FA-72746 / Check-digit algorithms / Open access

CPF second check digit reuses the first weight range · case 01

Most valid CPFs fail the second check digit.

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

ROOT CAUSE

k2 is weighted 10..2, so zip truncates the list and the computed k1 never enters the sum.

VERIFIED REPAIR

Weight the ten digits for k2 by 11 down to 2.

Unsuccessful approach: Shifting the range to 12..3 covers ten digits but with every weight one too large.

Case contract

Brazilian CPF taxpayer number: dots and hyphens removed, then 11 ASCII digits that are not all the same digit (else "malformed"). k1 = (sum of digits 1-9 weighted 10..2) * 10 mod 11 mod 10; k2 = (digits 1-9 and the computed k1 weighted 11..2) * 10 mod 11 mod 10. Return [k1, k2, whether digits 10-11 equal them].

Why this case matters

Onboarding and invoicing flows validate CPF numbers before tax reporting.

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 len(t) != 11 or not t.isascii() or not t.isdigit():
        return 'malformed'
    if len(set(t)) == 1:
        return 'malformed'
    d = [int(ch) for ch in t]
    k1 = sum(w * x for w, x in zip(range(10, 1, -1), d[:9])) * 10 % 11 % 10
    k2 = sum(w * x for w, x in zip(range(10, 1, -1), d[:9] + [k1])) * 10 % 11 % 10
    return [k1, k2, d[9] == k1 and d[10] == k2]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["42765277574"]', ['42765277574'], [9, 1, False]], ['regression ["04160821863"]', ['04160821863'], [1, 2, False]], ['control ["111.111.111-11"]', ['111.111.111-11'], 'malformed'], ['control ["00000000000"]', ['00000000000'], 'malformed'], ['control ["22222222222"]', ['22222222222'], 'malformed'], ['control ["1234567890"]', ['1234567890'], 'malformed'], ['control ["80112861152"]', ['80112861152'], [0, 5, False]], ['control ["61682621036"]', ['61682621036'], [5, 7, False]]], [['regression ["54166960081"]', ['54166960081'], [1, 6, False]], ['regression ["80112861152"]', ['80112861152'], [0, 5, False]], ['control ["00000000000"]', ['00000000000'], 'malformed'], ['control ["22222222222"]', ['22222222222'], 'malformed'], ['control ["1234567890"]', ['1234567890'], 'malformed'], ['control ["111.111.111-11"]', ['111.111.111-11'], 'malformed'], ['control ["11888021888"]', ['11888021888'], [6, 1, False]], ['control ["02970275879"]', ['02970275879'], [1, 3, False]]], [['regression ["91615291602"]', ['91615291602'], [8, 7, False]], ['regression ["38203173222"]', ['38203173222'], [5, 0, False]], ['control ["22222222222"]', ['22222222222'], 'malformed'], ['control ["1234567890"]', ['1234567890'], 'malformed'], ['control ["111.111.111-11"]', ['111.111.111-11'], 'malformed'], ['control ["00000000000"]', ['00000000000'], 'malformed'], ['control ["25998738965"]', ['25998738965'], [4, 2, False]], ['control ["52682522850"]', ['52682522850'], [3, 1, False]]], [['regression ["11888021888"]', ['11888021888'], [6, 1, False]], ['regression ["02970275879"]', ['02970275879'], [1, 3, False]], ['control ["1234567890"]', ['1234567890'], 'malformed'], ['control ["111.111.111-11"]', ['111.111.111-11'], 'malformed'], ['control ["00000000000"]', ['00000000000'], 'malformed'], ['control ["22222222222"]', ['22222222222'], 'malformed'], ['control ["37134793981"]', ['37134793981'], [9, 0, False]], ['control ["529.982.247-25"]', ['529.982.247-25'], [2, 5, True]]], [['regression ["29622049718"]', ['29622049718'], [0, 2, False]], ['regression ["22747397622"]', ['22747397622'], [5, 3, False]], ['control ["111.111.111-11"]', ['111.111.111-11'], 'malformed'], ['control ["00000000000"]', ['00000000000'], 'malformed'], ['control ["22222222222"]', ['22222222222'], 'malformed'], ['control ["1234567890"]', ['1234567890'], 'malformed'], ['control ["123.456.789-09"]', ['123.456.789-09'], [0, 9, True]], ['control ["123.456.789-00"]', ['123.456.789-00'], [0, 9, False]]]]
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 ["42765277574"]	`[9, 9, False]`	`[9, 1, False]`	Failed
regression ["04160821863"]	`[1, 1, False]`	`[1, 2, False]`	Failed
control ["111.111.111-11"]	`malformed`	`malformed`	Passed
control ["00000000000"]	`malformed`	`malformed`	Passed
control ["22222222222"]	`malformed`	`malformed`	Passed
control ["1234567890"]	`malformed`	`malformed`	Passed
control ["80112861152"]	`[0, 0, False]`	`[0, 5, False]`	Failed
control ["61682621036"]	`[5, 5, False]`	`[5, 7, False]`	Failed

SHA-256 / 396899f8dfd2fe2211390987409830d29f18cbb3e3030bb76c5415c8e771d71a

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 len(t) != 11 or not t.isascii() or not t.isdigit():
        return 'malformed'
    if len(set(t)) == 1:
        return 'malformed'
    d = [int(ch) for ch in t]
    k1 = sum(w * x for w, x in zip(range(10, 1, -1), d[:9])) * 10 % 11 % 10
    k2 = sum(w * x for w, x in zip(range(12, 2, -1), d[:9] + [k1])) * 10 % 11 % 10
    return [k1, k2, d[9] == k1 and d[10] == k2]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["42765277574"]', ['42765277574'], [9, 1, False]], ['regression ["04160821863"]', ['04160821863'], [1, 2, False]], ['control ["111.111.111-11"]', ['111.111.111-11'], 'malformed'], ['control ["00000000000"]', ['00000000000'], 'malformed'], ['control ["22222222222"]', ['22222222222'], 'malformed'], ['control ["1234567890"]', ['1234567890'], 'malformed'], ['control ["80112861152"]', ['80112861152'], [0, 5, False]], ['control ["61682621036"]', ['61682621036'], [5, 7, False]]], [['regression ["54166960081"]', ['54166960081'], [1, 6, False]], ['regression ["80112861152"]', ['80112861152'], [0, 5, False]], ['control ["00000000000"]', ['00000000000'], 'malformed'], ['control ["22222222222"]', ['22222222222'], 'malformed'], ['control ["1234567890"]', ['1234567890'], 'malformed'], ['control ["111.111.111-11"]', ['111.111.111-11'], 'malformed'], ['control ["11888021888"]', ['11888021888'], [6, 1, False]], ['control ["02970275879"]', ['02970275879'], [1, 3, False]]], [['regression ["91615291602"]', ['91615291602'], [8, 7, False]], ['regression ["38203173222"]', ['38203173222'], [5, 0, False]], ['control ["22222222222"]', ['22222222222'], 'malformed'], ['control ["1234567890"]', ['1234567890'], 'malformed'], ['control ["111.111.111-11"]', ['111.111.111-11'], 'malformed'], ['control ["00000000000"]', ['00000000000'], 'malformed'], ['control ["25998738965"]', ['25998738965'], [4, 2, False]], ['control ["52682522850"]', ['52682522850'], [3, 1, False]]], [['regression ["11888021888"]', ['11888021888'], [6, 1, False]], ['regression ["02970275879"]', ['02970275879'], [1, 3, False]], ['control ["1234567890"]', ['1234567890'], 'malformed'], ['control ["111.111.111-11"]', ['111.111.111-11'], 'malformed'], ['control ["00000000000"]', ['00000000000'], 'malformed'], ['control ["22222222222"]', ['22222222222'], 'malformed'], ['control ["37134793981"]', ['37134793981'], [9, 0, False]], ['control ["529.982.247-25"]', ['529.982.247-25'], [2, 5, True]]], [['regression ["29622049718"]', ['29622049718'], [0, 2, False]], ['regression ["22747397622"]', ['22747397622'], [5, 3, False]], ['control ["111.111.111-11"]', ['111.111.111-11'], 'malformed'], ['control ["00000000000"]', ['00000000000'], 'malformed'], ['control ["22222222222"]', ['22222222222'], 'malformed'], ['control ["1234567890"]', ['1234567890'], 'malformed'], ['control ["123.456.789-09"]', ['123.456.789-09'], [0, 9, True]], ['control ["123.456.789-00"]', ['123.456.789-00'], [0, 9, False]]]]
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 ["42765277574"]	`[9, 2, False]`	`[9, 1, False]`	Failed
regression ["04160821863"]	`[1, 4, False]`	`[1, 2, False]`	Failed
control ["111.111.111-11"]	`malformed`	`malformed`	Passed
control ["00000000000"]	`malformed`	`malformed`	Passed
control ["22222222222"]	`malformed`	`malformed`	Passed
control ["1234567890"]	`malformed`	`malformed`	Passed
control ["80112861152"]	`[0, 0, False]`	`[0, 5, False]`	Failed
control ["61682621036"]	`[5, 3, False]`	`[5, 7, False]`	Failed

SHA-256 / 61825751349d90752bf5e2f7653425a153c6aec18d5048a6652d5abf8b90a0a7

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 len(t) != 11 or not t.isascii() or not t.isdigit():
        return 'malformed'
    if len(set(t)) == 1:
        return 'malformed'
    d = [int(ch) for ch in t]
    k1 = sum(w * x for w, x in zip(range(10, 1, -1), d[:9])) * 10 % 11 % 10
    k2 = sum(w * x for w, x in zip(range(11, 1, -1), d[:9] + [k1])) * 10 % 11 % 10
    return [k1, k2, d[9] == k1 and d[10] == k2]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["42765277574"]', ['42765277574'], [9, 1, False]], ['regression ["04160821863"]', ['04160821863'], [1, 2, False]], ['control ["111.111.111-11"]', ['111.111.111-11'], 'malformed'], ['control ["00000000000"]', ['00000000000'], 'malformed'], ['control ["22222222222"]', ['22222222222'], 'malformed'], ['control ["1234567890"]', ['1234567890'], 'malformed'], ['control ["80112861152"]', ['80112861152'], [0, 5, False]], ['control ["61682621036"]', ['61682621036'], [5, 7, False]]], [['regression ["54166960081"]', ['54166960081'], [1, 6, False]], ['regression ["80112861152"]', ['80112861152'], [0, 5, False]], ['control ["00000000000"]', ['00000000000'], 'malformed'], ['control ["22222222222"]', ['22222222222'], 'malformed'], ['control ["1234567890"]', ['1234567890'], 'malformed'], ['control ["111.111.111-11"]', ['111.111.111-11'], 'malformed'], ['control ["11888021888"]', ['11888021888'], [6, 1, False]], ['control ["02970275879"]', ['02970275879'], [1, 3, False]]], [['regression ["91615291602"]', ['91615291602'], [8, 7, False]], ['regression ["38203173222"]', ['38203173222'], [5, 0, False]], ['control ["22222222222"]', ['22222222222'], 'malformed'], ['control ["1234567890"]', ['1234567890'], 'malformed'], ['control ["111.111.111-11"]', ['111.111.111-11'], 'malformed'], ['control ["00000000000"]', ['00000000000'], 'malformed'], ['control ["25998738965"]', ['25998738965'], [4, 2, False]], ['control ["52682522850"]', ['52682522850'], [3, 1, False]]], [['regression ["11888021888"]', ['11888021888'], [6, 1, False]], ['regression ["02970275879"]', ['02970275879'], [1, 3, False]], ['control ["1234567890"]', ['1234567890'], 'malformed'], ['control ["111.111.111-11"]', ['111.111.111-11'], 'malformed'], ['control ["00000000000"]', ['00000000000'], 'malformed'], ['control ["22222222222"]', ['22222222222'], 'malformed'], ['control ["37134793981"]', ['37134793981'], [9, 0, False]], ['control ["529.982.247-25"]', ['529.982.247-25'], [2, 5, True]]], [['regression ["29622049718"]', ['29622049718'], [0, 2, False]], ['regression ["22747397622"]', ['22747397622'], [5, 3, False]], ['control ["111.111.111-11"]', ['111.111.111-11'], 'malformed'], ['control ["00000000000"]', ['00000000000'], 'malformed'], ['control ["22222222222"]', ['22222222222'], 'malformed'], ['control ["1234567890"]', ['1234567890'], 'malformed'], ['control ["123.456.789-09"]', ['123.456.789-09'], [0, 9, True]], ['control ["123.456.789-00"]', ['123.456.789-00'], [0, 9, False]]]]
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 ["42765277574"]	`[9, 1, False]`	`[9, 1, False]`	Passed
regression ["04160821863"]	`[1, 2, False]`	`[1, 2, False]`	Passed
control ["111.111.111-11"]	`malformed`	`malformed`	Passed
control ["00000000000"]	`malformed`	`malformed`	Passed
control ["22222222222"]	`malformed`	`malformed`	Passed
control ["1234567890"]	`malformed`	`malformed`	Passed
control ["80112861152"]	`[0, 5, False]`	`[0, 5, False]`	Passed
control ["61682621036"]	`[5, 7, False]`	`[5, 7, False]`	Passed

SHA-256 / 8b68f9592b26610bb9eb66e58ded17f85cb2bcd0301d03f06143a56c7938f08a

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 2026-09-29T14:48:41.173861+00:00.

Case digest / 32c91633e4eef1832eb60c7bb0add5e8ea82913e8996483358aa25912027980d