FA-79811 / Barcode symbology encoding / Open access
Randomised pad wraps by 253 · case 01
Some pad codewords are one higher than the reference encoder produces.
ROOT CAUSE
Values above 254 are reduced by 253 instead of 254.
VERIFIED REPAIR
Subtract 254 when the value exceeds 254.
Unsuccessful approach: Wrapping above 255 lets 255 through, which is not a valid pad.
Case contract
Data Matrix ASCII encodation into `capacity` data codewords: two consecutive ASCII digits become 130 + their value; ASCII 0..127 becomes ord + 1; 128..255 becomes Upper Shift 235 then ord - 127; higher code points are unencodable. Too many codewords -> overflow. Padding: the first pad is 129; each later pad at 1-based position p is 129 + ((149 * p) mod 253) + 1, minus 254 if above 254.
Why this case matters
Retail, logistics, pharmacy and document workflows depend on encoders that produce exactly the module pattern, code-set switches, separators and quiet zones scanners expect; one misplaced module or separator makes a label unreadable or, worse, scan as different data.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(text, capacity):
cw = []
i = 0
while i < len(text):
c = text[i]
if c in '0123456789' and i + 1 < len(text) and text[i + 1] in '0123456789':
cw.append(130 + int(text[i:i + 2]))
i += 2
continue
o = ord(c)
if o > 255:
return {'error': 'unencodable'}
if o > 127:
cw += [235, o - 127]
else:
cw.append(o + 1)
i += 1
if len(cw) > capacity:
return {'error': 'overflow'}
if len(cw) < capacity:
cw.append(129)
while len(cw) < capacity:
p = len(cw) + 1
v = 129 + ((149 * p) % 253) + 1
if v > 254:
v -= 253
cw.append(v)
return cw
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[('', 6), [129, 175, 70, 220, 115, 11]], [('é99AB0', 10), [235, 106, 229, 66, 67, 49, 129, 56, 206, 101]], [('\x80', 4), [235, 1, 129, 220]], [('0AB12', 3), {'error': 'overflow'}], [('ABé', 1), {'error': 'overflow'}], [('AB€€', 10), {'error': 'unencodable'}], [('ÿAB', 5), [235, 128, 66, 67, 129]], [('99x', 5), [229, 121, 129, 220, 115]]], [[('0', 9), [49, 129, 70, 220, 115, 11, 161, 56, 206]], [('0 5', 12), [49, 33, 54, 129, 115, 11, 161, 56, 206, 101, 251, 147]], [('ABxx', 2), {'error': 'overflow'}], [(' AB', 4), [33, 66, 67, 129]], [('', 2), [129, 175]], [('x€', 10), {'error': 'unencodable'}], [(' 125', 1), {'error': 'overflow'}], [('0', 4), [49, 129, 70, 220]]], [[('', 4), [129, 175, 70, 220]], [('x', 5), [121, 129, 70, 220, 115]], [('éé', 3), {'error': 'overflow'}], [('é\x80\x80', 3), {'error': 'overflow'}], [('99ÿé', 7), [229, 235, 128, 235, 106, 129, 161]], [('0', 2), [49, 129]], [('99é0', 5), [229, 235, 106, 49, 129]], [('x99AB', 11), [121, 229, 66, 67, 129, 11, 161, 56, 206, 101, 251]]], [[('0xÿ', 8), [49, 121, 235, 128, 129, 11, 161, 56]], [(' 12', 9), [33, 142, 129, 220, 115, 11, 161, 56, 206]], [('\x8012x5', 1), {'error': 'overflow'}], [(' €ÿ\x80', 5), {'error': 'unencodable'}], [('AB€x', 2), {'error': 'unencodable'}], [('€ ', 4), {'error': 'unencodable'}], [('\x80x0', 5), [235, 1, 121, 49, 129]], [('', 6), [129, 175, 70, 220, 115, 11]]], [[('xÿ ', 8), [121, 235, 128, 33, 129, 11, 161, 56]], [('x5AB', 12), [121, 54, 66, 67, 129, 11, 161, 56, 206, 101, 251, 147]], [('990', 1), {'error': 'overflow'}], [('599AB€', 8), {'error': 'unencodable'}], [('\x80€ 0', 8), {'error': 'unencodable'}], [('AB\x805AB', 8), [66, 67, 235, 1, 54, 66, 67, 129]], [('€99', 7), {'error': 'unencodable'}], [('\x80ÿ', 9), [235, 1, 235, 128, 129, 11, 161, 56, 206]]]]
labels = ["regression: randomised pad wraparound", "repair trap", "combined fault", "control", "control", "boundary", "boundary", "control"]
for i, (args, expected) in enumerate(fixtures[N-1]):
check("%s %d" % (labels[i % len(labels)], i), 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: randomised pad wraparound 0 | [129, 175, 71, 220, 116, 12] | [129, 175, 70, 220, 115, 11] | Failed |
| repair trap 1 | [235, 106, 229, 66, 67, 49, 129, 57, 206, 102] | [235, 106, 229, 66, 67, 49, 129, 56, 206, 101] | Failed |
| combined fault 2 | [235, 1, 129, 220] | [235, 1, 129, 220] | Passed |
| control 3 | {'error': 'overflow'} | {'error': 'overflow'} | Passed |
| control 4 | {'error': 'overflow'} | {'error': 'overflow'} | Passed |
| boundary 5 | {'error': 'unencodable'} | {'error': 'unencodable'} | Passed |
| boundary 6 | [235, 128, 66, 67, 129] | [235, 128, 66, 67, 129] | Passed |
| control 7 | [229, 121, 129, 220, 116] | [229, 121, 129, 220, 115] | Failed |
SHA-256 / fd0738d7b8410603acbf79c0a02bd7d8cfb1f984d8315a7e34a76c689b6ea5df
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(text, capacity):
cw = []
i = 0
while i < len(text):
c = text[i]
if c in '0123456789' and i + 1 < len(text) and text[i + 1] in '0123456789':
cw.append(130 + int(text[i:i + 2]))
i += 2
continue
o = ord(c)
if o > 255:
return {'error': 'unencodable'}
if o > 127:
cw += [235, o - 127]
else:
cw.append(o + 1)
i += 1
if len(cw) > capacity:
return {'error': 'overflow'}
if len(cw) < capacity:
cw.append(129)
while len(cw) < capacity:
p = len(cw) + 1
v = 129 + ((149 * p) % 253) + 1
if v > 255:
v -= 255
cw.append(v)
return cw
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[('', 6), [129, 175, 70, 220, 115, 11]], [('é99AB0', 10), [235, 106, 229, 66, 67, 49, 129, 56, 206, 101]], [('\x80', 4), [235, 1, 129, 220]], [('0AB12', 3), {'error': 'overflow'}], [('ABé', 1), {'error': 'overflow'}], [('AB€€', 10), {'error': 'unencodable'}], [('ÿAB', 5), [235, 128, 66, 67, 129]], [('99x', 5), [229, 121, 129, 220, 115]]], [[('0', 9), [49, 129, 70, 220, 115, 11, 161, 56, 206]], [('0 5', 12), [49, 33, 54, 129, 115, 11, 161, 56, 206, 101, 251, 147]], [('ABxx', 2), {'error': 'overflow'}], [(' AB', 4), [33, 66, 67, 129]], [('', 2), [129, 175]], [('x€', 10), {'error': 'unencodable'}], [(' 125', 1), {'error': 'overflow'}], [('0', 4), [49, 129, 70, 220]]], [[('', 4), [129, 175, 70, 220]], [('x', 5), [121, 129, 70, 220, 115]], [('éé', 3), {'error': 'overflow'}], [('é\x80\x80', 3), {'error': 'overflow'}], [('99ÿé', 7), [229, 235, 128, 235, 106, 129, 161]], [('0', 2), [49, 129]], [('99é0', 5), [229, 235, 106, 49, 129]], [('x99AB', 11), [121, 229, 66, 67, 129, 11, 161, 56, 206, 101, 251]]], [[('0xÿ', 8), [49, 121, 235, 128, 129, 11, 161, 56]], [(' 12', 9), [33, 142, 129, 220, 115, 11, 161, 56, 206]], [('\x8012x5', 1), {'error': 'overflow'}], [(' €ÿ\x80', 5), {'error': 'unencodable'}], [('AB€x', 2), {'error': 'unencodable'}], [('€ ', 4), {'error': 'unencodable'}], [('\x80x0', 5), [235, 1, 121, 49, 129]], [('', 6), [129, 175, 70, 220, 115, 11]]], [[('xÿ ', 8), [121, 235, 128, 33, 129, 11, 161, 56]], [('x5AB', 12), [121, 54, 66, 67, 129, 11, 161, 56, 206, 101, 251, 147]], [('990', 1), {'error': 'overflow'}], [('599AB€', 8), {'error': 'unencodable'}], [('\x80€ 0', 8), {'error': 'unencodable'}], [('AB\x805AB', 8), [66, 67, 235, 1, 54, 66, 67, 129]], [('€99', 7), {'error': 'unencodable'}], [('\x80ÿ', 9), [235, 1, 235, 128, 129, 11, 161, 56, 206]]]]
labels = ["regression: randomised pad wraparound", "repair trap", "combined fault", "control", "control", "boundary", "boundary", "control"]
for i, (args, expected) in enumerate(fixtures[N-1]):
check("%s %d" % (labels[i % len(labels)], i), 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: randomised pad wraparound 0 | [129, 175, 69, 220, 114, 10] | [129, 175, 70, 220, 115, 11] | Failed |
| repair trap 1 | [235, 106, 229, 66, 67, 49, 129, 55, 206, 100] | [235, 106, 229, 66, 67, 49, 129, 56, 206, 101] | Failed |
| combined fault 2 | [235, 1, 129, 220] | [235, 1, 129, 220] | Passed |
| control 3 | {'error': 'overflow'} | {'error': 'overflow'} | Passed |
| control 4 | {'error': 'overflow'} | {'error': 'overflow'} | Passed |
| boundary 5 | {'error': 'unencodable'} | {'error': 'unencodable'} | Passed |
| boundary 6 | [235, 128, 66, 67, 129] | [235, 128, 66, 67, 129] | Passed |
| control 7 | [229, 121, 129, 220, 114] | [229, 121, 129, 220, 115] | Failed |
SHA-256 / 2e2994c88a5c54ebf33464d4b519fc0ac78d5984b3bf1b6f4a7c7e0aac1ffeeb
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(text, capacity):
cw = []
i = 0
while i < len(text):
c = text[i]
if c in '0123456789' and i + 1 < len(text) and text[i + 1] in '0123456789':
cw.append(130 + int(text[i:i + 2]))
i += 2
continue
o = ord(c)
if o > 255:
return {'error': 'unencodable'}
if o > 127:
cw += [235, o - 127]
else:
cw.append(o + 1)
i += 1
if len(cw) > capacity:
return {'error': 'overflow'}
if len(cw) < capacity:
cw.append(129)
while len(cw) < capacity:
p = len(cw) + 1
v = 129 + ((149 * p) % 253) + 1
if v > 254:
v -= 254
cw.append(v)
return cw
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[('', 6), [129, 175, 70, 220, 115, 11]], [('é99AB0', 10), [235, 106, 229, 66, 67, 49, 129, 56, 206, 101]], [('\x80', 4), [235, 1, 129, 220]], [('0AB12', 3), {'error': 'overflow'}], [('ABé', 1), {'error': 'overflow'}], [('AB€€', 10), {'error': 'unencodable'}], [('ÿAB', 5), [235, 128, 66, 67, 129]], [('99x', 5), [229, 121, 129, 220, 115]]], [[('0', 9), [49, 129, 70, 220, 115, 11, 161, 56, 206]], [('0 5', 12), [49, 33, 54, 129, 115, 11, 161, 56, 206, 101, 251, 147]], [('ABxx', 2), {'error': 'overflow'}], [(' AB', 4), [33, 66, 67, 129]], [('', 2), [129, 175]], [('x€', 10), {'error': 'unencodable'}], [(' 125', 1), {'error': 'overflow'}], [('0', 4), [49, 129, 70, 220]]], [[('', 4), [129, 175, 70, 220]], [('x', 5), [121, 129, 70, 220, 115]], [('éé', 3), {'error': 'overflow'}], [('é\x80\x80', 3), {'error': 'overflow'}], [('99ÿé', 7), [229, 235, 128, 235, 106, 129, 161]], [('0', 2), [49, 129]], [('99é0', 5), [229, 235, 106, 49, 129]], [('x99AB', 11), [121, 229, 66, 67, 129, 11, 161, 56, 206, 101, 251]]], [[('0xÿ', 8), [49, 121, 235, 128, 129, 11, 161, 56]], [(' 12', 9), [33, 142, 129, 220, 115, 11, 161, 56, 206]], [('\x8012x5', 1), {'error': 'overflow'}], [(' €ÿ\x80', 5), {'error': 'unencodable'}], [('AB€x', 2), {'error': 'unencodable'}], [('€ ', 4), {'error': 'unencodable'}], [('\x80x0', 5), [235, 1, 121, 49, 129]], [('', 6), [129, 175, 70, 220, 115, 11]]], [[('xÿ ', 8), [121, 235, 128, 33, 129, 11, 161, 56]], [('x5AB', 12), [121, 54, 66, 67, 129, 11, 161, 56, 206, 101, 251, 147]], [('990', 1), {'error': 'overflow'}], [('599AB€', 8), {'error': 'unencodable'}], [('\x80€ 0', 8), {'error': 'unencodable'}], [('AB\x805AB', 8), [66, 67, 235, 1, 54, 66, 67, 129]], [('€99', 7), {'error': 'unencodable'}], [('\x80ÿ', 9), [235, 1, 235, 128, 129, 11, 161, 56, 206]]]]
labels = ["regression: randomised pad wraparound", "repair trap", "combined fault", "control", "control", "boundary", "boundary", "control"]
for i, (args, expected) in enumerate(fixtures[N-1]):
check("%s %d" % (labels[i % len(labels)], i), 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: randomised pad wraparound 0 | [129, 175, 70, 220, 115, 11] | [129, 175, 70, 220, 115, 11] | Passed |
| repair trap 1 | [235, 106, 229, 66, 67, 49, 129, 56, 206, 101] | [235, 106, 229, 66, 67, 49, 129, 56, 206, 101] | Passed |
| combined fault 2 | [235, 1, 129, 220] | [235, 1, 129, 220] | Passed |
| control 3 | {'error': 'overflow'} | {'error': 'overflow'} | Passed |
| control 4 | {'error': 'overflow'} | {'error': 'overflow'} | Passed |
| boundary 5 | {'error': 'unencodable'} | {'error': 'unencodable'} | Passed |
| boundary 6 | [235, 128, 66, 67, 129] | [235, 128, 66, 67, 129] | Passed |
| control 7 | [229, 121, 129, 220, 115] | [229, 121, 129, 220, 115] | Passed |
SHA-256 / 4615be2fbff40d2fb86ab901daf81242d56625c7ac4781d5c21daac93be53538
Verification & scope
A deterministic bounded teaching model with a stipulated contract; it makes no claim of conformance to any published specification. 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 2026-09-29T14:49:47.984207+00:00.
Case digest / 44fd0ef007f0e6fc09f3dc0d7288f03cc97ebd39591ab565212135ac184f4baa