FA-72521 / Check-digit algorithms / Open access

ABA weights cycle as 7,3,1 · case 01

Legitimate routing numbers are rejected.

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

ROOT CAUSE

The repeating weight triple is written (7, 3, 1) instead of (3, 7, 1).

VERIFIED REPAIR

Use weights 3, 7, 1 repeating from the leftmost digit.

Unsuccessful approach: Rotating the triple to (1, 7, 3) is still a different weighting.

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 or p == 80):
        return 'malformed'
    total = sum(int(ch) * (7, 3, 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 ["056885062"]', ['056885062'], True], ['regression ["119218424"]', ['119218424'], True], ['partial-repair ["014060861"]', ['014060861'], True], ['control ["000396219"]', ['000396219'], True], ['control ["000396210"]', ['000396210'], False], ['control ["014060862"]', ['014060862'], False], ['control ["056885063"]', ['056885063'], False], ['control ["119218425"]', ['119218425'], False]], [['regression ["217283403"]', ['217283403'], True], ['regression ["262758598"]', ['262758598'], True], ['partial-repair ["311681228"]', ['311681228'], True], ['control ["121199383"]', ['121199383'], False], ['control ["217283404"]', ['217283404'], False], ['control ["262758599"]', ['262758599'], False], ['control ["311681229"]', ['311681229'], False], ['control ["324890049"]', ['324890049'], False]], [['regression ["616486212"]', ['616486212'], True], ['regression ["670455289"]', ['670455289'], True], ['control ["616486213"]', ['616486213'], False], ['control ["670455280"]', ['670455280'], False], ['control ["720402950"]', ['720402950'], False], ['control ["808489769"]', ['808489769'], False], ['control ["123311509"]', ['123311509'], False], ['control ["328477387"]', ['328477387'], False]], [['regression ["123311508"]', ['123311508'], True], ['regression ["328477386"]', ['328477386'], True], ['partial-repair ["808489768"]', ['808489768'], True], ['control ["328477387"]', ['328477387'], False], ['control ["721616855"]', ['721616855'], False], ['control ["803391247"]', ['803391247'], False], ['control ["011000016"]', ['011000016'], False], ['control ["131000015"]', ['131000015'], 'malformed']], [['regression ["011000015"]', ['011000015'], True], ['regression ["021000021"]', ['021000021'], True], ['partial-repair ["803391246"]', ['803391246'], True], ['control ["811000011"]', ['811000011'], 'malformed'], ['control ["0110000150"]', ['0110000150'], 'malformed'], ['control ["01100001a"]', ['01100001a'], 'malformed'], ['control ["730000000"]', ['730000000'], 'malformed'], ['control ["800000009"]', ['800000009'], False]]]
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 ["056885062"]	`False`	`True`	Failed
regression ["119218424"]	`False`	`True`	Failed
partial-repair ["014060861"]	`True`	`True`	Passed
control ["000396219"]	`True`	`True`	Passed
control ["000396210"]	`False`	`False`	Passed
control ["014060862"]	`False`	`False`	Passed
control ["056885063"]	`False`	`False`	Passed
control ["119218425"]	`False`	`False`	Passed

SHA-256 / 9d4f3272efd01aabfa8f6e39c47d2e2f3483c91708115919d56940ce4743ac6b

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) * (1, 7, 3)[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 ["056885062"]', ['056885062'], True], ['regression ["119218424"]', ['119218424'], True], ['partial-repair ["014060861"]', ['014060861'], True], ['control ["000396219"]', ['000396219'], True], ['control ["000396210"]', ['000396210'], False], ['control ["014060862"]', ['014060862'], False], ['control ["056885063"]', ['056885063'], False], ['control ["119218425"]', ['119218425'], False]], [['regression ["217283403"]', ['217283403'], True], ['regression ["262758598"]', ['262758598'], True], ['partial-repair ["311681228"]', ['311681228'], True], ['control ["121199383"]', ['121199383'], False], ['control ["217283404"]', ['217283404'], False], ['control ["262758599"]', ['262758599'], False], ['control ["311681229"]', ['311681229'], False], ['control ["324890049"]', ['324890049'], False]], [['regression ["616486212"]', ['616486212'], True], ['regression ["670455289"]', ['670455289'], True], ['control ["616486213"]', ['616486213'], False], ['control ["670455280"]', ['670455280'], False], ['control ["720402950"]', ['720402950'], False], ['control ["808489769"]', ['808489769'], False], ['control ["123311509"]', ['123311509'], False], ['control ["328477387"]', ['328477387'], False]], [['regression ["123311508"]', ['123311508'], True], ['regression ["328477386"]', ['328477386'], True], ['partial-repair ["808489768"]', ['808489768'], True], ['control ["328477387"]', ['328477387'], False], ['control ["721616855"]', ['721616855'], False], ['control ["803391247"]', ['803391247'], False], ['control ["011000016"]', ['011000016'], False], ['control ["131000015"]', ['131000015'], 'malformed']], [['regression ["011000015"]', ['011000015'], True], ['regression ["021000021"]', ['021000021'], True], ['partial-repair ["803391246"]', ['803391246'], True], ['control ["811000011"]', ['811000011'], 'malformed'], ['control ["0110000150"]', ['0110000150'], 'malformed'], ['control ["01100001a"]', ['01100001a'], 'malformed'], ['control ["730000000"]', ['730000000'], 'malformed'], ['control ["800000009"]', ['800000009'], False]]]
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 ["056885062"]	`True`	`True`	Passed
regression ["119218424"]	`False`	`True`	Failed
partial-repair ["014060861"]	`False`	`True`	Failed
control ["000396219"]	`True`	`True`	Passed
control ["000396210"]	`False`	`False`	Passed
control ["014060862"]	`False`	`False`	Passed
control ["056885063"]	`False`	`False`	Passed
control ["119218425"]	`False`	`False`	Passed

SHA-256 / 9539904ca21d9e84b7dde234f985b59d58a510143433a50bd5776b52f62561c7

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 ["056885062"]', ['056885062'], True], ['regression ["119218424"]', ['119218424'], True], ['partial-repair ["014060861"]', ['014060861'], True], ['control ["000396219"]', ['000396219'], True], ['control ["000396210"]', ['000396210'], False], ['control ["014060862"]', ['014060862'], False], ['control ["056885063"]', ['056885063'], False], ['control ["119218425"]', ['119218425'], False]], [['regression ["217283403"]', ['217283403'], True], ['regression ["262758598"]', ['262758598'], True], ['partial-repair ["311681228"]', ['311681228'], True], ['control ["121199383"]', ['121199383'], False], ['control ["217283404"]', ['217283404'], False], ['control ["262758599"]', ['262758599'], False], ['control ["311681229"]', ['311681229'], False], ['control ["324890049"]', ['324890049'], False]], [['regression ["616486212"]', ['616486212'], True], ['regression ["670455289"]', ['670455289'], True], ['control ["616486213"]', ['616486213'], False], ['control ["670455280"]', ['670455280'], False], ['control ["720402950"]', ['720402950'], False], ['control ["808489769"]', ['808489769'], False], ['control ["123311509"]', ['123311509'], False], ['control ["328477387"]', ['328477387'], False]], [['regression ["123311508"]', ['123311508'], True], ['regression ["328477386"]', ['328477386'], True], ['partial-repair ["808489768"]', ['808489768'], True], ['control ["328477387"]', ['328477387'], False], ['control ["721616855"]', ['721616855'], False], ['control ["803391247"]', ['803391247'], False], ['control ["011000016"]', ['011000016'], False], ['control ["131000015"]', ['131000015'], 'malformed']], [['regression ["011000015"]', ['011000015'], True], ['regression ["021000021"]', ['021000021'], True], ['partial-repair ["803391246"]', ['803391246'], True], ['control ["811000011"]', ['811000011'], 'malformed'], ['control ["0110000150"]', ['0110000150'], 'malformed'], ['control ["01100001a"]', ['01100001a'], 'malformed'], ['control ["730000000"]', ['730000000'], 'malformed'], ['control ["800000009"]', ['800000009'], False]]]
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 ["056885062"]	`True`	`True`	Passed
regression ["119218424"]	`True`	`True`	Passed
partial-repair ["014060861"]	`True`	`True`	Passed
control ["000396219"]	`True`	`True`	Passed
control ["000396210"]	`False`	`False`	Passed
control ["014060862"]	`False`	`False`	Passed
control ["056885063"]	`False`	`False`	Passed
control ["119218425"]	`False`	`False`	Passed

SHA-256 / 80a037a1db0624526e71306d714d8c05005ab3eb1ed0777397c2c51c07582050

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 2026-09-29T14:48:39.158453+00:00.

Case digest / d6e637e800af859cc616c6d022def6313045aeaa858f19bb6d8e60536d9560d9