': 34, 'NJ': 33, 'NY': 33}), ('boundary control', {'wage': 5000, 'days': {'NY': 0, 'NJ': 0}, 'resident': 'NJ'}, {'NJ': 5000}), ('normal control', {'wage': 231015, 'days': {'PA': 0}, 'resident': 'CT'}, {'CT': 231015}), ('normal control', {'wage': 874754, 'days': {'PA': 19}, 'resident': 'CT'}, {'PA': 874754}), ('normal control', {'wage': 761711, 'days': {'MA': 0}, 'resident': 'NJ'}, {'NJ': 761711}), ('normal control', {'wage': 1, 'days': {'NJ': 15}, 'resident': 'NY'}, {'NJ': 1})], [('regression', {'wage': 172162, 'days': {'MA': 6, 'CT': 3, 'PA': 11}, 'resident': 'NJ'}, {'PA': 94689, 'MA': 51649, 'CT': 25824}), ('regression', {'wage': 802876, 'days': {'NJ': 10, 'MA': 0, 'NY': 0, 'PA': 1}, 'resident': 'CT'}, {'NJ': 729887, 'PA': 72989}), ('partial-repair probe', {'wage': 525270, 'days': {'MA': 2, 'PA': 11, 'NJ': 22}, 'resident': 'NJ'}, {'NJ': 330170, 'PA': 165085, 'MA': 30015}), ('partial-repair probe', {'wage': 2, 'days': {'NJ': 2, 'PA': 2, 'NY': 0, 'MA': 1}, 'resident': 'CT'}, {'NJ': 1, 'PA': 1}), ('boundary control', {'wage': 100, 'days': {'NY': 1, 'NJ': 1, 'CT': 1}, 'resident': 'NJ'}, {'CT': 34, 'NJ': 33, 'NY': 33}), ('boundary control', {'wage': 5000, 'days': {'NY': 0, 'NJ': 0}, 'resident': 'NJ'}, {'NJ': 5000}), ('normal control', {'wage': 399573, 'days': {'CT': 0}, 'resident': 'CT'}, {'CT': 399573}), ('normal control', {'wage': 424602, 'days': {'PA': 2, 'CT': 0, 'NJ': 7, 'NY': 0}, 'resident': 'CT'}, {'NJ': 330246, 'PA': 94356}), ('normal control', {'wage': 2, 'days': {'NJ': 0}, 'resident': 'NJ'}, {'NJ': 2}), ('normal control', {'wage': 14, 'days': {'PA': 0, 'MA': 2}, 'resident': 'CT'}, {'MA': 14})], [('regression', {'wage': 802876, 'days': {'NJ': 10, 'MA': 0, 'NY': 0, 'PA': 1}, 'resident': 'CT'}, {'NJ': 729887, 'PA': 72989}), ('regression', {'wage': 5, 'days': {'MA': 17, 'NY': 2, 'PA': 9}, 'resident': 'NJ'}, {'MA': 3, 'PA': 2}), ('partial-repair probe', {'wage': 2, 'days': {'NJ': 2, 'PA': 2, 'NY': 0, 'MA': 1}, 'resident': 'CT'}, {'NJ': 1, 'PA': 1}), ('partial-repair probe', {'wage': 254323, 'days': {'NY': 1, 'PA': 8, 'NJ': 15, 'MA': 0}, 'resident': 'NY'}, {'NJ': 158952, 'PA': 84774, 'NY': 10597}), ('boundary control', {'wage': 100, 'days': {'NY': 1, 'NJ': 1, 'CT': 1}, 'resident': 'NJ'}, {'CT': 34, 'NJ': 33, 'NY': 33}), ('boundary control', {'wage': 5000, 'days': {'NY': 0, 'NJ': 0}, 'resident': 'NJ'}, {'NJ': 5000}), ('normal control', {'wage': 16, 'days': {'CT': 3, 'PA': 1}, 'resident': 'CT'}, {'CT': 12, 'PA': 4}), ('normal control', {'wage': 10, 'days': {'CT': 19, 'MA': 0}, 'resident': 'NJ'}, {'CT': 10}), ('normal control', {'wage': 200160, 'days': {'CT': 0, 'NJ': 3, 'NY': 17, 'PA': 0}, 'resident': 'CT'}, {'NY': 170136, 'NJ': 30024}), ('normal control', {'wage': 27, 'days': {'NY': 0}, 'resident': 'NY'}, {'NY': 27})], [('regression', {'wage': 5, 'days': {'MA': 17, 'NY': 2, 'PA': 9}, 'resident': 'NJ'}, {'MA': 3, 'PA': 2}), ('regression', {'wage': 254323, 'days': {'NY': 1, 'PA': 8, 'NJ': 15, 'MA': 0}, 'resident': 'NY'}, {'NJ': 158952, 'PA': 84774, 'NY': 10597}), ('partial-repair probe', {'wage': 646558, 'days': {'NY': 15, 'CT': 3, 'MA': 3, 'NJ': 2}, 'resident': 'NJ'}, {'NY': 421668, 'CT': 84334, 'MA': 84334, 'NJ': 56222}), ('partial-repair probe', {'wage': 22, 'days': {'PA': 0, 'CT': 1, 'MA': 2, 'NJ': 1}, 'resident': 'NY'}, {'MA': 11, 'CT': 6, 'NJ': 5}), ('boundary control', {'wage': 100, 'days': {'NY': 1, 'NJ': 1, 'CT': 1}, 'resident': 'NJ'}, {'CT': 34, 'NJ': 33, 'NY': 33}), ('boundary control', {'wage': 5000, 'days': {'NY': 0, 'NJ': 0}, 'resident': 'NJ'}, {'NJ': 5000}), ('normal control', {'wage': 29, 'days': {'PA': 2}, 'resident': 'NJ'}, {'PA': 29}), ('normal control', {'wage': 455522, 'days': {'MA': 0, 'CT': 0}, 'resident': 'NY'}, {'NY': 455522}), ('normal control', {'wage': 402912, 'days': {'CT': 0, 'NJ': 0}, 'resident': 'NJ'}, {'NJ': 402912}), ('normal control', {'wage': 891837, 'days': {'CT': 0}, 'resident': 'NY'}, {'NY': 891837})]]
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 fixtureActualExpectedOutcome
regression 0{'NJ': 2, 'NY': 8, 'PA': 7}{'NJ': 3, 'NY': 7, 'PA': 7}Failed
regression 1{'NJ': 16306, 'PA': 163068}{'NJ': 16307, 'PA': 163067}Failed
partial-repair probe 2{'CT': 52545, 'NY': 157636, 'PA': 105090}{'CT': 52545, 'NY': 157636, 'PA': 105090}Passed
partial-repair probe 3{'NJ': 204883, 'NY': 68294}{'NJ': 204883, 'NY': 68294}Passed
boundary control 4{'CT': 34, 'NJ': 33, 'NY': 33}{'CT': 34, 'NJ': 33, 'NY': 33}Passed
boundary control 5{'NJ': 5000}{'NJ': 5000}Passed
normal control 6{'PA': 410311}{'PA': 410311}Passed
normal control 7{'CT': 8, 'PA': 1}{'CT': 8, 'PA': 1}Passed
normal control 8{'NJ': 37582, 'PA': 23736}{'NJ': 37582, 'PA': 23736}Passed
normal control 9{'NY': 22}{'NY': 22}Passed

SHA-256 / ab5d50c401a31548fa231d87ac0bf2fb396eda01bd90477e6799d692d8da647e

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    days = x['days']
    total = sum(days.values())
    if total == 0:
        return {x['resident']: x['wage']}
    order = sorted(days, key=lambda s: (-days[s], s))
    alloc = {s: x['wage'] * days[s] // total for s in order}
    rema = sorted(order, key=lambda s: (x['wage'] * days[s] % total, order.index(s)))
    left = x['wage'] - sum(alloc.values())
    for s in rema[:left]:
        alloc[s] += 1
    return {s: v for s, v in alloc.items() if v}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'wage': 17, 'days': {'NJ': 1, 'PA': 3, 'NY': 3}, 'resident': 'NY'}, {'NY': 7, 'PA': 7, 'NJ': 3}), ('regression', {'wage': 179374, 'days': {'PA': 20, 'NJ': 2, 'MA': 0}, 'resident': 'NY'}, {'PA': 163067, 'NJ': 16307}), ('partial-repair probe', {'wage': 315271, 'days': {'PA': 2, 'NY': 3, 'CT': 1}, 'resident': 'NJ'}, {'NY': 157636, 'PA': 105090, 'CT': 52545}), ('partial-repair probe', {'wage': 273177, 'days': {'PA': 0, 'NY': 1, 'NJ': 3}, 'resident': 'NJ'}, {'NJ': 204883, 'NY': 68294}), ('boundary control', {'wage': 100, 'days': {'NY': 1, 'NJ': 1, 'CT': 1}, 'resident': 'NJ'}, {'CT': 34, 'NJ': 33, 'NY': 33}), ('boundary control', {'wage': 5000, 'days': {'NY': 0, 'NJ': 0}, 'resident': 'NJ'}, {'NJ': 5000}), ('normal control', {'wage': 410311, 'days': {'PA': 10}, 'resident': 'CT'}, {'PA': 410311}), ('normal control', {'wage': 9, 'days': {'PA': 1, 'CT': 8}, 'resident': 'NY'}, {'CT': 8, 'PA': 1}), ('normal control', {'wage': 61318, 'days': {'CT': 0, 'MA': 0, 'PA': 12, 'NJ': 19}, 'resident': 'NY'}, {'NJ': 37582, 'PA': 23736}), ('normal control', {'wage': 22, 'days': {'CT': 0}, 'resident': 'NY'}, {'NY': 22})], [('regression', {'wage': 179374, 'days': {'PA': 20, 'NJ': 2, 'MA': 0}, 'resident': 'NY'}, {'PA': 163067, 'NJ': 16307}), ('regression', {'wage': 172162, 'days': {'MA': 6, 'CT': 3, 'PA': 11}, 'resident': 'NJ'}, {'PA': 94689, 'MA': 51649, 'CT': 25824}), ('partial-repair probe', {'wage': 273177, 'days': {'PA': 0, 'NY': 1, 'NJ': 3}, 'resident': 'NJ'}, {'NJ': 204883, 'NY': 68294}), ('partial-repair probe', {'wage': 525270, 'days': {'MA': 2, 'PA': 11, 'NJ': 22}, 'resident': 'NJ'}, {'NJ': 330170, 'PA': 165085, 'MA': 30015}), ('boundary control', {'wage': 100, 'days': {'NY': 1, 'NJ': 1, 'CT': 1}, 'resident': 'NJ'}, {'CT': 34, 'NJ': 33, 'NY': 33}), ('boundary control', {'wage': 5000, 'days': {'NY': 0, 'NJ': 0}, 'resident': 'NJ'}, {'NJ': 5000}), ('normal control', {'wage': 231015, 'days': {'PA': 0}, 'resident': 'CT'}, {'CT': 231015}), ('normal control', {'wage': 874754, 'days': {'PA': 19}, 'resident': 'CT'}, {'PA': 874754}), ('normal control', {'wage': 761711, 'days': {'MA': 0}, 'resident': 'NJ'}, {'NJ': 761711}), ('normal control', {'wage': 1, 'days': {'NJ': 15}, 'resident': 'NY'}, {'NJ': 1})], [('regression', {'wage': 172162, 'days': {'MA': 6, 'CT': 3, 'PA': 11}, 'resident': 'NJ'}, {'PA': 94689, 'MA': 51649, 'CT': 25824}), ('regression', {'wage': 802876, 'days': {'NJ': 10, 'MA': 0, 'NY': 0, 'PA': 1}, 'resident': 'CT'}, {'NJ': 729887, 'PA': 72989}), ('partial-repair probe', {'wage': 525270, 'days': {'MA': 2, 'PA': 11, 'NJ': 22}, 'resident': 'NJ'}, {'NJ': 330170, 'PA': 165085, 'MA': 30015}), ('partial-repair probe', {'wage': 2, 'days': {'NJ': 2, 'PA': 2, 'NY': 0, 'MA': 1}, 'resident': 'CT'}, {'NJ': 1, 'PA': 1}), ('boundary control', {'wage': 100, 'days': {'NY': 1, 'NJ': 1, 'CT': 1}, 'resident': 'NJ'}, {'CT': 34, 'NJ': 33, 'NY': 33}), ('boundary control', {'wage': 5000, 'days': {'NY': 0, 'NJ': 0}, 'resident': 'NJ'}, {'NJ': 5000}), ('normal control', {'wage': 399573, 'days': {'CT': 0}, 'resident': 'CT'}, {'CT': 399573}), ('normal control', {'wage': 424602, 'days': {'PA': 2, 'CT': 0, 'NJ': 7, 'NY': 0}, 'resident': 'CT'}, {'NJ': 330246, 'PA': 94356}), ('normal control', {'wage': 2, 'days': {'NJ': 0}, 'resident': 'NJ'}, {'NJ': 2}), ('normal control', {'wage': 14, 'days': {'PA': 0, 'MA': 2}, 'resident': 'CT'}, {'MA': 14})], [('regression', {'wage': 802876, 'days': {'NJ': 10, 'MA': 0, 'NY': 0, 'PA': 1}, 'resident': 'CT'}, {'NJ': 729887, 'PA': 72989}), ('regression', {'wage': 5, 'days': {'MA': 17, 'NY': 2, 'PA': 9}, 'resident': 'NJ'}, {'MA': 3, 'PA': 2}), ('partial-repair probe', {'wage': 2, 'days': {'NJ': 2, 'PA': 2, 'NY': 0, 'MA': 1}, 'resident': 'CT'}, {'NJ': 1, 'PA': 1}), ('partial-repair probe', {'wage': 254323, 'days': {'NY': 1, 'PA': 8, 'NJ': 15, 'MA': 0}, 'resident': 'NY'}, {'NJ': 158952, 'PA': 84774, 'NY': 10597}), ('boundary control', {'wage': 100, 'days': {'NY': 1, 'NJ': 1, 'CT': 1}, 'resident': 'NJ'}, {'CT': 34, 'NJ': 33, 'NY': 33}), ('boundary control', {'wage': 5000, 'days': {'NY': 0, 'NJ': 0}, 'resident': 'NJ'}, {'NJ': 5000}), ('normal control', {'wage': 16, 'days': {'CT': 3, 'PA': 1}, 'resident': 'CT'}, {'CT': 12, 'PA': 4}), ('normal control', {'wage': 10, 'days': {'CT': 19, 'MA': 0}, 'resident': 'NJ'}, {'CT': 10}), ('normal control', {'wage': 200160, 'days': {'CT': 0, 'NJ': 3, 'NY': 17, 'PA': 0}, 'resident': 'CT'}, {'NY': 170136, 'NJ': 30024}), ('normal control', {'wage': 27, 'days': {'NY': 0}, 'resident': 'NY'}, {'NY': 27})], [('regression', {'wage': 5, 'days': {'MA': 17, 'NY': 2, 'PA': 9}, 'resident': 'NJ'}, {'MA': 3, 'PA': 2}), ('regression', {'wage': 254323, 'days': {'NY': 1, 'PA': 8, 'NJ': 15, 'MA': 0}, 'resident': 'NY'}, {'NJ': 158952, 'PA': 84774, 'NY': 10597}), ('partial-repair probe', {'wage': 646558, 'days': {'NY': 15, 'CT': 3, 'MA': 3, 'NJ': 2}, 'resident': 'NJ'}, {'NY': 421668, 'CT': 84334, 'MA': 84334, 'NJ': 56222}), ('partial-repair probe', {'wage': 22, 'days': {'PA': 0, 'CT': 1, 'MA': 2, 'NJ': 1}, 'resident': 'NY'}, {'MA': 11, 'CT': 6, 'NJ': 5}), ('boundary control', {'wage': 100, 'days': {'NY': 1, 'NJ': 1, 'CT': 1}, 'resident': 'NJ'}, {'CT': 34, 'NJ': 33, 'NY': 33}), ('boundary control', {'wage': 5000, 'days': {'NY': 0, 'NJ': 0}, 'resident': 'NJ'}, {'NJ': 5000}), ('normal control', {'wage': 29, 'days': {'PA': 2}, 'resident': 'NJ'}, {'PA': 29}), ('normal control', {'wage': 455522, 'days': {'MA': 0, 'CT': 0}, 'resident': 'NY'}, {'NY': 455522}), ('normal control', {'wage': 402912, 'days': {'CT': 0, 'NJ': 0}, 'resident': 'NJ'}, {'NJ': 402912}), ('normal control', {'wage': 891837, 'days': {'CT': 0}, 'resident': 'NY'}, {'NY': 891837})]]
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 fixtureActualExpectedOutcome
regression 0{'NJ': 2, 'NY': 8, 'PA': 7}{'NJ': 3, 'NY': 7, 'PA': 7}Failed
regression 1{'MA': 1, 'NJ': 16306, 'PA': 163067}{'NJ': 16307, 'PA': 163067}Failed
partial-repair probe 2{'CT': 52546, 'NY': 157635, 'PA': 105090}{'CT': 52545, 'NY': 157636, 'PA': 105090}Failed
partial-repair probe 3{'NJ': 204882, 'NY': 68294, 'PA': 1}{'NJ': 204883, 'NY': 68294}Failed
boundary control 4{'CT': 34, 'NJ': 33, 'NY': 33}{'CT': 34, 'NJ': 33, 'NY': 33}Passed
boundary control 5{'NJ': 5000}{'NJ': 5000}Passed
normal control 6{'PA': 410311}{'PA': 410311}Passed
normal control 7{'CT': 8, 'PA': 1}{'CT': 8, 'PA': 1}Passed
normal control 8{'NJ': 37582, 'PA': 23736}{'NJ': 37582, 'PA': 23736}Passed
normal control 9{'NY': 22}{'NY': 22}Passed

SHA-256 / 26d6f35765d0dc414abedbf28e9c87226ec5bfbf6ce4ecb7997f61ca7f324940

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 10 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

Sign in to the archive ↗

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 2026-09-29T14:46:34.077902+00:00.

Case digest / 317e2b0108fdb78cf7ff9b473de0155ca50ed93a25dcf59a174790bf0abe07a2