FA-72831 / Check-digit algorithms / Open access

ESR applies the carry table before adding the digit · case 01

Reference check digits disagree with the bank.

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

ROOT CAUSE

The update is written (T[carry] + digit) % 10, permuting the old carry instead of the sum.

VERIFIED REPAIR

Apply the table to the sum: carry = T[(carry + digit) % 10].

Unsuccessful approach: Permuting the digit and then adding the carry is still the wrong composition.

Case contract

Swiss ESR/QR reference check digit (modulo 10 recursive): spaces ignored, nonempty ASCII digits required (else None). carry starts at 0 and for each digit becomes T[(carry + digit) mod 10] with T = 0,9,4,6,8,2,7,1,3,5; the check digit is (10 - carry) mod 10.

Why this case matters

Payment slips carry a recursive mod-10 reference that billing systems regenerate for reconciliation.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(s):
    T = [0, 9, 4, 6, 8, 2, 7, 1, 3, 5]
    t = s.replace(' ', '')
    if not t or not t.isascii() or not t.isdigit():
        return None
    carry = 0
    for ch in t:
        carry = (T[carry] + int(ch)) % 10
    return (10 - carry) % 10
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["74553352741408306"]', ['74553352741408306'], 2], ['regression ["53572"]', ['53572'], 8], ['partial-repair ["2077434195614"]', ['2077434195614'], 0], ['control ["0"]', ['0'], 0], ['control [""]', [''], None], ['control ["12 ab"]', ['12 ab'], None], ['control ["00000000000000000000000000"]', ['00000000000000000000000000'], 0], ['control ["45013905312"]', ['45013905312'], 1]], [['regression ["1620895357382317345"]', ['1620895357382317345'], 4], ['regression ["29066637371762928589407375"]', ['29066637371762928589407375'], 8], ['partial-repair ["53572"]', ['53572'], 8], ['partial-repair ["45013905312"]', ['45013905312'], 1], ['control [""]', [''], None], ['control ["12 ab"]', ['12 ab'], None], ['control ["00000000000000000000000000"]', ['00000000000000000000000000'], 0], ['control ["0"]', ['0'], 0]], [['regression ["80"]', ['80'], 4], ['regression ["795943004839078191062840"]', ['795943004839078191062840'], 4], ['partial-repair ["29066637371762928589407375"]', ['29066637371762928589407375'], 8], ['partial-repair ["4577034845604675"]', ['4577034845604675'], 7], ['control ["12 ab"]', ['12 ab'], None], ['control ["00000000000000000000000000"]', ['00000000000000000000000000'], 0], ['control ["0"]', ['0'], 0], ['control [""]', [''], None]], [['regression ["06826"]', ['06826'], 2], ['regression ["06830652810379"]', ['06830652810379'], 4], ['partial-repair ["795943004839078191062840"]', ['795943004839078191062840'], 4], ['partial-repair ["846437545686321455"]', ['846437545686321455'], 0], ['control ["00000000000000000000000000"]', ['00000000000000000000000000'], 0], ['control ["0"]', ['0'], 0], ['control [""]', [''], None], ['control ["12 ab"]', ['12 ab'], None]], [['regression ["58511"]', ['58511'], 9], ['regression ["4"]', ['4'], 2], ['partial-repair ["79703713605975"]', ['79703713605975'], 0], ['partial-repair ["06826"]', ['06826'], 2], ['control ["0"]', ['0'], 0], ['control [""]', [''], None], ['control ["12 ab"]', ['12 ab'], None], ['control ["00000000000000000000000000"]', ['00000000000000000000000000'], 0]]]
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 ["74553352741408306"]	`6`	`2`	Failed
regression ["53572"]	`5`	`8`	Failed
partial-repair ["2077434195614"]	`0`	`0`	Passed
control ["0"]	`0`	`0`	Passed
control [""]	`None`	`None`	Passed
control ["12 ab"]	`None`	`None`	Passed
control ["00000000000000000000000000"]	`0`	`0`	Passed
control ["45013905312"]	`9`	`1`	Failed

SHA-256 / 95e11aec910d650dd1b3f2278b7b88224d8f8e4ca7d313762c2b5a5819ddb8ef

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(s):
    T = [0, 9, 4, 6, 8, 2, 7, 1, 3, 5]
    t = s.replace(' ', '')
    if not t or not t.isascii() or not t.isdigit():
        return None
    carry = 0
    for ch in t:
        carry = (T[int(ch)] + carry) % 10
    return (10 - carry) % 10
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["74553352741408306"]', ['74553352741408306'], 2], ['regression ["53572"]', ['53572'], 8], ['partial-repair ["2077434195614"]', ['2077434195614'], 0], ['control ["0"]', ['0'], 0], ['control [""]', [''], None], ['control ["12 ab"]', ['12 ab'], None], ['control ["00000000000000000000000000"]', ['00000000000000000000000000'], 0], ['control ["45013905312"]', ['45013905312'], 1]], [['regression ["1620895357382317345"]', ['1620895357382317345'], 4], ['regression ["29066637371762928589407375"]', ['29066637371762928589407375'], 8], ['partial-repair ["53572"]', ['53572'], 8], ['partial-repair ["45013905312"]', ['45013905312'], 1], ['control [""]', [''], None], ['control ["12 ab"]', ['12 ab'], None], ['control ["00000000000000000000000000"]', ['00000000000000000000000000'], 0], ['control ["0"]', ['0'], 0]], [['regression ["80"]', ['80'], 4], ['regression ["795943004839078191062840"]', ['795943004839078191062840'], 4], ['partial-repair ["29066637371762928589407375"]', ['29066637371762928589407375'], 8], ['partial-repair ["4577034845604675"]', ['4577034845604675'], 7], ['control ["12 ab"]', ['12 ab'], None], ['control ["00000000000000000000000000"]', ['00000000000000000000000000'], 0], ['control ["0"]', ['0'], 0], ['control [""]', [''], None]], [['regression ["06826"]', ['06826'], 2], ['regression ["06830652810379"]', ['06830652810379'], 4], ['partial-repair ["795943004839078191062840"]', ['795943004839078191062840'], 4], ['partial-repair ["846437545686321455"]', ['846437545686321455'], 0], ['control ["00000000000000000000000000"]', ['00000000000000000000000000'], 0], ['control ["0"]', ['0'], 0], ['control [""]', [''], None], ['control ["12 ab"]', ['12 ab'], None]], [['regression ["58511"]', ['58511'], 9], ['regression ["4"]', ['4'], 2], ['partial-repair ["79703713605975"]', ['79703713605975'], 0], ['partial-repair ["06826"]', ['06826'], 2], ['control ["0"]', ['0'], 0], ['control [""]', [''], None], ['control ["12 ab"]', ['12 ab'], None], ['control ["00000000000000000000000000"]', ['00000000000000000000000000'], 0]]]
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 ["74553352741408306"]	`7`	`2`	Failed
regression ["53572"]	`5`	`8`	Failed
partial-repair ["2077434195614"]	`2`	`0`	Failed
control ["0"]	`0`	`0`	Passed
control [""]	`None`	`None`	Passed
control ["12 ab"]	`None`	`None`	Passed
control ["00000000000000000000000000"]	`0`	`0`	Passed
control ["45013905312"]	`9`	`1`	Failed

SHA-256 / 3e797af116ec47fd6f1adf3647fa0b011acb6787b653e6cfbaf06335698ca133

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(s):
    T = [0, 9, 4, 6, 8, 2, 7, 1, 3, 5]
    t = s.replace(' ', '')
    if not t or not t.isascii() or not t.isdigit():
        return None
    carry = 0
    for ch in t:
        carry = T[(carry + int(ch)) % 10]
    return (10 - carry) % 10
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["74553352741408306"]', ['74553352741408306'], 2], ['regression ["53572"]', ['53572'], 8], ['partial-repair ["2077434195614"]', ['2077434195614'], 0], ['control ["0"]', ['0'], 0], ['control [""]', [''], None], ['control ["12 ab"]', ['12 ab'], None], ['control ["00000000000000000000000000"]', ['00000000000000000000000000'], 0], ['control ["45013905312"]', ['45013905312'], 1]], [['regression ["1620895357382317345"]', ['1620895357382317345'], 4], ['regression ["29066637371762928589407375"]', ['29066637371762928589407375'], 8], ['partial-repair ["53572"]', ['53572'], 8], ['partial-repair ["45013905312"]', ['45013905312'], 1], ['control [""]', [''], None], ['control ["12 ab"]', ['12 ab'], None], ['control ["00000000000000000000000000"]', ['00000000000000000000000000'], 0], ['control ["0"]', ['0'], 0]], [['regression ["80"]', ['80'], 4], ['regression ["795943004839078191062840"]', ['795943004839078191062840'], 4], ['partial-repair ["29066637371762928589407375"]', ['29066637371762928589407375'], 8], ['partial-repair ["4577034845604675"]', ['4577034845604675'], 7], ['control ["12 ab"]', ['12 ab'], None], ['control ["00000000000000000000000000"]', ['00000000000000000000000000'], 0], ['control ["0"]', ['0'], 0], ['control [""]', [''], None]], [['regression ["06826"]', ['06826'], 2], ['regression ["06830652810379"]', ['06830652810379'], 4], ['partial-repair ["795943004839078191062840"]', ['795943004839078191062840'], 4], ['partial-repair ["846437545686321455"]', ['846437545686321455'], 0], ['control ["00000000000000000000000000"]', ['00000000000000000000000000'], 0], ['control ["0"]', ['0'], 0], ['control [""]', [''], None], ['control ["12 ab"]', ['12 ab'], None]], [['regression ["58511"]', ['58511'], 9], ['regression ["4"]', ['4'], 2], ['partial-repair ["79703713605975"]', ['79703713605975'], 0], ['partial-repair ["06826"]', ['06826'], 2], ['control ["0"]', ['0'], 0], ['control [""]', [''], None], ['control ["12 ab"]', ['12 ab'], None], ['control ["00000000000000000000000000"]', ['00000000000000000000000000'], 0]]]
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 ["74553352741408306"]	`2`	`2`	Passed
regression ["53572"]	`8`	`8`	Passed
partial-repair ["2077434195614"]	`0`	`0`	Passed
control ["0"]	`0`	`0`	Passed
control [""]	`None`	`None`	Passed
control ["12 ab"]	`None`	`None`	Passed
control ["00000000000000000000000000"]	`0`	`0`	Passed
control ["45013905312"]	`1`	`1`	Passed

SHA-256 / 674cfe25e609c1076466dc7a5bb1f5f154d0ff5c99df411320e12abe0364bc50

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 2026-09-29T14:48:42.055614+00:00.

Case digest / 4a5ef1547b7b2f8c04fc4515087109fa0aaf4be9364daf2b0ee0b244b67610c7