FA-72361 / Check-digit algorithms / Open access

Luhn gate accepts non-ASCII decimal digits · case 01

Arabic-Indic digit strings are scored as valid or invalid instead of malformed.

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

ROOT CAUSE

The gate relies on str.isdigit without isascii, so Unicode digits pass and ord(ch) - 48 yields huge values.

VERIFIED REPAIR

Require ASCII before the digit test so only 0-9 reach the arithmetic.

Unsuccessful approach: Switching to isdecimal still admits every Unicode decimal digit.

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.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 ["١٨"]', ['١٨'], 'malformed'], ['regression ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['control ["59"]', ['59'], 'valid'], ['control ["182"]', ['182'], 'valid'], ['control ["97956"]', ['97956'], 'valid'], ['control ["60866456"]', ['60866456'], 'valid'], ['control ["49717735275"]', ['49717735275'], 'valid'], ['control ["9207919074163"]', ['9207919074163'], 'valid']], [['regression ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['regression ["١٨"]', ['١٨'], 'malformed'], ['control ["9207919074163"]', ['9207919074163'], 'valid'], ['control ["470663048070284"]', ['470663048070284'], 'valid'], ['control ["2300017738893848"]', ['2300017738893848'], 'valid'], ['control ["7985145013991721"]', ['7985145013991721'], 'valid'], ['control ["067122965057139178"]', ['067122965057139178'], 'valid'], ['control ["1513156399001929628"]', ['1513156399001929628'], 'valid']], [['regression ["١٨"]', ['١٨'], 'malformed'], ['regression ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['control ["1513156399001929628"]', ['1513156399001929628'], 'valid'], ['control ["9505094299844733505"]', ['9505094299844733505'], 'valid'], ['control ["0906050370970"]', ['0906050370970'], 'valid'], ['control ["3165356977"]', ['3165356977'], 'valid'], ['control ["91"]', ['91'], 'valid'], ['control ["992"]', ['992'], 'valid']], [['regression ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['regression ["١٨"]', ['١٨'], 'malformed'], ['control ["992"]', ['992'], 'valid'], ['control ["5553"]', ['5553'], 'valid'], ['control ["77777779"]', ['77777779'], 'valid'], ['control ["52"]', ['52'], 'invalid'], ['control ["185"]', ['185'], 'invalid'], ['control ["97959"]', ['97959'], 'invalid']], [['regression ["١٨"]', ['١٨'], 'malformed'], ['regression ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['control ["97959"]', ['97959'], 'invalid'], ['control ["60866459"]', ['60866459'], 'invalid'], ['control ["49717735278"]', ['49717735278'], 'invalid'], ['control ["9207919074166"]', ['9207919074166'], 'invalid'], ['control ["470663048070287"]', ['470663048070287'], 'invalid'], ['control ["2300017738893841"]', ['2300017738893841'], 'invalid']]]
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 fixture	Actual	Expected	Outcome
regression ["١٨"]	`invalid`	`malformed`	Failed
regression ["٣٤٥"]	`invalid`	`malformed`	Failed
control ["59"]	`valid`	`valid`	Passed
control ["182"]	`valid`	`valid`	Passed
control ["97956"]	`valid`	`valid`	Passed
control ["60866456"]	`valid`	`valid`	Passed
control ["49717735275"]	`valid`	`valid`	Passed
control ["9207919074163"]	`valid`	`valid`	Passed

SHA-256 / 2ef937e169432a71370ee16916dca4a8478be29f48412b7796e6423270b43b47

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.isdecimal() 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 ["١٨"]', ['١٨'], 'malformed'], ['regression ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['control ["59"]', ['59'], 'valid'], ['control ["182"]', ['182'], 'valid'], ['control ["97956"]', ['97956'], 'valid'], ['control ["60866456"]', ['60866456'], 'valid'], ['control ["49717735275"]', ['49717735275'], 'valid'], ['control ["9207919074163"]', ['9207919074163'], 'valid']], [['regression ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['regression ["١٨"]', ['١٨'], 'malformed'], ['control ["9207919074163"]', ['9207919074163'], 'valid'], ['control ["470663048070284"]', ['470663048070284'], 'valid'], ['control ["2300017738893848"]', ['2300017738893848'], 'valid'], ['control ["7985145013991721"]', ['7985145013991721'], 'valid'], ['control ["067122965057139178"]', ['067122965057139178'], 'valid'], ['control ["1513156399001929628"]', ['1513156399001929628'], 'valid']], [['regression ["١٨"]', ['١٨'], 'malformed'], ['regression ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['control ["1513156399001929628"]', ['1513156399001929628'], 'valid'], ['control ["9505094299844733505"]', ['9505094299844733505'], 'valid'], ['control ["0906050370970"]', ['0906050370970'], 'valid'], ['control ["3165356977"]', ['3165356977'], 'valid'], ['control ["91"]', ['91'], 'valid'], ['control ["992"]', ['992'], 'valid']], [['regression ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['regression ["١٨"]', ['١٨'], 'malformed'], ['control ["992"]', ['992'], 'valid'], ['control ["5553"]', ['5553'], 'valid'], ['control ["77777779"]', ['77777779'], 'valid'], ['control ["52"]', ['52'], 'invalid'], ['control ["185"]', ['185'], 'invalid'], ['control ["97959"]', ['97959'], 'invalid']], [['regression ["١٨"]', ['١٨'], 'malformed'], ['regression ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['control ["97959"]', ['97959'], 'invalid'], ['control ["60866459"]', ['60866459'], 'invalid'], ['control ["49717735278"]', ['49717735278'], 'invalid'], ['control ["9207919074166"]', ['9207919074166'], 'invalid'], ['control ["470663048070287"]', ['470663048070287'], 'invalid'], ['control ["2300017738893841"]', ['2300017738893841'], 'invalid']]]
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 fixture	Actual	Expected	Outcome
regression ["١٨"]	`invalid`	`malformed`	Failed
regression ["٣٤٥"]	`invalid`	`malformed`	Failed
control ["59"]	`valid`	`valid`	Passed
control ["182"]	`valid`	`valid`	Passed
control ["97956"]	`valid`	`valid`	Passed
control ["60866456"]	`valid`	`valid`	Passed
control ["49717735275"]	`valid`	`valid`	Passed
control ["9207919074163"]	`valid`	`valid`	Passed

SHA-256 / 386e83b82b84894eb3d522d6525138a17d2b234511241dade2f1954029d96592

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 ["١٨"]', ['١٨'], 'malformed'], ['regression ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['control ["59"]', ['59'], 'valid'], ['control ["182"]', ['182'], 'valid'], ['control ["97956"]', ['97956'], 'valid'], ['control ["60866456"]', ['60866456'], 'valid'], ['control ["49717735275"]', ['49717735275'], 'valid'], ['control ["9207919074163"]', ['9207919074163'], 'valid']], [['regression ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['regression ["١٨"]', ['١٨'], 'malformed'], ['control ["9207919074163"]', ['9207919074163'], 'valid'], ['control ["470663048070284"]', ['470663048070284'], 'valid'], ['control ["2300017738893848"]', ['2300017738893848'], 'valid'], ['control ["7985145013991721"]', ['7985145013991721'], 'valid'], ['control ["067122965057139178"]', ['067122965057139178'], 'valid'], ['control ["1513156399001929628"]', ['1513156399001929628'], 'valid']], [['regression ["١٨"]', ['١٨'], 'malformed'], ['regression ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['control ["1513156399001929628"]', ['1513156399001929628'], 'valid'], ['control ["9505094299844733505"]', ['9505094299844733505'], 'valid'], ['control ["0906050370970"]', ['0906050370970'], 'valid'], ['control ["3165356977"]', ['3165356977'], 'valid'], ['control ["91"]', ['91'], 'valid'], ['control ["992"]', ['992'], 'valid']], [['regression ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['regression ["١٨"]', ['١٨'], 'malformed'], ['control ["992"]', ['992'], 'valid'], ['control ["5553"]', ['5553'], 'valid'], ['control ["77777779"]', ['77777779'], 'valid'], ['control ["52"]', ['52'], 'invalid'], ['control ["185"]', ['185'], 'invalid'], ['control ["97959"]', ['97959'], 'invalid']], [['regression ["١٨"]', ['١٨'], 'malformed'], ['regression ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['control ["97959"]', ['97959'], 'invalid'], ['control ["60866459"]', ['60866459'], 'invalid'], ['control ["49717735278"]', ['49717735278'], 'invalid'], ['control ["9207919074166"]', ['9207919074166'], 'invalid'], ['control ["470663048070287"]', ['470663048070287'], 'invalid'], ['control ["2300017738893841"]', ['2300017738893841'], 'invalid']]]
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 fixture	Actual	Expected	Outcome
regression ["١٨"]	`malformed`	`malformed`	Passed
regression ["٣٤٥"]	`malformed`	`malformed`	Passed
control ["59"]	`valid`	`valid`	Passed
control ["182"]	`valid`	`valid`	Passed
control ["97956"]	`valid`	`valid`	Passed
control ["60866456"]	`valid`	`valid`	Passed
control ["49717735275"]	`valid`	`valid`	Passed
control ["9207919074163"]	`valid`	`valid`	Passed

SHA-256 / 86ddfaa2aa8cadd24939673b854b48ab64f4cadae336d0d8dc89e46b0038120f

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 2026-09-29T14:48:37.810974+00:00.

Case digest / aef8f43fa4763f176232a3a56e9d9a8980a1423561b8a940dd06f14561dc0ba3