FA-72571 / Check-digit algorithms / Open access

MOD 11,10 starts the fold at one · case 01

Check digits disagree with the hybrid system for most payloads.

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

ROOT CAUSE

The running value starts at 1 instead of the modulus 10 (starting at 0 would be harmless because of the mod-10 step).

VERIFIED REPAIR

Initialise p = 10.

Unsuccessful approach: Starting at 11 (the other modulus) is congruent to 1 mod 10 and repeats the same error.

Case contract

ISO 7064 MOD 11,10 hybrid check digit generation for a nonempty ASCII digit payload (else None). Start with p = 10; for each digit p = ((p + d) mod 10, with 0 replaced by 10) * 2 mod 11; the check digit is (11 - p) mod 10.

Why this case matters

Tax and personal identification numbers (for example OIB-style identifiers) use the hybrid MOD 11,10 system.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(s):
    if not s or not s.isascii() or not s.isdigit():
        return None
    p = 1
    for ch in s:
        p = ((p + int(ch)) % 10 or 10) * 2 % 11
    return (11 - p) % 10
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["9"]', ['9'], 4], ['regression ["12"]', ['12'], 3], ['control [""]', [''], None], ['control ["12a"]', ['12a'], None], ['control ["072"]', ['072'], 5], ['control ["36073"]', ['36073'], 5], ['control ["98772300"]', ['98772300'], 4], ['control ["3370345686"]', ['3370345686'], 4]], [['regression ["36073"]', ['36073'], 5], ['regression ["98772300"]', ['98772300'], 4], ['control ["12a"]', ['12a'], None], ['control [""]', [''], None], ['control ["2638206592"]', ['2638206592'], 8], ['control ["412595035658"]', ['412595035658'], 9], ['control ["0227566323850846"]', ['0227566323850846'], 4], ['control ["9477"]', ['9477'], 3]], [['regression ["6279939841"]', ['6279939841'], 2], ['regression ["2638206592"]', ['2638206592'], 8], ['control [""]', [''], None], ['control ["12a"]', ['12a'], None], ['control ["9795751"]', ['9795751'], 6], ['control ["6943515153"]', ['6943515153'], 0], ['control ["0"]', ['0'], 2], ['control ["1"]', ['1'], 9]], [['regression ["0227566323850846"]', ['0227566323850846'], 4], ['regression ["9477"]', ['9477'], 3], ['control ["12a"]', ['12a'], None], ['control [""]', [''], None], ['control ["3"]', ['3'], 5], ['control ["95"]', ['95'], 7], ['control ["55555"]', ['55555'], 1], ['control ["9"]', ['9'], 4]], [['regression ["9795751"]', ['9795751'], 6], ['regression ["6943515153"]', ['6943515153'], 0], ['control [""]', [''], None], ['control ["12a"]', ['12a'], None], ['control ["9"]', ['9'], 4], ['control ["12"]', ['12'], 3], ['control ["072"]', ['072'], 5], ['control ["36073"]', ['36073'], 5]]]
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 ["9"]	`2`	`4`	Failed
regression ["12"]	`0`	`3`	Failed
control [""]	`None`	`None`	Passed
control ["12a"]	`None`	`None`	Passed
control ["072"]	`4`	`5`	Failed
control ["36073"]	`8`	`5`	Failed
control ["98772300"]	`5`	`4`	Failed
control ["3370345686"]	`5`	`4`	Failed

SHA-256 / 961b2c861915bf1b5f8da1d2a435d902eb3656b93f77c9244bf2bf4d5b692bee

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(s):
    if not s or not s.isascii() or not s.isdigit():
        return None
    p = 11
    for ch in s:
        p = ((p + int(ch)) % 10 or 10) * 2 % 11
    return (11 - p) % 10
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["9"]', ['9'], 4], ['regression ["12"]', ['12'], 3], ['control [""]', [''], None], ['control ["12a"]', ['12a'], None], ['control ["072"]', ['072'], 5], ['control ["36073"]', ['36073'], 5], ['control ["98772300"]', ['98772300'], 4], ['control ["3370345686"]', ['3370345686'], 4]], [['regression ["36073"]', ['36073'], 5], ['regression ["98772300"]', ['98772300'], 4], ['control ["12a"]', ['12a'], None], ['control [""]', [''], None], ['control ["2638206592"]', ['2638206592'], 8], ['control ["412595035658"]', ['412595035658'], 9], ['control ["0227566323850846"]', ['0227566323850846'], 4], ['control ["9477"]', ['9477'], 3]], [['regression ["6279939841"]', ['6279939841'], 2], ['regression ["2638206592"]', ['2638206592'], 8], ['control [""]', [''], None], ['control ["12a"]', ['12a'], None], ['control ["9795751"]', ['9795751'], 6], ['control ["6943515153"]', ['6943515153'], 0], ['control ["0"]', ['0'], 2], ['control ["1"]', ['1'], 9]], [['regression ["0227566323850846"]', ['0227566323850846'], 4], ['regression ["9477"]', ['9477'], 3], ['control ["12a"]', ['12a'], None], ['control [""]', [''], None], ['control ["3"]', ['3'], 5], ['control ["95"]', ['95'], 7], ['control ["55555"]', ['55555'], 1], ['control ["9"]', ['9'], 4]], [['regression ["9795751"]', ['9795751'], 6], ['regression ["6943515153"]', ['6943515153'], 0], ['control [""]', [''], None], ['control ["12a"]', ['12a'], None], ['control ["9"]', ['9'], 4], ['control ["12"]', ['12'], 3], ['control ["072"]', ['072'], 5], ['control ["36073"]', ['36073'], 5]]]
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 ["9"]	`2`	`4`	Failed
regression ["12"]	`0`	`3`	Failed
control [""]	`None`	`None`	Passed
control ["12a"]	`None`	`None`	Passed
control ["072"]	`4`	`5`	Failed
control ["36073"]	`8`	`5`	Failed
control ["98772300"]	`5`	`4`	Failed
control ["3370345686"]	`5`	`4`	Failed

SHA-256 / 47c6391115fa943e7d5a2a576dbcd670ecae0619a2ad915ddc488bb304b5757e

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(s):
    if not s or not s.isascii() or not s.isdigit():
        return None
    p = 10
    for ch in s:
        p = ((p + int(ch)) % 10 or 10) * 2 % 11
    return (11 - p) % 10
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["9"]', ['9'], 4], ['regression ["12"]', ['12'], 3], ['control [""]', [''], None], ['control ["12a"]', ['12a'], None], ['control ["072"]', ['072'], 5], ['control ["36073"]', ['36073'], 5], ['control ["98772300"]', ['98772300'], 4], ['control ["3370345686"]', ['3370345686'], 4]], [['regression ["36073"]', ['36073'], 5], ['regression ["98772300"]', ['98772300'], 4], ['control ["12a"]', ['12a'], None], ['control [""]', [''], None], ['control ["2638206592"]', ['2638206592'], 8], ['control ["412595035658"]', ['412595035658'], 9], ['control ["0227566323850846"]', ['0227566323850846'], 4], ['control ["9477"]', ['9477'], 3]], [['regression ["6279939841"]', ['6279939841'], 2], ['regression ["2638206592"]', ['2638206592'], 8], ['control [""]', [''], None], ['control ["12a"]', ['12a'], None], ['control ["9795751"]', ['9795751'], 6], ['control ["6943515153"]', ['6943515153'], 0], ['control ["0"]', ['0'], 2], ['control ["1"]', ['1'], 9]], [['regression ["0227566323850846"]', ['0227566323850846'], 4], ['regression ["9477"]', ['9477'], 3], ['control ["12a"]', ['12a'], None], ['control [""]', [''], None], ['control ["3"]', ['3'], 5], ['control ["95"]', ['95'], 7], ['control ["55555"]', ['55555'], 1], ['control ["9"]', ['9'], 4]], [['regression ["9795751"]', ['9795751'], 6], ['regression ["6943515153"]', ['6943515153'], 0], ['control [""]', [''], None], ['control ["12a"]', ['12a'], None], ['control ["9"]', ['9'], 4], ['control ["12"]', ['12'], 3], ['control ["072"]', ['072'], 5], ['control ["36073"]', ['36073'], 5]]]
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 ["9"]	`4`	`4`	Passed
regression ["12"]	`3`	`3`	Passed
control [""]	`None`	`None`	Passed
control ["12a"]	`None`	`None`	Passed
control ["072"]	`5`	`5`	Passed
control ["36073"]	`5`	`5`	Passed
control ["98772300"]	`4`	`4`	Passed
control ["3370345686"]	`4`	`4`	Passed

SHA-256 / 3cfb78588b299fbbf781fe4060d4660da319d613f51b2fd7c62b4d7cfdc8f616

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 2026-09-29T14:48:39.650665+00:00.

Case digest / 831eaa1d844173de0cccaaae2d95f2d8e67a30396da0cd77fba514aa59ae4d94