FAILURE MAP
← Case archive

FA-72391 / Check-digit algorithms / Open access

Verhoeff walks digits left to right · case 01

Only palindromic payloads produce correct check digits.

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

ROOT CAUSE

The loop enumerates s from the left, so permutation powers are assigned to the wrong positions.

THE FAILURE

The loop enumerates s from the left, so permutation powers are assigned to the wrong positions.

Unsuccessful approach: Reversing but starting enumerate at 1 double-counts the offset and shifts every permutation by one.

Case contract

Verhoeff dihedral-group scheme. mode "generate" returns the check digit for a nonempty ASCII digit payload; mode "validate" returns whether a nonempty digit string ending in its check digit is correct. Digits are processed from the right with permutation P[(i + offset) % 8], offset 1 when generating and 0 when validating; the check digit is the dihedral inverse of the final state. Empty or non-digit input returns None.

Why this case matters

National identity and ticketing numbers use Verhoeff to catch all single-digit and adjacent transposition errors.

1 / The failure

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

N = 1
observations = []
def solve(s, mode):
    D = [[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,0,6,7,8,9,5],[2,3,4,0,1,7,8,9,5,6],[3,4,0,1,2,8,9,5,6,7],[4,0,1,2,3,9,5,6,7,8],[5,9,8,7,6,0,4,3,2,1],[6,5,9,8,7,1,0,4,3,2],[7,6,5,9,8,2,1,0,4,3],[8,7,6,5,9,3,2,1,0,4],[9,8,7,6,5,4,3,2,1,0]]
    P = [[0,1,2,3,4,5,6,7,8,9],[1,5,7,6,2,8,3,0,9,4],[5,8,0,3,7,9,6,1,4,2],[8,9,1,6,0,4,3,5,2,7],[9,4,5,3,1,2,8,7,6,0],[4,2,8,6,5,7,3,9,0,1],[2,7,9,3,8,0,6,4,1,5],[7,0,4,6,9,1,3,2,5,8]]
    INV = [0,4,3,2,1,5,6,7,8,9]
    if not s or not s.isascii() or not s.isdigit():
        return None
    offset = 1 if mode == 'generate' else 0
    c = 0
    for i, ch in enumerate(s):
        c = D[c][P[(i + offset) % 8][int(ch)]]
    if mode == 'generate':
        return INV[c]
    return c == 0
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["12", "generate"]', ['12', 'generate'], 1], ['regression ["600", "generate"]', ['600', 'generate'], 8], ['partial-repair ["7", "generate"]', ['7', 'generate'], 0], ['control ["73", "validate"]', ['73', 'validate'], False], ['control ["123", "validate"]', ['123', 'validate'], False], ['control ["317230", "validate"]', ['317230', 'validate'], False], ['control ["2864257569", "validate"]', ['2864257569', 'validate'], False], ['control ["426688793324", "validate"]', ['426688793324', 'validate'], False]], [['regression ["07668886", "generate"]', ['07668886', 'generate'], 2], ['regression ["286425756", "generate"]', ['286425756', 'generate'], 2], ['partial-repair ["6001", "validate"]', ['6001', 'validate'], False], ['control ["8115669551647", "validate"]', ['8115669551647', 'validate'], False], ['control ["6516456313406690", "validate"]', ['6516456313406690', 'validate'], False], ['control ["2364", "validate"]', ['2364', 'validate'], False], ['control ["", "generate"]', ['', 'generate'], None], ['control ["", "validate"]', ['', 'validate'], None]], [['regression ["811566955164", "generate"]', ['811566955164', 'generate'], 9], ['regression ["651645631340669", "generate"]', ['651645631340669', 'generate'], 8], ['partial-repair ["286425756", "generate"]', ['286425756', 'generate'], 2], ['partial-repair ["42668879332", "generate"]', ['42668879332', 'generate'], 9], ['control ["12a", "generate"]', ['12a', 'generate'], None], ['control ["1428572", "validate"]', ['1428572', 'validate'], False], ['control ["73", "validate"]', ['73', 'validate'], False], ['control ["123", "validate"]', ['123', 'validate'], False]], [['regression ["2363", "validate"]', ['2363', 'validate'], True], ['regression ["12345", "generate"]', ['12345', 'generate'], 1], ['partial-repair ["236", "generate"]', ['236', 'generate'], 3], ['control ["2864257569", "validate"]', ['2864257569', 'validate'], False], ['control ["426688793324", "validate"]', ['426688793324', 'validate'], False], ['control ["8115669551647", "validate"]', ['8115669551647', 'validate'], False], ['control ["6516456313406690", "validate"]', ['6516456313406690', 'validate'], False], ['control ["2364", "validate"]', ['2364', 'validate'], False]], [['regression ["142857", "generate"]', ['142857', 'generate'], 0], ['regression ["1428570", "validate"]', ['1428570', 'validate'], True], ['partial-repair ["0", "generate"]', ['0', 'generate'], 4], ['partial-repair ["0", "validate"]', ['0', 'validate'], True], ['control ["", "generate"]', ['', 'generate'], None], ['control ["", "validate"]', ['', 'validate'], None], ['control ["12a", "generate"]', ['12a', 'generate'], None], ['control ["1428572", "validate"]', ['1428572', 'validate'], 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 fixtureActualExpectedOutcome
regression ["12", "generate"]51Failed
regression ["600", "generate"]08Failed
partial-repair ["7", "generate"]00Passed
control ["73", "validate"]FalseFalsePassed
control ["123", "validate"]FalseFalsePassed
control ["317230", "validate"]FalseFalsePassed
control ["2864257569", "validate"]FalseFalsePassed
control ["426688793324", "validate"]FalseFalsePassed

SHA-256 / 87d174cef4ce245bafd08d2a67177673b31fb67954c49b74a7a9ec03a57aac88

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(s, mode):
    D = [[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,0,6,7,8,9,5],[2,3,4,0,1,7,8,9,5,6],[3,4,0,1,2,8,9,5,6,7],[4,0,1,2,3,9,5,6,7,8],[5,9,8,7,6,0,4,3,2,1],[6,5,9,8,7,1,0,4,3,2],[7,6,5,9,8,2,1,0,4,3],[8,7,6,5,9,3,2,1,0,4],[9,8,7,6,5,4,3,2,1,0]]
    P = [[0,1,2,3,4,5,6,7,8,9],[1,5,7,6,2,8,3,0,9,4],[5,8,0,3,7,9,6,1,4,2],[8,9,1,6,0,4,3,5,2,7],[9,4,5,3,1,2,8,7,6,0],[4,2,8,6,5,7,3,9,0,1],[2,7,9,3,8,0,6,4,1,5],[7,0,4,6,9,1,3,2,5,8]]
    INV = [0,4,3,2,1,5,6,7,8,9]
    if not s or not s.isascii() or not s.isdigit():
        return None
    offset = 1 if mode == 'generate' else 0
    c = 0
    for i, ch in enumerate(reversed(s), 1):
        c = D[c][P[(i + offset) % 8][int(ch)]]
    if mode == 'generate':
        return INV[c]
    return c == 0
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["12", "generate"]', ['12', 'generate'], 1], ['regression ["600", "generate"]', ['600', 'generate'], 8], ['partial-repair ["7", "generate"]', ['7', 'generate'], 0], ['control ["73", "validate"]', ['73', 'validate'], False], ['control ["123", "validate"]', ['123', 'validate'], False], ['control ["317230", "validate"]', ['317230', 'validate'], False], ['control ["2864257569", "validate"]', ['2864257569', 'validate'], False], ['control ["426688793324", "validate"]', ['426688793324', 'validate'], False]], [['regression ["07668886", "generate"]', ['07668886', 'generate'], 2], ['regression ["286425756", "generate"]', ['286425756', 'generate'], 2], ['partial-repair ["6001", "validate"]', ['6001', 'validate'], False], ['control ["8115669551647", "validate"]', ['8115669551647', 'validate'], False], ['control ["6516456313406690", "validate"]', ['6516456313406690', 'validate'], False], ['control ["2364", "validate"]', ['2364', 'validate'], False], ['control ["", "generate"]', ['', 'generate'], None], ['control ["", "validate"]', ['', 'validate'], None]], [['regression ["811566955164", "generate"]', ['811566955164', 'generate'], 9], ['regression ["651645631340669", "generate"]', ['651645631340669', 'generate'], 8], ['partial-repair ["286425756", "generate"]', ['286425756', 'generate'], 2], ['partial-repair ["42668879332", "generate"]', ['42668879332', 'generate'], 9], ['control ["12a", "generate"]', ['12a', 'generate'], None], ['control ["1428572", "validate"]', ['1428572', 'validate'], False], ['control ["73", "validate"]', ['73', 'validate'], False], ['control ["123", "validate"]', ['123', 'validate'], False]], [['regression ["2363", "validate"]', ['2363', 'validate'], True], ['regression ["12345", "generate"]', ['12345', 'generate'], 1], ['partial-repair ["236", "generate"]', ['236', 'generate'], 3], ['control ["2864257569", "validate"]', ['2864257569', 'validate'], False], ['control ["426688793324", "validate"]', ['426688793324', 'validate'], False], ['control ["8115669551647", "validate"]', ['8115669551647', 'validate'], False], ['control ["6516456313406690", "validate"]', ['6516456313406690', 'validate'], False], ['control ["2364", "validate"]', ['2364', 'validate'], False]], [['regression ["142857", "generate"]', ['142857', 'generate'], 0], ['regression ["1428570", "validate"]', ['1428570', 'validate'], True], ['partial-repair ["0", "generate"]', ['0', 'generate'], 4], ['partial-repair ["0", "validate"]', ['0', 'validate'], True], ['control ["", "generate"]', ['', 'generate'], None], ['control ["", "validate"]', ['', 'validate'], None], ['control ["12a", "generate"]', ['12a', 'generate'], None], ['control ["1428572", "validate"]', ['1428572', 'validate'], 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 fixtureActualExpectedOutcome
regression ["12", "generate"]91Failed
regression ["600", "generate"]58Failed
partial-repair ["7", "generate"]40Failed
control ["73", "validate"]FalseFalsePassed
control ["123", "validate"]FalseFalsePassed
control ["317230", "validate"]FalseFalsePassed
control ["2864257569", "validate"]FalseFalsePassed
control ["426688793324", "validate"]FalseFalsePassed

SHA-256 / b7c0d00a8edca88045291f557027b9d6c80ede0d515f7108ce232e7b5e46c127

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.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

Sign in to the archive ↗

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 2026-09-29T14:48:38.101124+00:00.

Case digest / df5dab887976d5e57f0a6d3b035f0f055fde5716f8ad0f3ac8bc546e2dfffd51