FAILURE MAP
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FA-72606 / Check-digit algorithms / Open access

Second control digit value ten is emitted · case 01

Base numbers whose second control digit would be 10 are reported as ordinary mismatches.

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

ROOT CAUSE

Only k1 is checked for the unassignable value 10.

VERIFIED REPAIR

Also return "unassignable" when k2 is 10.

Unsuccessful approach: Testing k2 > 10 can never trigger because ctrl returns at most 10.

Case contract

Norwegian-style 11-digit national identity number with two mod-11 control digits. k1 uses weights 3,7,6,1,8,9,4,5,2 on digits 1-9; k2 uses 5,4,3,2,7,6,5,4,3,2 on digits 1-9 followed by the computed k1. Each is 11 - (sum mod 11) with 11 mapped to 0; a value of 10 means the base number is "unassignable". Non-11-digit input is "malformed". Return [k1, k2, whether digits 10 and 11 equal k1 and k2].

Why this case matters

Population registers validate national identity numbers and report which control digit disagrees.

1 / The failure

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

N = 1
observations = []
def solve(s):
    if len(s) != 11 or not s.isascii() or not s.isdigit():
        return 'malformed'
    d = [int(ch) for ch in s]
    def ctrl(ws, ds):
        r = 11 - sum(w * x for w, x in zip(ws, ds)) % 11
        return 0 if r == 11 else r
    k1 = ctrl([3, 7, 6, 1, 8, 9, 4, 5, 2], d[:9])
    if k1 == 10:
        return 'unassignable'
    k2 = ctrl([5, 4, 3, 2, 7, 6, 5, 4, 3, 2], d[:9] + [k1])
    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 ["28098179001"]', ['28098179001'], 'unassignable'], ['regression ["13128514961"]', ['13128514961'], 'unassignable'], ['control ["15068218891"]', ['15068218891'], [1, 8, False]], ['control ["12026119886"]', ['12026119886'], [2, 9, False]], ['control ["05077807892"]', ['05077807892'], 'unassignable'], ['control ["03060130066"]', ['03060130066'], [7, 7, False]], ['control ["26096688213"]', ['26096688213'], [7, 9, False]], ['control ["08042619712"]', ['08042619712'], [5, 3, False]]], [['regression ["13128514961"]', ['13128514961'], 'unassignable'], ['regression ["28098179001"]', ['28098179001'], 'unassignable'], ['control ["08042619712"]', ['08042619712'], [5, 3, False]], ['control ["12060326049"]', ['12060326049'], [0, 0, False]], ['control ["20127609775"]', ['20127609775'], [4, 9, False]], ['control ["09117682532"]', ['09117682532'], 'unassignable'], ['control ["07030971548"]', ['07030971548'], [0, 1, False]], ['control ["23057551053"]', ['23057551053'], [7, 0, False]]], [['regression ["28098179001"]', ['28098179001'], 'unassignable'], ['regression ["13128514961"]', ['13128514961'], 'unassignable'], ['control ["23057551053"]', ['23057551053'], [7, 0, False]], ['control ["13094093660"]', ['13094093660'], [4, 8, False]], ['control ["15013338686"]', ['15013338686'], [0, 1, False]], ['control ["27043193556"]', ['27043193556'], [1, 7, False]], ['control ["18117616591"]', ['18117616591'], [0, 5, False]], ['control ["13114336351"]', ['13114336351'], [5, 6, False]]], [['regression ["13128514961"]', ['13128514961'], 'unassignable'], ['regression ["28098179001"]', ['28098179001'], 'unassignable'], ['control ["13114336351"]', ['13114336351'], [5, 6, False]], ['control ["10122564665"]', ['10122564665'], [4, 4, False]], ['control ["23021493559"]', ['23021493559'], [9, 7, False]], ['control ["01117093517"]', ['01117093517'], [1, 0, False]], ['control ["18115340042"]', ['18115340042'], [5, 7, False]], ['control ["23030552606"]', ['23030552606'], [4, 4, False]]], [['regression ["28098179001"]', ['28098179001'], 'unassignable'], ['regression ["13128514961"]', ['13128514961'], 'unassignable'], ['control ["23030552606"]', ['23030552606'], [4, 4, False]], ['control ["26042158718"]', ['26042158718'], [3, 8, False]], ['control ["23056929360"]', ['23056929360'], [0, 4, False]], ['control ["20063518913"]', ['20063518913'], [0, 6, False]], ['control ["01010012356"]', ['01010012356'], [5, 6, True]], ['control ["15076500565"]', ['15076500565'], [6, 5, True]]]]
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 ["28098179001"][3, 10, False]unassignableFailed
regression ["13128514961"][4, 10, False]unassignableFailed
control ["15068218891"][1, 8, False][1, 8, False]Passed
control ["12026119886"][2, 9, False][2, 9, False]Passed
control ["05077807892"]unassignableunassignablePassed
control ["03060130066"][7, 7, False][7, 7, False]Passed
control ["26096688213"][7, 9, False][7, 9, False]Passed
control ["08042619712"][5, 3, False][5, 3, False]Passed

SHA-256 / 3efe14f520274ff4beec4085bf1a71b4fb770d77cdb5b2767ae968c6b55ace7a

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(s):
    if len(s) != 11 or not s.isascii() or not s.isdigit():
        return 'malformed'
    d = [int(ch) for ch in s]
    def ctrl(ws, ds):
        r = 11 - sum(w * x for w, x in zip(ws, ds)) % 11
        return 0 if r == 11 else r
    k1 = ctrl([3, 7, 6, 1, 8, 9, 4, 5, 2], d[:9])
    if k1 == 10:
        return 'unassignable'
    k2 = ctrl([5, 4, 3, 2, 7, 6, 5, 4, 3, 2], d[:9] + [k1])
    if k2 > 10:
        return 'unassignable'
    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 ["28098179001"]', ['28098179001'], 'unassignable'], ['regression ["13128514961"]', ['13128514961'], 'unassignable'], ['control ["15068218891"]', ['15068218891'], [1, 8, False]], ['control ["12026119886"]', ['12026119886'], [2, 9, False]], ['control ["05077807892"]', ['05077807892'], 'unassignable'], ['control ["03060130066"]', ['03060130066'], [7, 7, False]], ['control ["26096688213"]', ['26096688213'], [7, 9, False]], ['control ["08042619712"]', ['08042619712'], [5, 3, False]]], [['regression ["13128514961"]', ['13128514961'], 'unassignable'], ['regression ["28098179001"]', ['28098179001'], 'unassignable'], ['control ["08042619712"]', ['08042619712'], [5, 3, False]], ['control ["12060326049"]', ['12060326049'], [0, 0, False]], ['control ["20127609775"]', ['20127609775'], [4, 9, False]], ['control ["09117682532"]', ['09117682532'], 'unassignable'], ['control ["07030971548"]', ['07030971548'], [0, 1, False]], ['control ["23057551053"]', ['23057551053'], [7, 0, False]]], [['regression ["28098179001"]', ['28098179001'], 'unassignable'], ['regression ["13128514961"]', ['13128514961'], 'unassignable'], ['control ["23057551053"]', ['23057551053'], [7, 0, False]], ['control ["13094093660"]', ['13094093660'], [4, 8, False]], ['control ["15013338686"]', ['15013338686'], [0, 1, False]], ['control ["27043193556"]', ['27043193556'], [1, 7, False]], ['control ["18117616591"]', ['18117616591'], [0, 5, False]], ['control ["13114336351"]', ['13114336351'], [5, 6, False]]], [['regression ["13128514961"]', ['13128514961'], 'unassignable'], ['regression ["28098179001"]', ['28098179001'], 'unassignable'], ['control ["13114336351"]', ['13114336351'], [5, 6, False]], ['control ["10122564665"]', ['10122564665'], [4, 4, False]], ['control ["23021493559"]', ['23021493559'], [9, 7, False]], ['control ["01117093517"]', ['01117093517'], [1, 0, False]], ['control ["18115340042"]', ['18115340042'], [5, 7, False]], ['control ["23030552606"]', ['23030552606'], [4, 4, False]]], [['regression ["28098179001"]', ['28098179001'], 'unassignable'], ['regression ["13128514961"]', ['13128514961'], 'unassignable'], ['control ["23030552606"]', ['23030552606'], [4, 4, False]], ['control ["26042158718"]', ['26042158718'], [3, 8, False]], ['control ["23056929360"]', ['23056929360'], [0, 4, False]], ['control ["20063518913"]', ['20063518913'], [0, 6, False]], ['control ["01010012356"]', ['01010012356'], [5, 6, True]], ['control ["15076500565"]', ['15076500565'], [6, 5, True]]]]
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 ["28098179001"][3, 10, False]unassignableFailed
regression ["13128514961"][4, 10, False]unassignableFailed
control ["15068218891"][1, 8, False][1, 8, False]Passed
control ["12026119886"][2, 9, False][2, 9, False]Passed
control ["05077807892"]unassignableunassignablePassed
control ["03060130066"][7, 7, False][7, 7, False]Passed
control ["26096688213"][7, 9, False][7, 9, False]Passed
control ["08042619712"][5, 3, False][5, 3, False]Passed

SHA-256 / 133e7826f49c36c7c6ccc547c8c652bea67c102a7d3806798b331379147ac4f6

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(s):
    if len(s) != 11 or not s.isascii() or not s.isdigit():
        return 'malformed'
    d = [int(ch) for ch in s]
    def ctrl(ws, ds):
        r = 11 - sum(w * x for w, x in zip(ws, ds)) % 11
        return 0 if r == 11 else r
    k1 = ctrl([3, 7, 6, 1, 8, 9, 4, 5, 2], d[:9])
    if k1 == 10:
        return 'unassignable'
    k2 = ctrl([5, 4, 3, 2, 7, 6, 5, 4, 3, 2], d[:9] + [k1])
    if k2 == 10:
        return 'unassignable'
    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 ["28098179001"]', ['28098179001'], 'unassignable'], ['regression ["13128514961"]', ['13128514961'], 'unassignable'], ['control ["15068218891"]', ['15068218891'], [1, 8, False]], ['control ["12026119886"]', ['12026119886'], [2, 9, False]], ['control ["05077807892"]', ['05077807892'], 'unassignable'], ['control ["03060130066"]', ['03060130066'], [7, 7, False]], ['control ["26096688213"]', ['26096688213'], [7, 9, False]], ['control ["08042619712"]', ['08042619712'], [5, 3, False]]], [['regression ["13128514961"]', ['13128514961'], 'unassignable'], ['regression ["28098179001"]', ['28098179001'], 'unassignable'], ['control ["08042619712"]', ['08042619712'], [5, 3, False]], ['control ["12060326049"]', ['12060326049'], [0, 0, False]], ['control ["20127609775"]', ['20127609775'], [4, 9, False]], ['control ["09117682532"]', ['09117682532'], 'unassignable'], ['control ["07030971548"]', ['07030971548'], [0, 1, False]], ['control ["23057551053"]', ['23057551053'], [7, 0, False]]], [['regression ["28098179001"]', ['28098179001'], 'unassignable'], ['regression ["13128514961"]', ['13128514961'], 'unassignable'], ['control ["23057551053"]', ['23057551053'], [7, 0, False]], ['control ["13094093660"]', ['13094093660'], [4, 8, False]], ['control ["15013338686"]', ['15013338686'], [0, 1, False]], ['control ["27043193556"]', ['27043193556'], [1, 7, False]], ['control ["18117616591"]', ['18117616591'], [0, 5, False]], ['control ["13114336351"]', ['13114336351'], [5, 6, False]]], [['regression ["13128514961"]', ['13128514961'], 'unassignable'], ['regression ["28098179001"]', ['28098179001'], 'unassignable'], ['control ["13114336351"]', ['13114336351'], [5, 6, False]], ['control ["10122564665"]', ['10122564665'], [4, 4, False]], ['control ["23021493559"]', ['23021493559'], [9, 7, False]], ['control ["01117093517"]', ['01117093517'], [1, 0, False]], ['control ["18115340042"]', ['18115340042'], [5, 7, False]], ['control ["23030552606"]', ['23030552606'], [4, 4, False]]], [['regression ["28098179001"]', ['28098179001'], 'unassignable'], ['regression ["13128514961"]', ['13128514961'], 'unassignable'], ['control ["23030552606"]', ['23030552606'], [4, 4, False]], ['control ["26042158718"]', ['26042158718'], [3, 8, False]], ['control ["23056929360"]', ['23056929360'], [0, 4, False]], ['control ["20063518913"]', ['20063518913'], [0, 6, False]], ['control ["01010012356"]', ['01010012356'], [5, 6, True]], ['control ["15076500565"]', ['15076500565'], [6, 5, True]]]]
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 ["28098179001"]unassignableunassignablePassed
regression ["13128514961"]unassignableunassignablePassed
control ["15068218891"][1, 8, False][1, 8, False]Passed
control ["12026119886"][2, 9, False][2, 9, False]Passed
control ["05077807892"]unassignableunassignablePassed
control ["03060130066"][7, 7, False][7, 7, False]Passed
control ["26096688213"][7, 9, False][7, 9, False]Passed
control ["08042619712"][5, 3, False][5, 3, False]Passed

SHA-256 / dd30fd96ecb5816a62d3721652af2af603f8f736f3f206bcb03b5f8fe4918bc3

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 2026-09-29T14:48:39.942694+00:00.

Case digest / 6e09294106f4ea89e6d09107df2944fe2641375ecfc96a861cd01a36f585561f