FA-72346 / Check-digit algorithms / Open access

Luhn doubled 9 collapses to zero through modulo nine · case 01

Numbers containing a doubled 9 are misjudged.

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

ROOT CAUSE

The doubled value is reduced with d % 9, so a doubled 9 (18) contributes 0 instead of 9.

VERIFIED REPAIR

Reduce a doubled value above 9 by subtracting 9 (equivalently summing its two decimal digits).

Unsuccessful approach: Subtracting 10 drops the carried tens digit and undercounts every doubled digit of 5 or more by one.

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) < 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 = 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 ["49717735275"]', ['49717735275'], 'valid'], ['regression ["7985145013991721"]', ['7985145013991721'], 'valid'], ['partial-repair ["59"]', ['59'], 'valid'], ['partial-repair ["182"]', ['182'], 'valid'], ['control ["52"]', ['52'], 'invalid'], ['control ["185"]', ['185'], 'invalid'], ['control ["97959"]', ['97959'], 'invalid'], ['control ["60866459"]', ['60866459'], 'invalid']], [['regression ["1513156399001929628"]', ['1513156399001929628'], 'valid'], ['regression ["9505094299844733505"]', ['9505094299844733505'], 'valid'], ['partial-repair ["60866456"]', ['60866456'], 'valid'], ['partial-repair ["49717735275"]', ['49717735275'], 'valid'], ['control ["9207919074166"]', ['9207919074166'], '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']], [['regression ["91"]', ['91'], 'valid'], ['regression ["992"]', ['992'], 'valid'], ['partial-repair ["470663048070284"]', ['470663048070284'], 'valid'], ['partial-repair ["2300017738893848"]', ['2300017738893848'], 'valid'], ['control ["0"]', ['0'], 'malformed'], ['control ["18"]', ['18'], 'valid'], ['control ["00"]', ['00'], 'valid'], ['control ["4111a1111"]', ['4111a1111'], 'malformed']], [['regression ["49717735275"]', ['49717735275'], 'valid'], ['regression ["7985145013991721"]', ['7985145013991721'], 'valid'], ['partial-repair ["067122965057139178"]', ['067122965057139178'], 'valid'], ['partial-repair ["1513156399001929628"]', ['1513156399001929628'], 'valid'], ['control ["١٨"]', ['١٨'], 'malformed'], ['control ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['control ["79927398710"]', ['79927398710'], 'invalid'], ['control ["-"]', ['-'], 'malformed']], [['regression ["1513156399001929628"]', ['1513156399001929628'], 'valid'], ['regression ["9505094299844733505"]', ['9505094299844733505'], 'valid'], ['partial-repair ["0906050370970"]', ['0906050370970'], 'valid'], ['partial-repair ["3165356977"]', ['3165356977'], 'valid'], ['control ["185"]', ['185'], 'invalid'], ['control ["97959"]', ['97959'], 'invalid'], ['control ["60866459"]', ['60866459'], 'invalid'], ['control ["49717735278"]', ['49717735278'], '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 ["49717735275"]	`invalid`	`valid`	Failed
regression ["7985145013991721"]	`invalid`	`valid`	Failed
partial-repair ["59"]	`valid`	`valid`	Passed
partial-repair ["182"]	`valid`	`valid`	Passed
control ["52"]	`invalid`	`invalid`	Passed
control ["185"]	`invalid`	`invalid`	Passed
control ["97959"]	`invalid`	`invalid`	Passed
control ["60866459"]	`invalid`	`invalid`	Passed

SHA-256 / d4fa204b000d49a1b643e1e0c4224920d15d5e0e43dccb053fd9fc24fe2c4c4c

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) < 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 -= 10
        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 ["49717735275"]', ['49717735275'], 'valid'], ['regression ["7985145013991721"]', ['7985145013991721'], 'valid'], ['partial-repair ["59"]', ['59'], 'valid'], ['partial-repair ["182"]', ['182'], 'valid'], ['control ["52"]', ['52'], 'invalid'], ['control ["185"]', ['185'], 'invalid'], ['control ["97959"]', ['97959'], 'invalid'], ['control ["60866459"]', ['60866459'], 'invalid']], [['regression ["1513156399001929628"]', ['1513156399001929628'], 'valid'], ['regression ["9505094299844733505"]', ['9505094299844733505'], 'valid'], ['partial-repair ["60866456"]', ['60866456'], 'valid'], ['partial-repair ["49717735275"]', ['49717735275'], 'valid'], ['control ["9207919074166"]', ['9207919074166'], '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']], [['regression ["91"]', ['91'], 'valid'], ['regression ["992"]', ['992'], 'valid'], ['partial-repair ["470663048070284"]', ['470663048070284'], 'valid'], ['partial-repair ["2300017738893848"]', ['2300017738893848'], 'valid'], ['control ["0"]', ['0'], 'malformed'], ['control ["18"]', ['18'], 'valid'], ['control ["00"]', ['00'], 'valid'], ['control ["4111a1111"]', ['4111a1111'], 'malformed']], [['regression ["49717735275"]', ['49717735275'], 'valid'], ['regression ["7985145013991721"]', ['7985145013991721'], 'valid'], ['partial-repair ["067122965057139178"]', ['067122965057139178'], 'valid'], ['partial-repair ["1513156399001929628"]', ['1513156399001929628'], 'valid'], ['control ["١٨"]', ['١٨'], 'malformed'], ['control ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['control ["79927398710"]', ['79927398710'], 'invalid'], ['control ["-"]', ['-'], 'malformed']], [['regression ["1513156399001929628"]', ['1513156399001929628'], 'valid'], ['regression ["9505094299844733505"]', ['9505094299844733505'], 'valid'], ['partial-repair ["0906050370970"]', ['0906050370970'], 'valid'], ['partial-repair ["3165356977"]', ['3165356977'], 'valid'], ['control ["185"]', ['185'], 'invalid'], ['control ["97959"]', ['97959'], 'invalid'], ['control ["60866459"]', ['60866459'], 'invalid'], ['control ["49717735278"]', ['49717735278'], '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 ["49717735275"]	`invalid`	`valid`	Failed
regression ["7985145013991721"]	`invalid`	`valid`	Failed
partial-repair ["59"]	`invalid`	`valid`	Failed
partial-repair ["182"]	`invalid`	`valid`	Failed
control ["52"]	`invalid`	`invalid`	Passed
control ["185"]	`invalid`	`invalid`	Passed
control ["97959"]	`invalid`	`invalid`	Passed
control ["60866459"]	`invalid`	`invalid`	Passed

SHA-256 / 8b6cd36d5c91598d19ea0c96c7c4288b1c0e9f68ffd928cf0dee73b78f017929

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 ["49717735275"]', ['49717735275'], 'valid'], ['regression ["7985145013991721"]', ['7985145013991721'], 'valid'], ['partial-repair ["59"]', ['59'], 'valid'], ['partial-repair ["182"]', ['182'], 'valid'], ['control ["52"]', ['52'], 'invalid'], ['control ["185"]', ['185'], 'invalid'], ['control ["97959"]', ['97959'], 'invalid'], ['control ["60866459"]', ['60866459'], 'invalid']], [['regression ["1513156399001929628"]', ['1513156399001929628'], 'valid'], ['regression ["9505094299844733505"]', ['9505094299844733505'], 'valid'], ['partial-repair ["60866456"]', ['60866456'], 'valid'], ['partial-repair ["49717735275"]', ['49717735275'], 'valid'], ['control ["9207919074166"]', ['9207919074166'], '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']], [['regression ["91"]', ['91'], 'valid'], ['regression ["992"]', ['992'], 'valid'], ['partial-repair ["470663048070284"]', ['470663048070284'], 'valid'], ['partial-repair ["2300017738893848"]', ['2300017738893848'], 'valid'], ['control ["0"]', ['0'], 'malformed'], ['control ["18"]', ['18'], 'valid'], ['control ["00"]', ['00'], 'valid'], ['control ["4111a1111"]', ['4111a1111'], 'malformed']], [['regression ["49717735275"]', ['49717735275'], 'valid'], ['regression ["7985145013991721"]', ['7985145013991721'], 'valid'], ['partial-repair ["067122965057139178"]', ['067122965057139178'], 'valid'], ['partial-repair ["1513156399001929628"]', ['1513156399001929628'], 'valid'], ['control ["١٨"]', ['١٨'], 'malformed'], ['control ["٣٤٥"]', ['٣٤٥'], 'malformed'], ['control ["79927398710"]', ['79927398710'], 'invalid'], ['control ["-"]', ['-'], 'malformed']], [['regression ["1513156399001929628"]', ['1513156399001929628'], 'valid'], ['regression ["9505094299844733505"]', ['9505094299844733505'], 'valid'], ['partial-repair ["0906050370970"]', ['0906050370970'], 'valid'], ['partial-repair ["3165356977"]', ['3165356977'], 'valid'], ['control ["185"]', ['185'], 'invalid'], ['control ["97959"]', ['97959'], 'invalid'], ['control ["60866459"]', ['60866459'], 'invalid'], ['control ["49717735278"]', ['49717735278'], '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 ["49717735275"]	`valid`	`valid`	Passed
regression ["7985145013991721"]	`valid`	`valid`	Passed
partial-repair ["59"]	`valid`	`valid`	Passed
partial-repair ["182"]	`valid`	`valid`	Passed
control ["52"]	`invalid`	`invalid`	Passed
control ["185"]	`invalid`	`invalid`	Passed
control ["97959"]	`invalid`	`invalid`	Passed
control ["60866459"]	`invalid`	`invalid`	Passed

SHA-256 / 0351b37a73bf63f10ff10c870176a53d721c1007e2acbccf373bf73b7f68ad3c

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 2026-09-29T14:48:37.770761+00:00.

Case digest / 287fdcea9c4287aef6efe27299488d8418bb3898baffbe83fb81706b231a7834