FAILURE MAP
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FA-59096 / Payroll withholding rules / Open access

Net-pay deduction priority and arrears: arrears carried into due amount · case 01

Previously missed deductions are never recovered.

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

ROOT CAUSE

The due amount ignores arrears carried from earlier paychecks.

THE FAILURE

The due amount ignores arrears carried from earlier paychecks.

Unsuccessful approach: The attempt takes the larger of the current amount and arrears instead of their sum.

Case contract

Input {gross, taxes, deductions: [[name, amount, priority, allow_partial]], arrears: {name: cents}}. Available = max(0, gross - taxes). Deductions run by ascending priority, ties in input order. Each is due amount + prior arrears; if due fits it is taken in full, else partial deductions take what is left and all-or-nothing deductions take 0. Any unpaid due becomes new arrears (only positive entries). Return {net, taken, arrears}.

Why this case matters

When net pay cannot cover every deduction, ordering and arrears carry-forward decide who gets paid.

1 / The failure

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

N = 1
observations = []
def solve(x):
    avail = max(0, x['gross'] - x['taxes'])
    taken = {}
    arrears = {}
    for name, amt, pri, partial in sorted(x['deductions'], key=lambda d: d[2]):
        due = amt
        if due <= avail:
            take = due
        elif partial:
            take = avail
        else:
            take = 0
        avail -= take
        taken[name] = take
        if due - take > 0:
            arrears[name] = due - take
    return {'net': avail, 'taken': taken, 'arrears': arrears}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'gross': 134653, 'taxes': 27454, 'deductions': [['parking', 26770, 3, False], ['loan', 12315, 2, False], ['union', 3364, 1, False], ['support', 11662, 3, True]], 'arrears': {'parking': 10177, 'loan': 15972, 'support': 6216}}, {'net': 20723, 'taken': {'union': 3364, 'loan': 28287, 'parking': 36947, 'support': 17878}, 'arrears': {}}), ('regression', {'gross': 138327, 'taxes': 24358, 'deductions': [['loan', 12004, 3, True], ['union', 4120, 2, True], ['medical', 35331, 3, False], ['parking', 697, 1, True], ['support', 15166, 2, True]], 'arrears': {'loan': 5341, 'union': 19151, 'support': 16971}}, {'net': 5188, 'taken': {'parking': 697, 'union': 23271, 'support': 32137, 'loan': 17345, 'medical': 35331}, 'arrears': {}}), ('partial-repair probe', {'gross': 102757, 'taxes': 16339, 'deductions': [['medical', 20312, 1, False]], 'arrears': {'medical': 12422}}, {'net': 53684, 'taken': {'medical': 32734}, 'arrears': {}}), ('partial-repair probe', {'gross': 6593, 'taxes': 872, 'deductions': [['parking', 5312, 3, False], ['union', 4345, 3, False], ['medical', 14587, 3, False], ['loan', 24540, 2, True], ['support', 7319, 3, True]], 'arrears': {'parking': 388, 'medical': 17218}}, {'net': 0, 'taken': {'loan': 5721, 'parking': 0, 'union': 0, 'medical': 0, 'support': 0}, 'arrears': {'loan': 18819, 'parking': 5700, 'union': 4345, 'medical': 31805, 'support': 7319}}), ('normal control', {'gross': 3515, 'taxes': 674, 'deductions': [['parking', 20962, 1, False], ['union', 18985, 3, True], ['loan', 33701, 1, True]], 'arrears': {}}, {'net': 0, 'taken': {'parking': 0, 'loan': 2841, 'union': 0}, 'arrears': {'parking': 20962, 'loan': 30860, 'union': 18985}}), ('normal control', {'gross': 106436, 'taxes': 29897, 'deductions': [['parking', 39254, 1, True]], 'arrears': {}}, {'net': 37285, 'taken': {'parking': 39254}, 'arrears': {}}), ('normal control', {'gross': 32919, 'taxes': 7584, 'deductions': [['parking', 36420, 3, True], ['charity', 19693, 3, False], ['loan', 12305, 1, True], ['medical', 7400, 2, True], ['support', 39536, 2, True]], 'arrears': {}}, {'net': 0, 'taken': {'loan': 12305, 'medical': 7400, 'support': 5630, 'parking': 0, 'charity': 0}, 'arrears': {'support': 33906, 'parking': 36420, 'charity': 19693}}), ('normal control', {'gross': 42097, 'taxes': 527, 'deductions': [['medical', 23283, 1, False], ['union', 33588, 1, False]], 'arrears': {}}, {'net': 18287, 'taken': {'medical': 23283, 'union': 0}, 'arrears': {'union': 33588}})], [('regression', {'gross': 138327, 'taxes': 24358, 'deductions': [['loan', 12004, 3, True], ['union', 4120, 2, True], ['medical', 35331, 3, False], ['parking', 697, 1, True], ['support', 15166, 2, True]], 'arrears': {'loan': 5341, 'union': 19151, 'support': 16971}}, {'net': 5188, 'taken': {'parking': 697, 'union': 23271, 'support': 32137, 'loan': 17345, 'medical': 35331}, 'arrears': {}}), ('regression', {'gross': 102757, 'taxes': 16339, 'deductions': [['medical', 20312, 1, False]], 'arrears': {'medical': 12422}}, {'net': 53684, 'taken': {'medical': 32734}, 'arrears': {}}), ('partial-repair probe', {'gross': 6593, 'taxes': 872, 'deductions': [['parking', 5312, 3, False], ['union', 4345, 3, False], ['medical', 14587, 3, False], ['loan', 24540, 2, True], ['support', 7319, 3, True]], 'arrears': {'parking': 388, 'medical': 17218}}, {'net': 0, 'taken': {'loan': 5721, 'parking': 0, 'union': 0, 'medical': 0, 'support': 0}, 'arrears': {'loan': 18819, 'parking': 5700, 'union': 4345, 'medical': 31805, 'support': 7319}}), ('partial-repair probe', {'gross': 45406, 'taxes': 3941, 'deductions': [['parking', 32509, 3, True], ['loan', 15062, 3, True], ['charity', 31648, 1, False]], 'arrears': {'parking': 1472, 'charity': 15167}}, {'net': 0, 'taken': {'charity': 0, 'parking': 33981, 'loan': 7484}, 'arrears': {'charity': 46815, 'loan': 7578}}), ('normal control', {'gross': 123929, 'taxes': 27738, 'deductions': [['parking', 24255, 3, False]], 'arrears': {}}, {'net': 71936, 'taken': {'parking': 24255}, 'arrears': {}}), ('normal control', {'gross': 60703, 'taxes': 11543, 'deductions': [['support', 14720, 2, False], ['loan', 10777, 3, False], ['medical', 34788, 2, True]], 'arrears': {}}, {'net': 0, 'taken': {'support': 14720, 'medical': 34440, 'loan': 0}, 'arrears': {'medical': 348, 'loan': 10777}}), ('normal control', {'gross': 121022, 'taxes': 14438, 'deductions': [['charity', 24183, 2, False], ['loan', 4420, 2, True]], 'arrears': {}}, {'net': 77981, 'taken': {'charity': 24183, 'loan': 4420}, 'arrears': {}}), ('normal control', {'gross': 131039, 'taxes': 2132, 'deductions': [['charity', 22460, 2, True], ['loan', 32332, 3, False]], 'arrears': {}}, {'net': 74115, 'taken': {'charity': 22460, 'loan': 32332}, 'arrears': {}})], [('regression', {'gross': 102757, 'taxes': 16339, 'deductions': [['medical', 20312, 1, False]], 'arrears': {'medical': 12422}}, {'net': 53684, 'taken': {'medical': 32734}, 'arrears': {}}), ('regression', {'gross': 6593, 'taxes': 872, 'deductions': [['parking', 5312, 3, False], ['union', 4345, 3, False], ['medical', 14587, 3, False], ['loan', 24540, 2, True], ['support', 7319, 3, True]], 'arrears': {'parking': 388, 'medical': 17218}}, {'net': 0, 'taken': {'loan': 5721, 'parking': 0, 'union': 0, 'medical': 0, 'support': 0}, 'arrears': {'loan': 18819, 'parking': 5700, 'union': 4345, 'medical': 31805, 'support': 7319}}), ('partial-repair probe', {'gross': 45406, 'taxes': 3941, 'deductions': [['parking', 32509, 3, True], ['loan', 15062, 3, True], ['charity', 31648, 1, False]], 'arrears': {'parking': 1472, 'charity': 15167}}, {'net': 0, 'taken': {'charity': 0, 'parking': 33981, 'loan': 7484}, 'arrears': {'charity': 46815, 'loan': 7578}}), ('partial-repair probe', {'gross': 132719, 'taxes': 9617, 'deductions': [['charity', 21694, 1, False], ['loan', 11829, 1, True], ['parking', 18178, 3, True], ['union', 1782, 3, True]], 'arrears': {'loan': 14963, 'parking': 3722, 'union': 3447}}, {'net': 47487, 'taken': {'charity': 21694, 'loan': 26792, 'parking': 21900, 'union': 5229}, 'arrears': {}}), ('normal control', {'gross': 93080, 'taxes': 11717, 'deductions': [['medical', 15825, 3, False]], 'arrears': {}}, {'net': 65538, 'taken': {'medical': 15825}, 'arrears': {}}), ('normal control', {'gross': 58263, 'taxes': 3517, 'deductions': [['loan', 34211, 3, False], ['support', 2445, 1, True], ['parking', 6724, 3, False]], 'arrears': {}}, {'net': 11366, 'taken': {'support': 2445, 'loan': 34211, 'parking': 6724}, 'arrears': {}}), ('normal control', {'gross': 111695, 'taxes': 33699, 'deductions': [['loan', 33780, 3, True], ['parking', 23393, 3, False], ['support', 21898, 2, False], ['charity', 33451, 1, False], ['union', 625, 2, True]], 'arrears': {}}, {'net': 0, 'taken': {'charity': 33451, 'support': 21898, 'union': 625, 'loan': 22022, 'parking': 0}, 'arrears': {'loan': 11758, 'parking': 23393}}), ('normal control', {'gross': 26399, 'taxes': 6362, 'deductions': [['charity', 39113, 3, True], ['parking', 3658, 2, True], ['loan', 30168, 3, True]], 'arrears': {}}, {'net': 0, 'taken': {'parking': 3658, 'charity': 16379, 'loan': 0}, 'arrears': {'charity': 22734, 'loan': 30168}})], [('regression', {'gross': 6593, 'taxes': 872, 'deductions': [['parking', 5312, 3, False], ['union', 4345, 3, False], ['medical', 14587, 3, False], ['loan', 24540, 2, True], ['support', 7319, 3, True]], 'arrears': {'parking': 388, 'medical': 17218}}, {'net': 0, 'taken': {'loan': 5721, 'parking': 0, 'union': 0, 'medical': 0, 'support': 0}, 'arrears': {'loan': 18819, 'parking': 5700, 'union': 4345, 'medical': 31805, 'support': 7319}}), ('regression', {'gross': 45406, 'taxes': 3941, 'deductions': [['parking', 32509, 3, True], ['loan', 15062, 3, True], ['charity', 31648, 1, False]], 'arrears': {'parking': 1472, 'charity': 15167}}, {'net': 0, 'taken': {'charity': 0, 'parking': 33981, 'loan': 7484}, 'arrears': {'charity': 46815, 'loan': 7578}}), ('partial-repair probe', {'gross': 91681, 'taxes': 9563, 'deductions': [['union', 25760, 2, False], ['parking', 28566, 1, False], ['support', 8036, 1, False], ['medical', 15864, 1, False], ['charity', 5966, 2, True]], 'arrears': {'parking': 5836, 'support': 18944, 'charity': 5663}}, {'net': 0, 'taken': {'parking': 34402, 'support': 26980, 'medical': 15864, 'union': 0, 'charity': 4872}, 'arrears': {'union': 25760, 'charity': 6757}}), ('partial-repair probe', {'gross': 13592, 'taxes': 3481, 'deductions': [['union', 941, 2, False], ['medical', 37170, 2, False], ['charity', 11425, 3, True], ['support', 36894, 2, False], ['parking', 10277, 3, True]], 'arrears': {'medical': 2360}}, {'net': 0, 'taken': {'union': 941, 'medical': 0, 'support': 0, 'charity': 9170, 'parking': 0}, 'arrears': {'medical': 39530, 'support': 36894, 'charity': 2255, 'parking': 10277}}), ('normal control', {'gross': 77880, 'taxes': 19549, 'deductions': [['loan', 3379, 3, True]], 'arrears': {}}, {'net': 54952, 'taken': {'loan': 3379}, 'arrears': {}}), ('normal control', {'gross': 21943, 'taxes': 4843, 'deductions': [['parking', 33670, 3, False], ['charity', 24679, 3, True]], 'arrears': {}}, {'net': 0, 'taken': {'parking': 0, 'charity': 17100}, 'arrears': {'parking': 33670, 'charity': 7579}}), ('normal control', {'gross': 46334, 'taxes': 3174, 'deductions': [['loan', 24433, 2, False], ['parking', 37324, 2, True], ['medical', 22420, 1, True], ['union', 9797, 1, True], ['charity', 28327, 2, False]], 'arrears': {}}, {'net': 0, 'taken': {'medical': 22420, 'union': 9797, 'loan': 0, 'parking': 10943, 'charity': 0}, 'arrears': {'loan': 24433, 'parking': 26381, 'charity': 28327}}), ('normal control', {'gross': 134030, 'taxes': 44349, 'deductions': [['support', 11357, 2, False]], 'arrears': {}}, {'net': 78324, 'taken': {'support': 11357}, 'arrears': {}})], [('regression', {'gross': 45406, 'taxes': 3941, 'deductions': [['parking', 32509, 3, True], ['loan', 15062, 3, True], ['charity', 31648, 1, False]], 'arrears': {'parking': 1472, 'charity': 15167}}, {'net': 0, 'taken': {'charity': 0, 'parking': 33981, 'loan': 7484}, 'arrears': {'charity': 46815, 'loan': 7578}}), ('regression', {'gross': 132719, 'taxes': 9617, 'deductions': [['charity', 21694, 1, False], ['loan', 11829, 1, True], ['parking', 18178, 3, True], ['union', 1782, 3, True]], 'arrears': {'loan': 14963, 'parking': 3722, 'union': 3447}}, {'net': 47487, 'taken': {'charity': 21694, 'loan': 26792, 'parking': 21900, 'union': 5229}, 'arrears': {}}), ('partial-repair probe', {'gross': 71403, 'taxes': 15182, 'deductions': [['support', 561, 2, True], ['charity', 7949, 1, True], ['parking', 31674, 1, False], ['medical', 37176, 1, False]], 'arrears': {'support': 13700}}, {'net': 2337, 'taken': {'charity': 7949, 'parking': 31674, 'medical': 0, 'support': 14261}, 'arrears': {'medical': 37176}}), ('partial-repair probe', {'gross': 13589, 'taxes': 714, 'deductions': [['charity', 299, 3, True]], 'arrears': {'charity': 4459}}, {'net': 8117, 'taken': {'charity': 4758}, 'arrears': {}}), ('normal control', {'gross': 109707, 'taxes': 1323, 'deductions': [['union', 39866, 3, True], ['loan', 38020, 1, True], ['support', 11077, 3, False]], 'arrears': {}}, {'net': 19421, 'taken': {'loan': 38020, 'union': 39866, 'support': 11077}, 'arrears': {}}), ('normal control', {'gross': 56861, 'taxes': 5156, 'deductions': [['loan', 39411, 2, True], ['support', 27265, 1, False], ['union', 39662, 3, True]], 'arrears': {}}, {'net': 0, 'taken': {'support': 27265, 'loan': 24440, 'union': 0}, 'arrears': {'loan': 14971, 'union': 39662}}), ('normal control', {'gross': 134888, 'taxes': 11264, 'deductions': [['union', 12074, 3, True], ['charity', 22324, 1, True], ['parking', 15797, 3, True], ['support', 20440, 2, False], ['loan', 14221, 3, True]], 'arrears': {}}, {'net': 38768, 'taken': {'charity': 22324, 'support': 20440, 'union': 12074, 'parking': 15797, 'loan': 14221}, 'arrears': {}}), ('normal control', {'gross': 52145, 'taxes': 5283, 'deductions': [['charity', 22477, 3, False], ['support', 31082, 1, True]], 'arrears': {}}, {'net': 15780, 'taken': {'support': 31082, 'charity': 0}, 'arrears': {'charity': 22477}})]]
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{'arrears': {}, 'net': 53088, 'taken': {'loan': 12315, 'parking': 26770, 'support': 11662, 'union': 3364}}{'arrears': {}, 'net': 20723, 'taken': {'loan': 28287, 'parking': 36947, 'support': 17878, 'union': 3364}}Failed
regression 1{'arrears': {}, 'net': 46651, 'taken': {'loan': 12004, 'medical': 35331, 'parking': 697, 'support': 15166, 'union': 4120}}{'arrears': {}, 'net': 5188, 'taken': {'loan': 17345, 'medical': 35331, 'parking': 697, 'support': 32137, 'union': 23271}}Failed
partial-repair probe 2{'arrears': {}, 'net': 66106, 'taken': {'medical': 20312}}{'arrears': {}, 'net': 53684, 'taken': {'medical': 32734}}Failed
partial-repair probe 3{'arrears': {'loan': 18819, 'medical': 14587, 'parking': 5312, 'support': 7319, 'union': 4345}, 'net': 0, 'taken': {'loan': 5721, 'medical': 0, 'parking': 0, 'support': 0, 'union': 0}}{'arrears': {'loan': 18819, 'medical': 31805, 'parking': 5700, 'support': 7319, 'union': 4345}, 'net': 0, 'taken': {'loan': 5721, 'medical': 0, 'parking': 0, 'support': 0, 'union': 0}}Failed
normal control 4{'arrears': {'loan': 30860, 'parking': 20962, 'union': 18985}, 'net': 0, 'taken': {'loan': 2841, 'parking': 0, 'union': 0}}{'arrears': {'loan': 30860, 'parking': 20962, 'union': 18985}, 'net': 0, 'taken': {'loan': 2841, 'parking': 0, 'union': 0}}Passed
normal control 5{'arrears': {}, 'net': 37285, 'taken': {'parking': 39254}}{'arrears': {}, 'net': 37285, 'taken': {'parking': 39254}}Passed
normal control 6{'arrears': {'charity': 19693, 'parking': 36420, 'support': 33906}, 'net': 0, 'taken': {'charity': 0, 'loan': 12305, 'medical': 7400, 'parking': 0, 'support': 5630}}{'arrears': {'charity': 19693, 'parking': 36420, 'support': 33906}, 'net': 0, 'taken': {'charity': 0, 'loan': 12305, 'medical': 7400, 'parking': 0, 'support': 5630}}Passed
normal control 7{'arrears': {'union': 33588}, 'net': 18287, 'taken': {'medical': 23283, 'union': 0}}{'arrears': {'union': 33588}, 'net': 18287, 'taken': {'medical': 23283, 'union': 0}}Passed

SHA-256 / 39a7c342188aa2afc9fc04e9a1f3b91159ca7817fe5bf2d5975e11a5102c29cb

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(x):
    avail = max(0, x['gross'] - x['taxes'])
    taken = {}
    arrears = {}
    for name, amt, pri, partial in sorted(x['deductions'], key=lambda d: d[2]):
        due = max(amt, x['arrears'].get(name, 0))
        if due <= avail:
            take = due
        elif partial:
            take = avail
        else:
            take = 0
        avail -= take
        taken[name] = take
        if due - take > 0:
            arrears[name] = due - take
    return {'net': avail, 'taken': taken, 'arrears': arrears}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression', {'gross': 134653, 'taxes': 27454, 'deductions': [['parking', 26770, 3, False], ['loan', 12315, 2, False], ['union', 3364, 1, False], ['support', 11662, 3, True]], 'arrears': {'parking': 10177, 'loan': 15972, 'support': 6216}}, {'net': 20723, 'taken': {'union': 3364, 'loan': 28287, 'parking': 36947, 'support': 17878}, 'arrears': {}}), ('regression', {'gross': 138327, 'taxes': 24358, 'deductions': [['loan', 12004, 3, True], ['union', 4120, 2, True], ['medical', 35331, 3, False], ['parking', 697, 1, True], ['support', 15166, 2, True]], 'arrears': {'loan': 5341, 'union': 19151, 'support': 16971}}, {'net': 5188, 'taken': {'parking': 697, 'union': 23271, 'support': 32137, 'loan': 17345, 'medical': 35331}, 'arrears': {}}), ('partial-repair probe', {'gross': 102757, 'taxes': 16339, 'deductions': [['medical', 20312, 1, False]], 'arrears': {'medical': 12422}}, {'net': 53684, 'taken': {'medical': 32734}, 'arrears': {}}), ('partial-repair probe', {'gross': 6593, 'taxes': 872, 'deductions': [['parking', 5312, 3, False], ['union', 4345, 3, False], ['medical', 14587, 3, False], ['loan', 24540, 2, True], ['support', 7319, 3, True]], 'arrears': {'parking': 388, 'medical': 17218}}, {'net': 0, 'taken': {'loan': 5721, 'parking': 0, 'union': 0, 'medical': 0, 'support': 0}, 'arrears': {'loan': 18819, 'parking': 5700, 'union': 4345, 'medical': 31805, 'support': 7319}}), ('normal control', {'gross': 3515, 'taxes': 674, 'deductions': [['parking', 20962, 1, False], ['union', 18985, 3, True], ['loan', 33701, 1, True]], 'arrears': {}}, {'net': 0, 'taken': {'parking': 0, 'loan': 2841, 'union': 0}, 'arrears': {'parking': 20962, 'loan': 30860, 'union': 18985}}), ('normal control', {'gross': 106436, 'taxes': 29897, 'deductions': [['parking', 39254, 1, True]], 'arrears': {}}, {'net': 37285, 'taken': {'parking': 39254}, 'arrears': {}}), ('normal control', {'gross': 32919, 'taxes': 7584, 'deductions': [['parking', 36420, 3, True], ['charity', 19693, 3, False], ['loan', 12305, 1, True], ['medical', 7400, 2, True], ['support', 39536, 2, True]], 'arrears': {}}, {'net': 0, 'taken': {'loan': 12305, 'medical': 7400, 'support': 5630, 'parking': 0, 'charity': 0}, 'arrears': {'support': 33906, 'parking': 36420, 'charity': 19693}}), ('normal control', {'gross': 42097, 'taxes': 527, 'deductions': [['medical', 23283, 1, False], ['union', 33588, 1, False]], 'arrears': {}}, {'net': 18287, 'taken': {'medical': 23283, 'union': 0}, 'arrears': {'union': 33588}})], [('regression', {'gross': 138327, 'taxes': 24358, 'deductions': [['loan', 12004, 3, True], ['union', 4120, 2, True], ['medical', 35331, 3, False], ['parking', 697, 1, True], ['support', 15166, 2, True]], 'arrears': {'loan': 5341, 'union': 19151, 'support': 16971}}, {'net': 5188, 'taken': {'parking': 697, 'union': 23271, 'support': 32137, 'loan': 17345, 'medical': 35331}, 'arrears': {}}), ('regression', {'gross': 102757, 'taxes': 16339, 'deductions': [['medical', 20312, 1, False]], 'arrears': {'medical': 12422}}, {'net': 53684, 'taken': {'medical': 32734}, 'arrears': {}}), ('partial-repair probe', {'gross': 6593, 'taxes': 872, 'deductions': [['parking', 5312, 3, False], ['union', 4345, 3, False], ['medical', 14587, 3, False], ['loan', 24540, 2, True], ['support', 7319, 3, True]], 'arrears': {'parking': 388, 'medical': 17218}}, {'net': 0, 'taken': {'loan': 5721, 'parking': 0, 'union': 0, 'medical': 0, 'support': 0}, 'arrears': {'loan': 18819, 'parking': 5700, 'union': 4345, 'medical': 31805, 'support': 7319}}), ('partial-repair probe', {'gross': 45406, 'taxes': 3941, 'deductions': [['parking', 32509, 3, True], ['loan', 15062, 3, True], ['charity', 31648, 1, False]], 'arrears': {'parking': 1472, 'charity': 15167}}, {'net': 0, 'taken': {'charity': 0, 'parking': 33981, 'loan': 7484}, 'arrears': {'charity': 46815, 'loan': 7578}}), ('normal control', {'gross': 123929, 'taxes': 27738, 'deductions': [['parking', 24255, 3, False]], 'arrears': {}}, {'net': 71936, 'taken': {'parking': 24255}, 'arrears': {}}), ('normal control', {'gross': 60703, 'taxes': 11543, 'deductions': [['support', 14720, 2, False], ['loan', 10777, 3, False], ['medical', 34788, 2, True]], 'arrears': {}}, {'net': 0, 'taken': {'support': 14720, 'medical': 34440, 'loan': 0}, 'arrears': {'medical': 348, 'loan': 10777}}), ('normal control', {'gross': 121022, 'taxes': 14438, 'deductions': [['charity', 24183, 2, False], ['loan', 4420, 2, True]], 'arrears': {}}, {'net': 77981, 'taken': {'charity': 24183, 'loan': 4420}, 'arrears': {}}), ('normal control', {'gross': 131039, 'taxes': 2132, 'deductions': [['charity', 22460, 2, True], ['loan', 32332, 3, False]], 'arrears': {}}, {'net': 74115, 'taken': {'charity': 22460, 'loan': 32332}, 'arrears': {}})], [('regression', {'gross': 102757, 'taxes': 16339, 'deductions': [['medical', 20312, 1, False]], 'arrears': {'medical': 12422}}, {'net': 53684, 'taken': {'medical': 32734}, 'arrears': {}}), ('regression', {'gross': 6593, 'taxes': 872, 'deductions': [['parking', 5312, 3, False], ['union', 4345, 3, False], ['medical', 14587, 3, False], ['loan', 24540, 2, True], ['support', 7319, 3, True]], 'arrears': {'parking': 388, 'medical': 17218}}, {'net': 0, 'taken': {'loan': 5721, 'parking': 0, 'union': 0, 'medical': 0, 'support': 0}, 'arrears': {'loan': 18819, 'parking': 5700, 'union': 4345, 'medical': 31805, 'support': 7319}}), ('partial-repair probe', {'gross': 45406, 'taxes': 3941, 'deductions': [['parking', 32509, 3, True], ['loan', 15062, 3, True], ['charity', 31648, 1, False]], 'arrears': {'parking': 1472, 'charity': 15167}}, {'net': 0, 'taken': {'charity': 0, 'parking': 33981, 'loan': 7484}, 'arrears': {'charity': 46815, 'loan': 7578}}), ('partial-repair probe', {'gross': 132719, 'taxes': 9617, 'deductions': [['charity', 21694, 1, False], ['loan', 11829, 1, True], ['parking', 18178, 3, True], ['union', 1782, 3, True]], 'arrears': {'loan': 14963, 'parking': 3722, 'union': 3447}}, {'net': 47487, 'taken': {'charity': 21694, 'loan': 26792, 'parking': 21900, 'union': 5229}, 'arrears': {}}), ('normal control', {'gross': 93080, 'taxes': 11717, 'deductions': [['medical', 15825, 3, False]], 'arrears': {}}, {'net': 65538, 'taken': {'medical': 15825}, 'arrears': {}}), ('normal control', {'gross': 58263, 'taxes': 3517, 'deductions': [['loan', 34211, 3, False], ['support', 2445, 1, True], ['parking', 6724, 3, False]], 'arrears': {}}, {'net': 11366, 'taken': {'support': 2445, 'loan': 34211, 'parking': 6724}, 'arrears': {}}), ('normal control', {'gross': 111695, 'taxes': 33699, 'deductions': [['loan', 33780, 3, True], ['parking', 23393, 3, False], ['support', 21898, 2, False], ['charity', 33451, 1, False], ['union', 625, 2, True]], 'arrears': {}}, {'net': 0, 'taken': {'charity': 33451, 'support': 21898, 'union': 625, 'loan': 22022, 'parking': 0}, 'arrears': {'loan': 11758, 'parking': 23393}}), ('normal control', {'gross': 26399, 'taxes': 6362, 'deductions': [['charity', 39113, 3, True], ['parking', 3658, 2, True], ['loan', 30168, 3, True]], 'arrears': {}}, {'net': 0, 'taken': {'parking': 3658, 'charity': 16379, 'loan': 0}, 'arrears': {'charity': 22734, 'loan': 30168}})], [('regression', {'gross': 6593, 'taxes': 872, 'deductions': [['parking', 5312, 3, False], ['union', 4345, 3, False], ['medical', 14587, 3, False], ['loan', 24540, 2, True], ['support', 7319, 3, True]], 'arrears': {'parking': 388, 'medical': 17218}}, {'net': 0, 'taken': {'loan': 5721, 'parking': 0, 'union': 0, 'medical': 0, 'support': 0}, 'arrears': {'loan': 18819, 'parking': 5700, 'union': 4345, 'medical': 31805, 'support': 7319}}), ('regression', {'gross': 45406, 'taxes': 3941, 'deductions': [['parking', 32509, 3, True], ['loan', 15062, 3, True], ['charity', 31648, 1, False]], 'arrears': {'parking': 1472, 'charity': 15167}}, {'net': 0, 'taken': {'charity': 0, 'parking': 33981, 'loan': 7484}, 'arrears': {'charity': 46815, 'loan': 7578}}), ('partial-repair probe', {'gross': 91681, 'taxes': 9563, 'deductions': [['union', 25760, 2, False], ['parking', 28566, 1, False], ['support', 8036, 1, False], ['medical', 15864, 1, False], ['charity', 5966, 2, True]], 'arrears': {'parking': 5836, 'support': 18944, 'charity': 5663}}, {'net': 0, 'taken': {'parking': 34402, 'support': 26980, 'medical': 15864, 'union': 0, 'charity': 4872}, 'arrears': {'union': 25760, 'charity': 6757}}), ('partial-repair probe', {'gross': 13592, 'taxes': 3481, 'deductions': [['union', 941, 2, False], ['medical', 37170, 2, False], ['charity', 11425, 3, True], ['support', 36894, 2, False], ['parking', 10277, 3, True]], 'arrears': {'medical': 2360}}, {'net': 0, 'taken': {'union': 941, 'medical': 0, 'support': 0, 'charity': 9170, 'parking': 0}, 'arrears': {'medical': 39530, 'support': 36894, 'charity': 2255, 'parking': 10277}}), ('normal control', {'gross': 77880, 'taxes': 19549, 'deductions': [['loan', 3379, 3, True]], 'arrears': {}}, {'net': 54952, 'taken': {'loan': 3379}, 'arrears': {}}), ('normal control', {'gross': 21943, 'taxes': 4843, 'deductions': [['parking', 33670, 3, False], ['charity', 24679, 3, True]], 'arrears': {}}, {'net': 0, 'taken': {'parking': 0, 'charity': 17100}, 'arrears': {'parking': 33670, 'charity': 7579}}), ('normal control', {'gross': 46334, 'taxes': 3174, 'deductions': [['loan', 24433, 2, False], ['parking', 37324, 2, True], ['medical', 22420, 1, True], ['union', 9797, 1, True], ['charity', 28327, 2, False]], 'arrears': {}}, {'net': 0, 'taken': {'medical': 22420, 'union': 9797, 'loan': 0, 'parking': 10943, 'charity': 0}, 'arrears': {'loan': 24433, 'parking': 26381, 'charity': 28327}}), ('normal control', {'gross': 134030, 'taxes': 44349, 'deductions': [['support', 11357, 2, False]], 'arrears': {}}, {'net': 78324, 'taken': {'support': 11357}, 'arrears': {}})], [('regression', {'gross': 45406, 'taxes': 3941, 'deductions': [['parking', 32509, 3, True], ['loan', 15062, 3, True], ['charity', 31648, 1, False]], 'arrears': {'parking': 1472, 'charity': 15167}}, {'net': 0, 'taken': {'charity': 0, 'parking': 33981, 'loan': 7484}, 'arrears': {'charity': 46815, 'loan': 7578}}), ('regression', {'gross': 132719, 'taxes': 9617, 'deductions': [['charity', 21694, 1, False], ['loan', 11829, 1, True], ['parking', 18178, 3, True], ['union', 1782, 3, True]], 'arrears': {'loan': 14963, 'parking': 3722, 'union': 3447}}, {'net': 47487, 'taken': {'charity': 21694, 'loan': 26792, 'parking': 21900, 'union': 5229}, 'arrears': {}}), ('partial-repair probe', {'gross': 71403, 'taxes': 15182, 'deductions': [['support', 561, 2, True], ['charity', 7949, 1, True], ['parking', 31674, 1, False], ['medical', 37176, 1, False]], 'arrears': {'support': 13700}}, {'net': 2337, 'taken': {'charity': 7949, 'parking': 31674, 'medical': 0, 'support': 14261}, 'arrears': {'medical': 37176}}), ('partial-repair probe', {'gross': 13589, 'taxes': 714, 'deductions': [['charity', 299, 3, True]], 'arrears': {'charity': 4459}}, {'net': 8117, 'taken': {'charity': 4758}, 'arrears': {}}), ('normal control', {'gross': 109707, 'taxes': 1323, 'deductions': [['union', 39866, 3, True], ['loan', 38020, 1, True], ['support', 11077, 3, False]], 'arrears': {}}, {'net': 19421, 'taken': {'loan': 38020, 'union': 39866, 'support': 11077}, 'arrears': {}}), ('normal control', {'gross': 56861, 'taxes': 5156, 'deductions': [['loan', 39411, 2, True], ['support', 27265, 1, False], ['union', 39662, 3, True]], 'arrears': {}}, {'net': 0, 'taken': {'support': 27265, 'loan': 24440, 'union': 0}, 'arrears': {'loan': 14971, 'union': 39662}}), ('normal control', {'gross': 134888, 'taxes': 11264, 'deductions': [['union', 12074, 3, True], ['charity', 22324, 1, True], ['parking', 15797, 3, True], ['support', 20440, 2, False], ['loan', 14221, 3, True]], 'arrears': {}}, {'net': 38768, 'taken': {'charity': 22324, 'support': 20440, 'union': 12074, 'parking': 15797, 'loan': 14221}, 'arrears': {}}), ('normal control', {'gross': 52145, 'taxes': 5283, 'deductions': [['charity', 22477, 3, False], ['support', 31082, 1, True]], 'arrears': {}}, {'net': 15780, 'taken': {'support': 31082, 'charity': 0}, 'arrears': {'charity': 22477}})]]
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{'arrears': {}, 'net': 49431, 'taken': {'loan': 15972, 'parking': 26770, 'support': 11662, 'union': 3364}}{'arrears': {}, 'net': 20723, 'taken': {'loan': 28287, 'parking': 36947, 'support': 17878, 'union': 3364}}Failed
regression 1{'arrears': {}, 'net': 29815, 'taken': {'loan': 12004, 'medical': 35331, 'parking': 697, 'support': 16971, 'union': 19151}}{'arrears': {}, 'net': 5188, 'taken': {'loan': 17345, 'medical': 35331, 'parking': 697, 'support': 32137, 'union': 23271}}Failed
partial-repair probe 2{'arrears': {}, 'net': 66106, 'taken': {'medical': 20312}}{'arrears': {}, 'net': 53684, 'taken': {'medical': 32734}}Failed
partial-repair probe 3{'arrears': {'loan': 18819, 'medical': 17218, 'parking': 5312, 'support': 7319, 'union': 4345}, 'net': 0, 'taken': {'loan': 5721, 'medical': 0, 'parking': 0, 'support': 0, 'union': 0}}{'arrears': {'loan': 18819, 'medical': 31805, 'parking': 5700, 'support': 7319, 'union': 4345}, 'net': 0, 'taken': {'loan': 5721, 'medical': 0, 'parking': 0, 'support': 0, 'union': 0}}Failed
normal control 4{'arrears': {'loan': 30860, 'parking': 20962, 'union': 18985}, 'net': 0, 'taken': {'loan': 2841, 'parking': 0, 'union': 0}}{'arrears': {'loan': 30860, 'parking': 20962, 'union': 18985}, 'net': 0, 'taken': {'loan': 2841, 'parking': 0, 'union': 0}}Passed
normal control 5{'arrears': {}, 'net': 37285, 'taken': {'parking': 39254}}{'arrears': {}, 'net': 37285, 'taken': {'parking': 39254}}Passed
normal control 6{'arrears': {'charity': 19693, 'parking': 36420, 'support': 33906}, 'net': 0, 'taken': {'charity': 0, 'loan': 12305, 'medical': 7400, 'parking': 0, 'support': 5630}}{'arrears': {'charity': 19693, 'parking': 36420, 'support': 33906}, 'net': 0, 'taken': {'charity': 0, 'loan': 12305, 'medical': 7400, 'parking': 0, 'support': 5630}}Passed
normal control 7{'arrears': {'union': 33588}, 'net': 18287, 'taken': {'medical': 23283, 'union': 0}}{'arrears': {'union': 33588}, 'net': 18287, 'taken': {'medical': 23283, 'union': 0}}Passed

SHA-256 / 0b4a26277d97d530f17a3b29ffb8779962b114223b48c44849327b55d767dc5a

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 8 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.

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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 2026-09-29T14:46:32.911613+00:00.

Case digest / 50d054c94efadf5c2da697de32aef52872733891c26c5d5b0051159785773996