FA-72816 / Check-digit algorithms / Open access

Bank-slip mod 11 maps 10 and 11 to zero · case 01

Slips whose remainder is 0 or 1 get verifying digit 0, which is reserved.

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

ROOT CAUSE

The substitution for 10 and 11 uses 0 instead of 1.

VERIFIED REPAIR

Replace both 10 and 11 by 1.

Unsuccessful approach: Using r % 10 sends 10 to 0 and 11 to 1, fixing only one case.

Case contract

Bank-slip style mod-11 verifying digit: nonempty ASCII digits (else None); weights 2,3,...,9 cycle from the rightmost digit; r = 11 - sum mod 11; results 10 and 11 are replaced by 1.

Why this case matters

Payment slip barcodes carry a general verifying digit that banks recompute on capture.

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
    total = 0
    for i, ch in enumerate(reversed(s)):
        total += int(ch) * (2 + i % 8)
    r = 11 - total % 11
    return 0 if r in (10, 11) else r
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["19275955179485910051680234501004684803"]', ['19275955179485910051680234501004684803'], 1], ['regression ["067817050276532142767980812420339104011"]', ['067817050276532142767980812420339104011'], 1], ['partial-repair ["54"]', ['54'], 1], ['control ["81787654"]', ['81787654'], 5], ['control ["4216186312776190006424731500839778176090"]', ['4216186312776190006424731500839778176090'], 9], ['control ["0154413110088423"]', ['0154413110088423'], 4], ['control ["2265387292381697"]', ['2265387292381697'], 4], ['control ["157141363073674774805"]', ['157141363073674774805'], 2]], [['regression ["883588303"]', ['883588303'], 1], ['regression ["54"]', ['54'], 1], ['partial-repair ["19275955179485910051680234501004684803"]', ['19275955179485910051680234501004684803'], 1], ['control ["32390980174642183951992567"]', ['32390980174642183951992567'], 6], ['control ["31028572572652095"]', ['31028572572652095'], 8], ['control ["1013803677685407598527336083735651"]', ['1013803677685407598527336083735651'], 1], ['control ["541856920526325212396079880824962283"]', ['541856920526325212396079880824962283'], 9], ['control ["90636853841379"]', ['90636853841379'], 8]], [['regression ["27981996326643088365414819731338534"]', ['27981996326643088365414819731338534'], 1], ['regression ["0"]', ['0'], 1], ['partial-repair ["19275955179485910051680234501004684803"]', ['19275955179485910051680234501004684803'], 1], ['partial-repair ["54"]', ['54'], 1], ['control ["815243122823727656729727617889"]', ['815243122823727656729727617889'], 4], ['control ["866534787261435696309320"]', ['866534787261435696309320'], 1], ['control ["59608070035358359099925603574938148494060"]', ['59608070035358359099925603574938148494060'], 2], ['control ["2567041842604142121509116255"]', ['2567041842604142121509116255'], 9]], [['regression ["19275955179485910051680234501004684803"]', ['19275955179485910051680234501004684803'], 1], ['regression ["067817050276532142767980812420339104011"]', ['067817050276532142767980812420339104011'], 1], ['partial-repair ["54"]', ['54'], 1], ['control ["666316543903176040"]', ['666316543903176040'], 7], ['control ["221858430508251943268773964844902173"]', ['221858430508251943268773964844902173'], 8], ['control ["26064317433322755425"]', ['26064317433322755425'], 2], ['control ["635756761654188"]', ['635756761654188'], 1], ['control ["1"]', ['1'], 9]], [['regression ["883588303"]', ['883588303'], 1], ['regression ["54"]', ['54'], 1], ['partial-repair ["19275955179485910051680234501004684803"]', ['19275955179485910051680234501004684803'], 1], ['control [""]', [''], None], ['control ["12x"]', ['12x'], None], ['control ["9999999999999999999999999999999999999999999"]', ['9999999999999999999999999999999999999999999'], 7], ['control ["81787654"]', ['81787654'], 5], ['control ["4216186312776190006424731500839778176090"]', ['4216186312776190006424731500839778176090'], 9]]]
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 ["19275955179485910051680234501004684803"]	`0`	`1`	Failed
regression ["067817050276532142767980812420339104011"]	`0`	`1`	Failed
partial-repair ["54"]	`0`	`1`	Failed
control ["81787654"]	`5`	`5`	Passed
control ["4216186312776190006424731500839778176090"]	`9`	`9`	Passed
control ["0154413110088423"]	`4`	`4`	Passed
control ["2265387292381697"]	`4`	`4`	Passed
control ["157141363073674774805"]	`2`	`2`	Passed

SHA-256 / 5a1f9f7bfe22f491a6ffb5c74a6545b32394fd01c4806c9684e54f28c3dc1350

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
    total = 0
    for i, ch in enumerate(reversed(s)):
        total += int(ch) * (2 + i % 8)
    r = 11 - total % 11
    return r % 10
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["19275955179485910051680234501004684803"]', ['19275955179485910051680234501004684803'], 1], ['regression ["067817050276532142767980812420339104011"]', ['067817050276532142767980812420339104011'], 1], ['partial-repair ["54"]', ['54'], 1], ['control ["81787654"]', ['81787654'], 5], ['control ["4216186312776190006424731500839778176090"]', ['4216186312776190006424731500839778176090'], 9], ['control ["0154413110088423"]', ['0154413110088423'], 4], ['control ["2265387292381697"]', ['2265387292381697'], 4], ['control ["157141363073674774805"]', ['157141363073674774805'], 2]], [['regression ["883588303"]', ['883588303'], 1], ['regression ["54"]', ['54'], 1], ['partial-repair ["19275955179485910051680234501004684803"]', ['19275955179485910051680234501004684803'], 1], ['control ["32390980174642183951992567"]', ['32390980174642183951992567'], 6], ['control ["31028572572652095"]', ['31028572572652095'], 8], ['control ["1013803677685407598527336083735651"]', ['1013803677685407598527336083735651'], 1], ['control ["541856920526325212396079880824962283"]', ['541856920526325212396079880824962283'], 9], ['control ["90636853841379"]', ['90636853841379'], 8]], [['regression ["27981996326643088365414819731338534"]', ['27981996326643088365414819731338534'], 1], ['regression ["0"]', ['0'], 1], ['partial-repair ["19275955179485910051680234501004684803"]', ['19275955179485910051680234501004684803'], 1], ['partial-repair ["54"]', ['54'], 1], ['control ["815243122823727656729727617889"]', ['815243122823727656729727617889'], 4], ['control ["866534787261435696309320"]', ['866534787261435696309320'], 1], ['control ["59608070035358359099925603574938148494060"]', ['59608070035358359099925603574938148494060'], 2], ['control ["2567041842604142121509116255"]', ['2567041842604142121509116255'], 9]], [['regression ["19275955179485910051680234501004684803"]', ['19275955179485910051680234501004684803'], 1], ['regression ["067817050276532142767980812420339104011"]', ['067817050276532142767980812420339104011'], 1], ['partial-repair ["54"]', ['54'], 1], ['control ["666316543903176040"]', ['666316543903176040'], 7], ['control ["221858430508251943268773964844902173"]', ['221858430508251943268773964844902173'], 8], ['control ["26064317433322755425"]', ['26064317433322755425'], 2], ['control ["635756761654188"]', ['635756761654188'], 1], ['control ["1"]', ['1'], 9]], [['regression ["883588303"]', ['883588303'], 1], ['regression ["54"]', ['54'], 1], ['partial-repair ["19275955179485910051680234501004684803"]', ['19275955179485910051680234501004684803'], 1], ['control [""]', [''], None], ['control ["12x"]', ['12x'], None], ['control ["9999999999999999999999999999999999999999999"]', ['9999999999999999999999999999999999999999999'], 7], ['control ["81787654"]', ['81787654'], 5], ['control ["4216186312776190006424731500839778176090"]', ['4216186312776190006424731500839778176090'], 9]]]
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 ["19275955179485910051680234501004684803"]	`0`	`1`	Failed
regression ["067817050276532142767980812420339104011"]	`1`	`1`	Passed
partial-repair ["54"]	`0`	`1`	Failed
control ["81787654"]	`5`	`5`	Passed
control ["4216186312776190006424731500839778176090"]	`9`	`9`	Passed
control ["0154413110088423"]	`4`	`4`	Passed
control ["2265387292381697"]	`4`	`4`	Passed
control ["157141363073674774805"]	`2`	`2`	Passed

SHA-256 / 0dce811cd98225d3de6b48195686391dc8e42c67e9bf7204c28912cd3ebdb6b0

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
    total = 0
    for i, ch in enumerate(reversed(s)):
        total += int(ch) * (2 + i % 8)
    r = 11 - total % 11
    return 1 if r in (10, 11) else r
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["19275955179485910051680234501004684803"]', ['19275955179485910051680234501004684803'], 1], ['regression ["067817050276532142767980812420339104011"]', ['067817050276532142767980812420339104011'], 1], ['partial-repair ["54"]', ['54'], 1], ['control ["81787654"]', ['81787654'], 5], ['control ["4216186312776190006424731500839778176090"]', ['4216186312776190006424731500839778176090'], 9], ['control ["0154413110088423"]', ['0154413110088423'], 4], ['control ["2265387292381697"]', ['2265387292381697'], 4], ['control ["157141363073674774805"]', ['157141363073674774805'], 2]], [['regression ["883588303"]', ['883588303'], 1], ['regression ["54"]', ['54'], 1], ['partial-repair ["19275955179485910051680234501004684803"]', ['19275955179485910051680234501004684803'], 1], ['control ["32390980174642183951992567"]', ['32390980174642183951992567'], 6], ['control ["31028572572652095"]', ['31028572572652095'], 8], ['control ["1013803677685407598527336083735651"]', ['1013803677685407598527336083735651'], 1], ['control ["541856920526325212396079880824962283"]', ['541856920526325212396079880824962283'], 9], ['control ["90636853841379"]', ['90636853841379'], 8]], [['regression ["27981996326643088365414819731338534"]', ['27981996326643088365414819731338534'], 1], ['regression ["0"]', ['0'], 1], ['partial-repair ["19275955179485910051680234501004684803"]', ['19275955179485910051680234501004684803'], 1], ['partial-repair ["54"]', ['54'], 1], ['control ["815243122823727656729727617889"]', ['815243122823727656729727617889'], 4], ['control ["866534787261435696309320"]', ['866534787261435696309320'], 1], ['control ["59608070035358359099925603574938148494060"]', ['59608070035358359099925603574938148494060'], 2], ['control ["2567041842604142121509116255"]', ['2567041842604142121509116255'], 9]], [['regression ["19275955179485910051680234501004684803"]', ['19275955179485910051680234501004684803'], 1], ['regression ["067817050276532142767980812420339104011"]', ['067817050276532142767980812420339104011'], 1], ['partial-repair ["54"]', ['54'], 1], ['control ["666316543903176040"]', ['666316543903176040'], 7], ['control ["221858430508251943268773964844902173"]', ['221858430508251943268773964844902173'], 8], ['control ["26064317433322755425"]', ['26064317433322755425'], 2], ['control ["635756761654188"]', ['635756761654188'], 1], ['control ["1"]', ['1'], 9]], [['regression ["883588303"]', ['883588303'], 1], ['regression ["54"]', ['54'], 1], ['partial-repair ["19275955179485910051680234501004684803"]', ['19275955179485910051680234501004684803'], 1], ['control [""]', [''], None], ['control ["12x"]', ['12x'], None], ['control ["9999999999999999999999999999999999999999999"]', ['9999999999999999999999999999999999999999999'], 7], ['control ["81787654"]', ['81787654'], 5], ['control ["4216186312776190006424731500839778176090"]', ['4216186312776190006424731500839778176090'], 9]]]
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 ["19275955179485910051680234501004684803"]	`1`	`1`	Passed
regression ["067817050276532142767980812420339104011"]	`1`	`1`	Passed
partial-repair ["54"]	`1`	`1`	Passed
control ["81787654"]	`5`	`5`	Passed
control ["4216186312776190006424731500839778176090"]	`9`	`9`	Passed
control ["0154413110088423"]	`4`	`4`	Passed
control ["2265387292381697"]	`4`	`4`	Passed
control ["157141363073674774805"]	`2`	`2`	Passed

SHA-256 / e646eca0c8b25da3491b44694c7f740e682661020b2c23159de30be4d6e9e421

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 2026-09-29T14:48:41.807199+00:00.

Case digest / e9bd2c71d56ed0a35c130e95c2332a41dfe15ea025ed7e445b24fdd4a1680d2e