FA-72531 / Check-digit algorithms / Open access

ABA rejects the electronic prefix 80 · case 01

Traveler-check routing numbers beginning 80 are reported malformed.

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

ROOT CAUSE

The special prefix 80 was left out of the allowed ranges.

VERIFIED REPAIR

Allow p == 80 alongside the three district ranges.

Unsuccessful approach: Allowing every prefix of 80 and above admits unassigned 81-99 prefixes.

Case contract

US ABA routing transit number: exactly nine ASCII digits whose first two digits lie in 00-12, 21-32, 61-72 or equal 80 (else "malformed"). Weights 3,7,1 repeat from the left; return whether the weighted sum is a multiple of 10.

Why this case matters

ACH origination checks routing numbers before transmitting a batch.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(s):
    if len(s) != 9 or not s.isascii() or not s.isdigit():
        return 'malformed'
    p = int(s[:2])
    if not (0 <= p <= 12 or 21 <= p <= 32 or 61 <= p <= 72):
        return 'malformed'
    total = sum(int(ch) * (3, 7, 1)[i % 3] for i, ch in enumerate(s))
    return total % 10 == 0
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["808489768"]', ['808489768'], True], ['regression ["808489769"]', ['808489769'], False], ['partial-repair ["811000011"]', ['811000011'], 'malformed'], ['control ["000396219"]', ['000396219'], True], ['control ["000396210"]', ['000396210'], False], ['control ["014060861"]', ['014060861'], True], ['control ["014060862"]', ['014060862'], False], ['control ["056885062"]', ['056885062'], True]], [['regression ["803391247"]', ['803391247'], False], ['regression ["800000009"]', ['800000009'], False], ['partial-repair ["811000011"]', ['811000011'], 'malformed'], ['control ["056885063"]', ['056885063'], False], ['control ["119218424"]', ['119218424'], True], ['control ["119218425"]', ['119218425'], False], ['control ["121199382"]', ['121199382'], True], ['control ["121199383"]', ['121199383'], False]], [['regression ["808489769"]', ['808489769'], False], ['regression ["803391246"]', ['803391246'], True], ['partial-repair ["811000011"]', ['811000011'], 'malformed'], ['control ["217283403"]', ['217283403'], True], ['control ["217283404"]', ['217283404'], False], ['control ["262758598"]', ['262758598'], True], ['control ["262758599"]', ['262758599'], False], ['control ["311681228"]', ['311681228'], True]], [['regression ["800000009"]', ['800000009'], False], ['regression ["808489768"]', ['808489768'], True], ['partial-repair ["811000011"]', ['811000011'], 'malformed'], ['control ["311681229"]', ['311681229'], False], ['control ["324890048"]', ['324890048'], True], ['control ["324890049"]', ['324890049'], False], ['control ["616486212"]', ['616486212'], True], ['control ["616486213"]', ['616486213'], False]], [['regression ["803391246"]', ['803391246'], True], ['regression ["803391247"]', ['803391247'], False], ['partial-repair ["811000011"]', ['811000011'], 'malformed'], ['control ["670455289"]', ['670455289'], True], ['control ["670455280"]', ['670455280'], False], ['control ["720402959"]', ['720402959'], True], ['control ["720402950"]', ['720402950'], False], ['control ["123311508"]', ['123311508'], 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 fixture	Actual	Expected	Outcome
regression ["808489768"]	`malformed`	`True`	Failed
regression ["808489769"]	`malformed`	`False`	Failed
partial-repair ["811000011"]	`malformed`	`malformed`	Passed
control ["000396219"]	`True`	`True`	Passed
control ["000396210"]	`False`	`False`	Passed
control ["014060861"]	`True`	`True`	Passed
control ["014060862"]	`False`	`False`	Passed
control ["056885062"]	`True`	`True`	Passed

SHA-256 / ffcd20b9751895abf4a775fa38c2e4dd7fe6f75a57ab9fcb3547956d959a784d

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) != 9 or not s.isascii() or not s.isdigit():
        return 'malformed'
    p = int(s[:2])
    if not (0 <= p <= 12 or 21 <= p <= 32 or 61 <= p <= 72 or p >= 80):
        return 'malformed'
    total = sum(int(ch) * (3, 7, 1)[i % 3] for i, ch in enumerate(s))
    return total % 10 == 0
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["808489768"]', ['808489768'], True], ['regression ["808489769"]', ['808489769'], False], ['partial-repair ["811000011"]', ['811000011'], 'malformed'], ['control ["000396219"]', ['000396219'], True], ['control ["000396210"]', ['000396210'], False], ['control ["014060861"]', ['014060861'], True], ['control ["014060862"]', ['014060862'], False], ['control ["056885062"]', ['056885062'], True]], [['regression ["803391247"]', ['803391247'], False], ['regression ["800000009"]', ['800000009'], False], ['partial-repair ["811000011"]', ['811000011'], 'malformed'], ['control ["056885063"]', ['056885063'], False], ['control ["119218424"]', ['119218424'], True], ['control ["119218425"]', ['119218425'], False], ['control ["121199382"]', ['121199382'], True], ['control ["121199383"]', ['121199383'], False]], [['regression ["808489769"]', ['808489769'], False], ['regression ["803391246"]', ['803391246'], True], ['partial-repair ["811000011"]', ['811000011'], 'malformed'], ['control ["217283403"]', ['217283403'], True], ['control ["217283404"]', ['217283404'], False], ['control ["262758598"]', ['262758598'], True], ['control ["262758599"]', ['262758599'], False], ['control ["311681228"]', ['311681228'], True]], [['regression ["800000009"]', ['800000009'], False], ['regression ["808489768"]', ['808489768'], True], ['partial-repair ["811000011"]', ['811000011'], 'malformed'], ['control ["311681229"]', ['311681229'], False], ['control ["324890048"]', ['324890048'], True], ['control ["324890049"]', ['324890049'], False], ['control ["616486212"]', ['616486212'], True], ['control ["616486213"]', ['616486213'], False]], [['regression ["803391246"]', ['803391246'], True], ['regression ["803391247"]', ['803391247'], False], ['partial-repair ["811000011"]', ['811000011'], 'malformed'], ['control ["670455289"]', ['670455289'], True], ['control ["670455280"]', ['670455280'], False], ['control ["720402959"]', ['720402959'], True], ['control ["720402950"]', ['720402950'], False], ['control ["123311508"]', ['123311508'], 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 fixture	Actual	Expected	Outcome
regression ["808489768"]	`True`	`True`	Passed
regression ["808489769"]	`False`	`False`	Passed
partial-repair ["811000011"]	`True`	`malformed`	Failed
control ["000396219"]	`True`	`True`	Passed
control ["000396210"]	`False`	`False`	Passed
control ["014060861"]	`True`	`True`	Passed
control ["014060862"]	`False`	`False`	Passed
control ["056885062"]	`True`	`True`	Passed

SHA-256 / 3fd3ec8a0018bab95b4e17acfaff60d3793ab112eeb4674453f3b735dcaa4c08

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) != 9 or not s.isascii() or not s.isdigit():
        return 'malformed'
    p = int(s[:2])
    if not (0 <= p <= 12 or 21 <= p <= 32 or 61 <= p <= 72 or p == 80):
        return 'malformed'
    total = sum(int(ch) * (3, 7, 1)[i % 3] for i, ch in enumerate(s))
    return total % 10 == 0
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression ["808489768"]', ['808489768'], True], ['regression ["808489769"]', ['808489769'], False], ['partial-repair ["811000011"]', ['811000011'], 'malformed'], ['control ["000396219"]', ['000396219'], True], ['control ["000396210"]', ['000396210'], False], ['control ["014060861"]', ['014060861'], True], ['control ["014060862"]', ['014060862'], False], ['control ["056885062"]', ['056885062'], True]], [['regression ["803391247"]', ['803391247'], False], ['regression ["800000009"]', ['800000009'], False], ['partial-repair ["811000011"]', ['811000011'], 'malformed'], ['control ["056885063"]', ['056885063'], False], ['control ["119218424"]', ['119218424'], True], ['control ["119218425"]', ['119218425'], False], ['control ["121199382"]', ['121199382'], True], ['control ["121199383"]', ['121199383'], False]], [['regression ["808489769"]', ['808489769'], False], ['regression ["803391246"]', ['803391246'], True], ['partial-repair ["811000011"]', ['811000011'], 'malformed'], ['control ["217283403"]', ['217283403'], True], ['control ["217283404"]', ['217283404'], False], ['control ["262758598"]', ['262758598'], True], ['control ["262758599"]', ['262758599'], False], ['control ["311681228"]', ['311681228'], True]], [['regression ["800000009"]', ['800000009'], False], ['regression ["808489768"]', ['808489768'], True], ['partial-repair ["811000011"]', ['811000011'], 'malformed'], ['control ["311681229"]', ['311681229'], False], ['control ["324890048"]', ['324890048'], True], ['control ["324890049"]', ['324890049'], False], ['control ["616486212"]', ['616486212'], True], ['control ["616486213"]', ['616486213'], False]], [['regression ["803391246"]', ['803391246'], True], ['regression ["803391247"]', ['803391247'], False], ['partial-repair ["811000011"]', ['811000011'], 'malformed'], ['control ["670455289"]', ['670455289'], True], ['control ["670455280"]', ['670455280'], False], ['control ["720402959"]', ['720402959'], True], ['control ["720402950"]', ['720402950'], False], ['control ["123311508"]', ['123311508'], 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 fixture	Actual	Expected	Outcome
regression ["808489768"]	`True`	`True`	Passed
regression ["808489769"]	`False`	`False`	Passed
partial-repair ["811000011"]	`malformed`	`malformed`	Passed
control ["000396219"]	`True`	`True`	Passed
control ["000396210"]	`False`	`False`	Passed
control ["014060861"]	`True`	`True`	Passed
control ["014060862"]	`False`	`False`	Passed
control ["056885062"]	`True`	`True`	Passed

SHA-256 / 72f24617f0ee601fb7b0ca8cb44647a39af285ff67b756aa499152cd927d2595

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 2026-09-29T14:48:39.324005+00:00.

Case digest / 81d7118a33fe68df61b43a4e69a14e9b213eab6079f739c83104ed8e9b2f9439