FAILURE MAP
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FA-72356 / Check-digit algorithms / Open access

Luhn gate admits a lone check digit · case 01

A single "0" is accepted as a valid account number.

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

ROOT CAUSE

The length gate rejects only empty input (len(t) < 1), so one digit with no payload validates.

VERIFIED REPAIR

Require at least two digits: one payload digit plus the check digit.

Unsuccessful approach: Raising the minimum to three digits rejects legitimate two-digit numbers such as 18.

Case contract

Input a card-style number that may contain spaces or hyphens as group separators. After removing them the text must be 2..19 ASCII digits, otherwise "malformed". Doubling applies to every second digit counting from the rightmost (check) digit, doubled values above 9 lose 9, and the number is "valid" when the sum is a multiple of 10, else "invalid".

Why this case matters

Payment-card, loyalty and account numbers are screened with the Luhn mod-10 check before any lookup.

1 / The failure

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

N = 1
observations = []
def solve(s):
    t = s.replace(' ', '').replace('-', '')
    if not t.isascii() or not t.isdigit() or len(t) < 1 or len(t) > 19:
        return 'malformed'
    total = 0
    for i, ch in enumerate(reversed(t)):
        d = ord(ch) - 48
        if i % 2 == 1:
            d *= 2
            if d > 9:
                d -= 9
        total += d
    return 'valid' if total % 10 == 0 else 'invalid'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["0"]', ['0'], 'malformed'], ['partial-repair ["59"]', ['59'], 'valid'], ['partial-repair ["91"]', ['91'], 'valid'], ['control ["182"]', ['182'], 'valid'], ['control ["97956"]', ['97956'], 'valid'], ['control ["60866456"]', ['60866456'], 'valid'], ['control ["49717735275"]', ['49717735275'], 'valid'], ['control ["9207919074163"]', ['9207919074163'], 'valid']], [['regression ["0"]', ['0'], 'malformed'], ['partial-repair ["18"]', ['18'], 'valid'], ['partial-repair ["00"]', ['00'], 'valid'], ['control ["470663048070284"]', ['470663048070284'], 'valid'], ['control ["2300017738893848"]', ['2300017738893848'], 'valid'], ['control ["7985145013991721"]', ['7985145013991721'], 'valid'], ['control ["067122965057139178"]', ['067122965057139178'], 'valid'], ['control ["1513156399001929628"]', ['1513156399001929628'], 'valid']], [['regression ["0"]', ['0'], 'malformed'], ['partial-repair ["91"]', ['91'], 'valid'], ['partial-repair ["52"]', ['52'], 'invalid'], ['control ["9505094299844733505"]', ['9505094299844733505'], 'valid'], ['control ["0906050370970"]', ['0906050370970'], 'valid'], ['control ["3165356977"]', ['3165356977'], 'valid'], ['control ["992"]', ['992'], 'valid'], ['control ["5553"]', ['5553'], 'valid']], [['regression ["0"]', ['0'], 'malformed'], ['partial-repair ["00"]', ['00'], 'valid'], ['partial-repair ["59"]', ['59'], 'valid'], ['control ["77777779"]', ['77777779'], 'valid'], ['control ["185"]', ['185'], 'invalid'], ['control ["97959"]', ['97959'], 'invalid'], ['control ["60866459"]', ['60866459'], 'invalid'], ['control ["49717735278"]', ['49717735278'], 'invalid']], [['regression ["0"]', ['0'], 'malformed'], ['partial-repair ["52"]', ['52'], 'invalid'], ['partial-repair ["18"]', ['18'], 'valid'], ['control ["9207919074166"]', ['9207919074166'], 'invalid'], ['control ["470663048070287"]', ['470663048070287'], 'invalid'], ['control ["2300017738893841"]', ['2300017738893841'], 'invalid'], ['control ["4111-1111-1111-1111"]', ['4111-1111-1111-1111'], 'valid'], ['control ["4111 1111 1111 1111"]', ['4111 1111 1111 1111'], 'valid']]]
for label, args, expected in fixtures[N - 1]:
    check(label, 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"]validmalformedFailed
partial-repair ["59"]validvalidPassed
partial-repair ["91"]validvalidPassed
control ["182"]validvalidPassed
control ["97956"]validvalidPassed
control ["60866456"]validvalidPassed
control ["49717735275"]validvalidPassed
control ["9207919074163"]validvalidPassed

SHA-256 / 4307c7b299ba878325496f99b95ea6f4980e948feb9923690dba8622aed8cea9

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(s):
    t = s.replace(' ', '').replace('-', '')
    if not t.isascii() or not t.isdigit() or len(t) < 3 or len(t) > 19:
        return 'malformed'
    total = 0
    for i, ch in enumerate(reversed(t)):
        d = ord(ch) - 48
        if i % 2 == 1:
            d *= 2
            if d > 9:
                d -= 9
        total += d
    return 'valid' if total % 10 == 0 else 'invalid'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["0"]', ['0'], 'malformed'], ['partial-repair ["59"]', ['59'], 'valid'], ['partial-repair ["91"]', ['91'], 'valid'], ['control ["182"]', ['182'], 'valid'], ['control ["97956"]', ['97956'], 'valid'], ['control ["60866456"]', ['60866456'], 'valid'], ['control ["49717735275"]', ['49717735275'], 'valid'], ['control ["9207919074163"]', ['9207919074163'], 'valid']], [['regression ["0"]', ['0'], 'malformed'], ['partial-repair ["18"]', ['18'], 'valid'], ['partial-repair ["00"]', ['00'], 'valid'], ['control ["470663048070284"]', ['470663048070284'], 'valid'], ['control ["2300017738893848"]', ['2300017738893848'], 'valid'], ['control ["7985145013991721"]', ['7985145013991721'], 'valid'], ['control ["067122965057139178"]', ['067122965057139178'], 'valid'], ['control ["1513156399001929628"]', ['1513156399001929628'], 'valid']], [['regression ["0"]', ['0'], 'malformed'], ['partial-repair ["91"]', ['91'], 'valid'], ['partial-repair ["52"]', ['52'], 'invalid'], ['control ["9505094299844733505"]', ['9505094299844733505'], 'valid'], ['control ["0906050370970"]', ['0906050370970'], 'valid'], ['control ["3165356977"]', ['3165356977'], 'valid'], ['control ["992"]', ['992'], 'valid'], ['control ["5553"]', ['5553'], 'valid']], [['regression ["0"]', ['0'], 'malformed'], ['partial-repair ["00"]', ['00'], 'valid'], ['partial-repair ["59"]', ['59'], 'valid'], ['control ["77777779"]', ['77777779'], 'valid'], ['control ["185"]', ['185'], 'invalid'], ['control ["97959"]', ['97959'], 'invalid'], ['control ["60866459"]', ['60866459'], 'invalid'], ['control ["49717735278"]', ['49717735278'], 'invalid']], [['regression ["0"]', ['0'], 'malformed'], ['partial-repair ["52"]', ['52'], 'invalid'], ['partial-repair ["18"]', ['18'], 'valid'], ['control ["9207919074166"]', ['9207919074166'], 'invalid'], ['control ["470663048070287"]', ['470663048070287'], 'invalid'], ['control ["2300017738893841"]', ['2300017738893841'], 'invalid'], ['control ["4111-1111-1111-1111"]', ['4111-1111-1111-1111'], 'valid'], ['control ["4111 1111 1111 1111"]', ['4111 1111 1111 1111'], 'valid']]]
for label, args, expected in fixtures[N - 1]:
    check(label, 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"]malformedmalformedPassed
partial-repair ["59"]malformedvalidFailed
partial-repair ["91"]malformedvalidFailed
control ["182"]validvalidPassed
control ["97956"]validvalidPassed
control ["60866456"]validvalidPassed
control ["49717735275"]validvalidPassed
control ["9207919074163"]validvalidPassed

SHA-256 / 3cb58a47fce18aff76aa014439c37cbf9b760f9eb52f6f5b7bfe235fd62985c9

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(s):
    t = s.replace(' ', '').replace('-', '')
    if not t.isascii() or not t.isdigit() or len(t) < 2 or len(t) > 19:
        return 'malformed'
    total = 0
    for i, ch in enumerate(reversed(t)):
        d = ord(ch) - 48
        if i % 2 == 1:
            d *= 2
            if d > 9:
                d -= 9
        total += d
    return 'valid' if total % 10 == 0 else 'invalid'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["0"]', ['0'], 'malformed'], ['partial-repair ["59"]', ['59'], 'valid'], ['partial-repair ["91"]', ['91'], 'valid'], ['control ["182"]', ['182'], 'valid'], ['control ["97956"]', ['97956'], 'valid'], ['control ["60866456"]', ['60866456'], 'valid'], ['control ["49717735275"]', ['49717735275'], 'valid'], ['control ["9207919074163"]', ['9207919074163'], 'valid']], [['regression ["0"]', ['0'], 'malformed'], ['partial-repair ["18"]', ['18'], 'valid'], ['partial-repair ["00"]', ['00'], 'valid'], ['control ["470663048070284"]', ['470663048070284'], 'valid'], ['control ["2300017738893848"]', ['2300017738893848'], 'valid'], ['control ["7985145013991721"]', ['7985145013991721'], 'valid'], ['control ["067122965057139178"]', ['067122965057139178'], 'valid'], ['control ["1513156399001929628"]', ['1513156399001929628'], 'valid']], [['regression ["0"]', ['0'], 'malformed'], ['partial-repair ["91"]', ['91'], 'valid'], ['partial-repair ["52"]', ['52'], 'invalid'], ['control ["9505094299844733505"]', ['9505094299844733505'], 'valid'], ['control ["0906050370970"]', ['0906050370970'], 'valid'], ['control ["3165356977"]', ['3165356977'], 'valid'], ['control ["992"]', ['992'], 'valid'], ['control ["5553"]', ['5553'], 'valid']], [['regression ["0"]', ['0'], 'malformed'], ['partial-repair ["00"]', ['00'], 'valid'], ['partial-repair ["59"]', ['59'], 'valid'], ['control ["77777779"]', ['77777779'], 'valid'], ['control ["185"]', ['185'], 'invalid'], ['control ["97959"]', ['97959'], 'invalid'], ['control ["60866459"]', ['60866459'], 'invalid'], ['control ["49717735278"]', ['49717735278'], 'invalid']], [['regression ["0"]', ['0'], 'malformed'], ['partial-repair ["52"]', ['52'], 'invalid'], ['partial-repair ["18"]', ['18'], 'valid'], ['control ["9207919074166"]', ['9207919074166'], 'invalid'], ['control ["470663048070287"]', ['470663048070287'], 'invalid'], ['control ["2300017738893841"]', ['2300017738893841'], 'invalid'], ['control ["4111-1111-1111-1111"]', ['4111-1111-1111-1111'], 'valid'], ['control ["4111 1111 1111 1111"]', ['4111 1111 1111 1111'], 'valid']]]
for label, args, expected in fixtures[N - 1]:
    check(label, 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"]malformedmalformedPassed
partial-repair ["59"]validvalidPassed
partial-repair ["91"]validvalidPassed
control ["182"]validvalidPassed
control ["97956"]validvalidPassed
control ["60866456"]validvalidPassed
control ["49717735275"]validvalidPassed
control ["9207919074163"]validvalidPassed

SHA-256 / be6e38f46d76a8f10d5eae7db57436ed417f9bb56f486592cdc73cfc6956ac2a

Verification & scope

A deterministic, bounded teaching model of the named scheme under the stated contract; not a certified validator. 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 2026-09-29T14:48:37.810993+00:00.

Case digest / 0de07fad48f71d163d8605a0a95bc908f1eb8b0bf07b13b0630075347703f928