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FA-72441 / Check-digit algorithms / Open access

ISBN-13 conversion weights the prefix digit by three · case 01

Converted ISBN-13 numbers fail barcode scanners.

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

ROOT CAUSE

The EAN weights start with 3 at the leftmost digit instead of 1.

VERIFIED REPAIR

Weight even 0-based positions from the left by 1 and odd positions by 3.

Unsuccessful approach: Weighting from the right of the 12-digit body by 1,3 is the same wrong phase in disguise.

Case contract

Convert a hyphenated or plain ISBN-10 to ISBN-13. The input must be a valid ISBN-10 (mod 11, X allowed as the final character) or None is returned. The result is "978" + the nine ISBN-10 payload digits + a freshly computed EAN-13 check digit (weights 1,3 alternating from the left).

Why this case matters

Library and retail systems migrate legacy ISBN-10 records to 13-digit EAN identifiers.

1 / The failure

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

N = 1
observations = []
def solve(s):
    t = s.replace('-', '')
    if len(t) != 10 or not t.isascii() or not t[:9].isdigit() or not (t[9].isdigit() or t[9] == 'X'):
        return None
    if sum((10 - i) * (10 if ch == 'X' else int(ch)) for i, ch in enumerate(t)) % 11:
        return None
    body = '978' + t[:9]
    total = sum(int(ch) * (3 if i % 2 == 0 else 1) for i, ch in enumerate(body))
    return body + str((10 - total % 10) % 10)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["5892872939"]', ['5892872939'], '9785892872935'], ['regression ["2399553950"]', ['2399553950'], '9782399553954'], ['control ["2266685686"]', ['2266685686'], '9782266685689'], ['control ["1475433131"]', ['1475433131'], '9781475433135'], ['control ["0436178273"]', ['0436178273'], '9780436178276'], ['control ["0306406152"]', ['0306406152'], '9780306406157'], ['control ["0000000000"]', ['0000000000'], '9780000000002'], ['control ["123456789X"]', ['123456789X'], '9781234567897']], [['regression ["829284466X"]', ['829284466X'], '9788292844663'], ['regression ["9379774826"]', ['9379774826'], '9789379774828'], ['control ["123456789X"]', ['123456789X'], '9781234567897'], ['control ["5892872930"]', ['5892872930'], None], ['control ["2399553951"]', ['2399553951'], None], ['control ["9465545440"]', ['9465545440'], None], ['control ["8292844660"]', ['8292844660'], None], ['control ["9379774827"]', ['9379774827'], None]], [['regression ["5900307905"]', ['5900307905'], '9785900307909'], ['regression ["3905987139"]', ['3905987139'], '9783905987133'], ['control ["9379774827"]', ['9379774827'], None], ['control ["2266685687"]', ['2266685687'], None], ['control ["0-306-40615-2"]', ['0-306-40615-2'], '9780306406157'], ['control ["0306406153"]', ['0306406153'], None], ['control ["12345"]', ['12345'], None], ['control ["2266685686"]', ['2266685686'], '9782266685689']], [['regression ["3407375115"]', ['3407375115'], '9783407375117'], ['regression ["8449627923"]', ['8449627923'], '9788449627927'], ['control ["2266685686"]', ['2266685686'], '9782266685689'], ['control ["1475433131"]', ['1475433131'], '9781475433135'], ['control ["0436178273"]', ['0436178273'], '9780436178276'], ['control ["0306406152"]', ['0306406152'], '9780306406157'], ['control ["0000000000"]', ['0000000000'], '9780000000002'], ['control ["123456789X"]', ['123456789X'], '9781234567897']], [['regression ["9999999999"]', ['9999999999'], '9789999999991'], ['regression ["097522980X"]', ['097522980X'], '9780975229804'], ['control ["123456789X"]', ['123456789X'], '9781234567897'], ['control ["5892872930"]', ['5892872930'], None], ['control ["2399553951"]', ['2399553951'], None], ['control ["9465545440"]', ['9465545440'], None], ['control ["8292844660"]', ['8292844660'], None], ['control ["9379774827"]', ['9379774827'], None]]]
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 ["5892872939"]97858928729379785892872935Failed
regression ["2399553950"]97823995539509782399553954Failed
control ["2266685686"]97822666856899782266685689Passed
control ["1475433131"]97814754331359781475433135Passed
control ["0436178273"]97804361782769780436178276Passed
control ["0306406152"]97803064061579780306406157Passed
control ["0000000000"]97800000000029780000000002Passed
control ["123456789X"]97812345678979781234567897Passed

SHA-256 / 1758875ab130b9dd0e03d4d73d4dad1117c912696222666bc172c0fe0c0397ba

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('-', '')
    if len(t) != 10 or not t.isascii() or not t[:9].isdigit() or not (t[9].isdigit() or t[9] == 'X'):
        return None
    if sum((10 - i) * (10 if ch == 'X' else int(ch)) for i, ch in enumerate(t)) % 11:
        return None
    body = '978' + t[:9]
    total = sum(int(ch) * (1 if i % 2 == 0 else 3) for i, ch in enumerate(reversed(body)))
    return body + str((10 - total % 10) % 10)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["5892872939"]', ['5892872939'], '9785892872935'], ['regression ["2399553950"]', ['2399553950'], '9782399553954'], ['control ["2266685686"]', ['2266685686'], '9782266685689'], ['control ["1475433131"]', ['1475433131'], '9781475433135'], ['control ["0436178273"]', ['0436178273'], '9780436178276'], ['control ["0306406152"]', ['0306406152'], '9780306406157'], ['control ["0000000000"]', ['0000000000'], '9780000000002'], ['control ["123456789X"]', ['123456789X'], '9781234567897']], [['regression ["829284466X"]', ['829284466X'], '9788292844663'], ['regression ["9379774826"]', ['9379774826'], '9789379774828'], ['control ["123456789X"]', ['123456789X'], '9781234567897'], ['control ["5892872930"]', ['5892872930'], None], ['control ["2399553951"]', ['2399553951'], None], ['control ["9465545440"]', ['9465545440'], None], ['control ["8292844660"]', ['8292844660'], None], ['control ["9379774827"]', ['9379774827'], None]], [['regression ["5900307905"]', ['5900307905'], '9785900307909'], ['regression ["3905987139"]', ['3905987139'], '9783905987133'], ['control ["9379774827"]', ['9379774827'], None], ['control ["2266685687"]', ['2266685687'], None], ['control ["0-306-40615-2"]', ['0-306-40615-2'], '9780306406157'], ['control ["0306406153"]', ['0306406153'], None], ['control ["12345"]', ['12345'], None], ['control ["2266685686"]', ['2266685686'], '9782266685689']], [['regression ["3407375115"]', ['3407375115'], '9783407375117'], ['regression ["8449627923"]', ['8449627923'], '9788449627927'], ['control ["2266685686"]', ['2266685686'], '9782266685689'], ['control ["1475433131"]', ['1475433131'], '9781475433135'], ['control ["0436178273"]', ['0436178273'], '9780436178276'], ['control ["0306406152"]', ['0306406152'], '9780306406157'], ['control ["0000000000"]', ['0000000000'], '9780000000002'], ['control ["123456789X"]', ['123456789X'], '9781234567897']], [['regression ["9999999999"]', ['9999999999'], '9789999999991'], ['regression ["097522980X"]', ['097522980X'], '9780975229804'], ['control ["123456789X"]', ['123456789X'], '9781234567897'], ['control ["5892872930"]', ['5892872930'], None], ['control ["2399553951"]', ['2399553951'], None], ['control ["9465545440"]', ['9465545440'], None], ['control ["8292844660"]', ['8292844660'], None], ['control ["9379774827"]', ['9379774827'], None]]]
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 ["5892872939"]97858928729379785892872935Failed
regression ["2399553950"]97823995539509782399553954Failed
control ["2266685686"]97822666856899782266685689Passed
control ["1475433131"]97814754331359781475433135Passed
control ["0436178273"]97804361782769780436178276Passed
control ["0306406152"]97803064061579780306406157Passed
control ["0000000000"]97800000000029780000000002Passed
control ["123456789X"]97812345678979781234567897Passed

SHA-256 / 84274641d8f1d7bb1b07f9eab319a7c89b2ccc728bb981406f81324ed9410891

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('-', '')
    if len(t) != 10 or not t.isascii() or not t[:9].isdigit() or not (t[9].isdigit() or t[9] == 'X'):
        return None
    if sum((10 - i) * (10 if ch == 'X' else int(ch)) for i, ch in enumerate(t)) % 11:
        return None
    body = '978' + t[:9]
    total = sum(int(ch) * (1 if i % 2 == 0 else 3) for i, ch in enumerate(body))
    return body + str((10 - total % 10) % 10)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["5892872939"]', ['5892872939'], '9785892872935'], ['regression ["2399553950"]', ['2399553950'], '9782399553954'], ['control ["2266685686"]', ['2266685686'], '9782266685689'], ['control ["1475433131"]', ['1475433131'], '9781475433135'], ['control ["0436178273"]', ['0436178273'], '9780436178276'], ['control ["0306406152"]', ['0306406152'], '9780306406157'], ['control ["0000000000"]', ['0000000000'], '9780000000002'], ['control ["123456789X"]', ['123456789X'], '9781234567897']], [['regression ["829284466X"]', ['829284466X'], '9788292844663'], ['regression ["9379774826"]', ['9379774826'], '9789379774828'], ['control ["123456789X"]', ['123456789X'], '9781234567897'], ['control ["5892872930"]', ['5892872930'], None], ['control ["2399553951"]', ['2399553951'], None], ['control ["9465545440"]', ['9465545440'], None], ['control ["8292844660"]', ['8292844660'], None], ['control ["9379774827"]', ['9379774827'], None]], [['regression ["5900307905"]', ['5900307905'], '9785900307909'], ['regression ["3905987139"]', ['3905987139'], '9783905987133'], ['control ["9379774827"]', ['9379774827'], None], ['control ["2266685687"]', ['2266685687'], None], ['control ["0-306-40615-2"]', ['0-306-40615-2'], '9780306406157'], ['control ["0306406153"]', ['0306406153'], None], ['control ["12345"]', ['12345'], None], ['control ["2266685686"]', ['2266685686'], '9782266685689']], [['regression ["3407375115"]', ['3407375115'], '9783407375117'], ['regression ["8449627923"]', ['8449627923'], '9788449627927'], ['control ["2266685686"]', ['2266685686'], '9782266685689'], ['control ["1475433131"]', ['1475433131'], '9781475433135'], ['control ["0436178273"]', ['0436178273'], '9780436178276'], ['control ["0306406152"]', ['0306406152'], '9780306406157'], ['control ["0000000000"]', ['0000000000'], '9780000000002'], ['control ["123456789X"]', ['123456789X'], '9781234567897']], [['regression ["9999999999"]', ['9999999999'], '9789999999991'], ['regression ["097522980X"]', ['097522980X'], '9780975229804'], ['control ["123456789X"]', ['123456789X'], '9781234567897'], ['control ["5892872930"]', ['5892872930'], None], ['control ["2399553951"]', ['2399553951'], None], ['control ["9465545440"]', ['9465545440'], None], ['control ["8292844660"]', ['8292844660'], None], ['control ["9379774827"]', ['9379774827'], None]]]
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 ["5892872939"]97858928729359785892872935Passed
regression ["2399553950"]97823995539549782399553954Passed
control ["2266685686"]97822666856899782266685689Passed
control ["1475433131"]97814754331359781475433135Passed
control ["0436178273"]97804361782769780436178276Passed
control ["0306406152"]97803064061579780306406157Passed
control ["0000000000"]97800000000029780000000002Passed
control ["123456789X"]97812345678979781234567897Passed

SHA-256 / 98eaecb59fb1d3e0ddcf577b9b85da43c08a84c6d9d161d3987c43379ab087a8

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 2026-09-29T14:48:38.555500+00:00.

Case digest / 7d757cc62ef23854ddd5bd68b80546387f28d4e91fa51e0eb0c13e8eb726f694