FA-59206 / Payroll withholding rules / Open access

Multi-state wage allocation by work days: leftover distribution · case 01

All leftover cents land in a single state.

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

ROOT CAUSE

The entire remainder is given to the top-ranked state instead of one cent each.

VERIFIED REPAIR

Restore the contract rule at the leftover distribution step: use `for s in rema[:left]: alloc[s] += 1`.

Unsuccessful approach: The attempt lumps the remainder onto the state with most days.

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 = sorted(order, key=lambda s: (-(x['wage'] * days[s] % total), order.index(s)))
    left = x['wage'] - sum(alloc.values())
    for s in rema[:1]:
        alloc[s] += left
    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': 525270, 'days': {'MA': 2, 'PA': 11, 'NJ': 22}, 'resident': 'NJ'}, {'NJ': 330170, 'PA': 165085, 'MA': 30015}), ('regression', {'wage': 2, 'days': {'NJ': 2, 'PA': 2, 'NY': 0, 'MA': 1}, 'resident': 'CT'}, {'NJ': 1, 'PA': 1}), ('partial-repair probe', {'wage': 17, 'days': {'NJ': 1, 'PA': 3, 'NY': 3}, 'resident': 'NY'}, {'NY': 7, 'PA': 7, 'NJ': 3}), ('partial-repair probe', {'wage': 179374, 'days': {'PA': 20, 'NJ': 2, 'MA': 0}, 'resident': 'NY'}, {'PA': 163067, 'NJ': 16307}), ('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': 2, 'days': {'NJ': 2, 'PA': 2, 'NY': 0, 'MA': 1}, 'resident': 'CT'}, {'NJ': 1, 'PA': 1}), ('regression', {'wage': 254323, 'days': {'NY': 1, 'PA': 8, 'NJ': 15, 'MA': 0}, 'resident': 'NY'}, {'NJ': 158952, 'PA': 84774, 'NY': 10597}), ('partial-repair probe', {'wage': 172162, 'days': {'MA': 6, 'CT': 3, 'PA': 11}, 'resident': 'NJ'}, {'PA': 94689, 'MA': 51649, 'CT': 25824}), ('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': 315271, 'days': {'PA': 2, 'NY': 3, 'CT': 1}, 'resident': 'NJ'}, {'NY': 157636, 'PA': 105090, 'CT': 52545}), ('normal control', {'wage': 761711, 'days': {'MA': 0}, 'resident': 'NJ'}, {'NJ': 761711})], [('regression', {'wage': 254323, 'days': {'NY': 1, 'PA': 8, 'NJ': 15, 'MA': 0}, 'resident': 'NY'}, {'NJ': 158952, 'PA': 84774, 'NY': 10597}), ('regression', {'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': 2, 'days': {'NJ': 2, 'PA': 2, 'NY': 0, 'MA': 1}, 'resident': 'CT'}, {'NJ': 1, 'PA': 1}), ('partial-repair probe', {'wage': 802876, 'days': {'NJ': 10, 'MA': 0, 'NY': 0, 'PA': 1}, 'resident': 'CT'}, {'NJ': 729887, 'PA': 72989}), ('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': 273177, 'days': {'PA': 0, 'NY': 1, 'NJ': 3}, 'resident': 'NJ'}, {'NJ': 204883, 'NY': 68294}), ('normal control', {'wage': 1, 'days': {'NJ': 15}, 'resident': 'NY'}, {'NJ': 1}), ('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})], [('regression', {'wage': 646558, 'days': {'NY': 15, 'CT': 3, 'MA': 3, 'NJ': 2}, 'resident': 'NJ'}, {'NY': 421668, 'CT': 84334, 'MA': 84334, 'NJ': 56222}), ('regression', {'wage': 15, 'days': {'NY': 2, 'MA': 0, 'PA': 2, 'NJ': 13}, 'resident': 'CT'}, {'NJ': 11, 'NY': 2, 'PA': 2}), ('partial-repair probe', {'wage': 5, 'days': {'MA': 17, 'NY': 2, 'PA': 9}, 'resident': 'NJ'}, {'MA': 3, 'PA': 2}), ('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': 2, 'days': {'NJ': 0}, 'resident': 'NJ'}, {'NJ': 2}), ('normal control', {'wage': 14, 'days': {'PA': 0, 'MA': 2}, 'resident': 'CT'}, {'MA': 14}), ('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})], [('regression', {'wage': 15, 'days': {'NY': 2, 'MA': 0, 'PA': 2, 'NJ': 13}, 'resident': 'CT'}, {'NJ': 11, 'NY': 2, 'PA': 2}), ('regression', {'wage': 4, 'days': {'NJ': 3, 'CT': 1, 'MA': 3}, 'resident': 'CT'}, {'MA': 2, 'NJ': 2}), ('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': 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}), ('normal control', {'wage': 29, 'days': {'PA': 2}, 'resident': 'NJ'}, {'PA': 29}), ('normal control', {'wage': 455522, 'days': {'MA': 0, 'CT': 0}, 'resident': 'NY'}, {'NY': 455522})]]
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	`{'MA': 30015, 'NJ': 330169, 'PA': 165086}`	`{'MA': 30015, 'NJ': 330170, 'PA': 165085}`	Failed
regression 1	`{'NJ': 2}`	`{'NJ': 1, 'PA': 1}`	Failed
partial-repair probe 2	`{'NJ': 3, 'NY': 7, 'PA': 7}`	`{'NJ': 3, 'NY': 7, 'PA': 7}`	Passed
partial-repair probe 3	`{'NJ': 16307, 'PA': 163067}`	`{'NJ': 16307, 'PA': 163067}`	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 / cf437b8c7eaad7e7800fc410eb09d5e47f3f52ac24b8d3e9a318e88a76478282

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 order[:1]:
        alloc[s] += left
    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': 525270, 'days': {'MA': 2, 'PA': 11, 'NJ': 22}, 'resident': 'NJ'}, {'NJ': 330170, 'PA': 165085, 'MA': 30015}), ('regression', {'wage': 2, 'days': {'NJ': 2, 'PA': 2, 'NY': 0, 'MA': 1}, 'resident': 'CT'}, {'NJ': 1, 'PA': 1}), ('partial-repair probe', {'wage': 17, 'days': {'NJ': 1, 'PA': 3, 'NY': 3}, 'resident': 'NY'}, {'NY': 7, 'PA': 7, 'NJ': 3}), ('partial-repair probe', {'wage': 179374, 'days': {'PA': 20, 'NJ': 2, 'MA': 0}, 'resident': 'NY'}, {'PA': 163067, 'NJ': 16307}), ('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': 2, 'days': {'NJ': 2, 'PA': 2, 'NY': 0, 'MA': 1}, 'resident': 'CT'}, {'NJ': 1, 'PA': 1}), ('regression', {'wage': 254323, 'days': {'NY': 1, 'PA': 8, 'NJ': 15, 'MA': 0}, 'resident': 'NY'}, {'NJ': 158952, 'PA': 84774, 'NY': 10597}), ('partial-repair probe', {'wage': 172162, 'days': {'MA': 6, 'CT': 3, 'PA': 11}, 'resident': 'NJ'}, {'PA': 94689, 'MA': 51649, 'CT': 25824}), ('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': 315271, 'days': {'PA': 2, 'NY': 3, 'CT': 1}, 'resident': 'NJ'}, {'NY': 157636, 'PA': 105090, 'CT': 52545}), ('normal control', {'wage': 761711, 'days': {'MA': 0}, 'resident': 'NJ'}, {'NJ': 761711})], [('regression', {'wage': 254323, 'days': {'NY': 1, 'PA': 8, 'NJ': 15, 'MA': 0}, 'resident': 'NY'}, {'NJ': 158952, 'PA': 84774, 'NY': 10597}), ('regression', {'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': 2, 'days': {'NJ': 2, 'PA': 2, 'NY': 0, 'MA': 1}, 'resident': 'CT'}, {'NJ': 1, 'PA': 1}), ('partial-repair probe', {'wage': 802876, 'days': {'NJ': 10, 'MA': 0, 'NY': 0, 'PA': 1}, 'resident': 'CT'}, {'NJ': 729887, 'PA': 72989}), ('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': 273177, 'days': {'PA': 0, 'NY': 1, 'NJ': 3}, 'resident': 'NJ'}, {'NJ': 204883, 'NY': 68294}), ('normal control', {'wage': 1, 'days': {'NJ': 15}, 'resident': 'NY'}, {'NJ': 1}), ('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})], [('regression', {'wage': 646558, 'days': {'NY': 15, 'CT': 3, 'MA': 3, 'NJ': 2}, 'resident': 'NJ'}, {'NY': 421668, 'CT': 84334, 'MA': 84334, 'NJ': 56222}), ('regression', {'wage': 15, 'days': {'NY': 2, 'MA': 0, 'PA': 2, 'NJ': 13}, 'resident': 'CT'}, {'NJ': 11, 'NY': 2, 'PA': 2}), ('partial-repair probe', {'wage': 5, 'days': {'MA': 17, 'NY': 2, 'PA': 9}, 'resident': 'NJ'}, {'MA': 3, 'PA': 2}), ('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': 2, 'days': {'NJ': 0}, 'resident': 'NJ'}, {'NJ': 2}), ('normal control', {'wage': 14, 'days': {'PA': 0, 'MA': 2}, 'resident': 'CT'}, {'MA': 14}), ('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})], [('regression', {'wage': 15, 'days': {'NY': 2, 'MA': 0, 'PA': 2, 'NJ': 13}, 'resident': 'CT'}, {'NJ': 11, 'NY': 2, 'PA': 2}), ('regression', {'wage': 4, 'days': {'NJ': 3, 'CT': 1, 'MA': 3}, 'resident': 'CT'}, {'MA': 2, 'NJ': 2}), ('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': 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}), ('normal control', {'wage': 29, 'days': {'PA': 2}, 'resident': 'NJ'}, {'PA': 29}), ('normal control', {'wage': 455522, 'days': {'MA': 0, 'CT': 0}, 'resident': 'NY'}, {'NY': 455522})]]
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	`{'MA': 30015, 'NJ': 330171, 'PA': 165084}`	`{'MA': 30015, 'NJ': 330170, 'PA': 165085}`	Failed
regression 1	`{'NJ': 2}`	`{'NJ': 1, 'PA': 1}`	Failed
partial-repair probe 2	`{'NJ': 2, 'NY': 8, 'PA': 7}`	`{'NJ': 3, 'NY': 7, 'PA': 7}`	Failed
partial-repair probe 3	`{'NJ': 16306, 'PA': 163068}`	`{'NJ': 16307, 'PA': 163067}`	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 / 3a10e97e868d0d4e7f71448c4ee742f4d46d0ddee839439ee4db91452046a888

3 / The verified repair

Exit 0

"""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': 525270, 'days': {'MA': 2, 'PA': 11, 'NJ': 22}, 'resident': 'NJ'}, {'NJ': 330170, 'PA': 165085, 'MA': 30015}), ('regression', {'wage': 2, 'days': {'NJ': 2, 'PA': 2, 'NY': 0, 'MA': 1}, 'resident': 'CT'}, {'NJ': 1, 'PA': 1}), ('partial-repair probe', {'wage': 17, 'days': {'NJ': 1, 'PA': 3, 'NY': 3}, 'resident': 'NY'}, {'NY': 7, 'PA': 7, 'NJ': 3}), ('partial-repair probe', {'wage': 179374, 'days': {'PA': 20, 'NJ': 2, 'MA': 0}, 'resident': 'NY'}, {'PA': 163067, 'NJ': 16307}), ('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': 2, 'days': {'NJ': 2, 'PA': 2, 'NY': 0, 'MA': 1}, 'resident': 'CT'}, {'NJ': 1, 'PA': 1}), ('regression', {'wage': 254323, 'days': {'NY': 1, 'PA': 8, 'NJ': 15, 'MA': 0}, 'resident': 'NY'}, {'NJ': 158952, 'PA': 84774, 'NY': 10597}), ('partial-repair probe', {'wage': 172162, 'days': {'MA': 6, 'CT': 3, 'PA': 11}, 'resident': 'NJ'}, {'PA': 94689, 'MA': 51649, 'CT': 25824}), ('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': 315271, 'days': {'PA': 2, 'NY': 3, 'CT': 1}, 'resident': 'NJ'}, {'NY': 157636, 'PA': 105090, 'CT': 52545}), ('normal control', {'wage': 761711, 'days': {'MA': 0}, 'resident': 'NJ'}, {'NJ': 761711})], [('regression', {'wage': 254323, 'days': {'NY': 1, 'PA': 8, 'NJ': 15, 'MA': 0}, 'resident': 'NY'}, {'NJ': 158952, 'PA': 84774, 'NY': 10597}), ('regression', {'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': 2, 'days': {'NJ': 2, 'PA': 2, 'NY': 0, 'MA': 1}, 'resident': 'CT'}, {'NJ': 1, 'PA': 1}), ('partial-repair probe', {'wage': 802876, 'days': {'NJ': 10, 'MA': 0, 'NY': 0, 'PA': 1}, 'resident': 'CT'}, {'NJ': 729887, 'PA': 72989}), ('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': 273177, 'days': {'PA': 0, 'NY': 1, 'NJ': 3}, 'resident': 'NJ'}, {'NJ': 204883, 'NY': 68294}), ('normal control', {'wage': 1, 'days': {'NJ': 15}, 'resident': 'NY'}, {'NJ': 1}), ('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})], [('regression', {'wage': 646558, 'days': {'NY': 15, 'CT': 3, 'MA': 3, 'NJ': 2}, 'resident': 'NJ'}, {'NY': 421668, 'CT': 84334, 'MA': 84334, 'NJ': 56222}), ('regression', {'wage': 15, 'days': {'NY': 2, 'MA': 0, 'PA': 2, 'NJ': 13}, 'resident': 'CT'}, {'NJ': 11, 'NY': 2, 'PA': 2}), ('partial-repair probe', {'wage': 5, 'days': {'MA': 17, 'NY': 2, 'PA': 9}, 'resident': 'NJ'}, {'MA': 3, 'PA': 2}), ('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': 2, 'days': {'NJ': 0}, 'resident': 'NJ'}, {'NJ': 2}), ('normal control', {'wage': 14, 'days': {'PA': 0, 'MA': 2}, 'resident': 'CT'}, {'MA': 14}), ('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})], [('regression', {'wage': 15, 'days': {'NY': 2, 'MA': 0, 'PA': 2, 'NJ': 13}, 'resident': 'CT'}, {'NJ': 11, 'NY': 2, 'PA': 2}), ('regression', {'wage': 4, 'days': {'NJ': 3, 'CT': 1, 'MA': 3}, 'resident': 'CT'}, {'MA': 2, 'NJ': 2}), ('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': 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}), ('normal control', {'wage': 29, 'days': {'PA': 2}, 'resident': 'NJ'}, {'PA': 29}), ('normal control', {'wage': 455522, 'days': {'MA': 0, 'CT': 0}, 'resident': 'NY'}, {'NY': 455522})]]
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	`{'MA': 30015, 'NJ': 330170, 'PA': 165085}`	`{'MA': 30015, 'NJ': 330170, 'PA': 165085}`	Passed
regression 1	`{'NJ': 1, 'PA': 1}`	`{'NJ': 1, 'PA': 1}`	Passed
partial-repair probe 2	`{'NJ': 3, 'NY': 7, 'PA': 7}`	`{'NJ': 3, 'NY': 7, 'PA': 7}`	Passed
partial-repair probe 3	`{'NJ': 16307, 'PA': 163067}`	`{'NJ': 16307, 'PA': 163067}`	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 / 07dacd2d4ef1c73f35a91009c11124ce63e464c0e8b7c8fef74853c5b97de441

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 2026-09-29T14:46:34.125496+00:00.

Case digest / d91144e9df34e35637d02b19ce0c644bca32ef3cfb6a9213271019b7dd941bc3