FAILURE MAP
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FA-79786 / Barcode symbology encoding / Open access

Data Matrix digit pairs are offset by 128 · case 01

Numeric pairs 00 and 01 collide with the pad and upper-shift range and serial numbers decode wrongly.

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

ROOT CAUSE

Digit pairs are encoded as 128 + value instead of 130 + value.

VERIFIED REPAIR

Encode a digit pair as 130 + its two-digit value.

Unsuccessful approach: value + 1 encodes the pair as a single ASCII character.

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(128 + 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 = [[[('99x', 5), [229, 121, 129, 220, 115]], [('ÿÿ\x8012', 7), [235, 128, 235, 128, 235, 1, 142]], [('', 6), [129, 175, 70, 220, 115, 11]], [('', 11), [129, 175, 70, 220, 115, 11, 161, 56, 206, 101, 251]], [('\x80', 4), [235, 1, 129, 220]], [('0AB12', 3), {'error': 'overflow'}], [('ABé', 1), {'error': 'overflow'}], [('é99AB0', 10), [235, 106, 229, 66, 67, 49, 129, 56, 206, 101]]], [[(' x99x', 10), [33, 121, 229, 121, 129, 11, 161, 56, 206, 101]], [('55xé', 9), [185, 121, 235, 106, 129, 11, 161, 56, 206]], [('ABxx', 2), {'error': 'overflow'}], [(' AB', 4), [33, 66, 67, 129]], [('0', 9), [49, 129, 70, 220, 115, 11, 161, 56, 206]], [('', 2), [129, 175]], [('0', 4), [49, 129, 70, 220]], [('AB\x8012', 10), [66, 67, 235, 1, 142, 129, 161, 56, 206, 101]]], [[('99ÿé', 7), [229, 235, 128, 235, 106, 129, 161]], [('12', 3), [142, 129, 70]], [('é€5', 6), {'error': 'unencodable'}], [('éé', 3), {'error': 'overflow'}], [('é\x80\x80', 3), {'error': 'overflow'}], [('', 4), [129, 175, 70, 220]], [('', 5), [129, 175, 70, 220, 115]], [('ÿé12', 9), [235, 128, 235, 106, 142, 129, 161, 56, 206]]], [[('120ÿ', 6), [142, 49, 235, 128, 129, 11]], [('55', 8), [185, 129, 70, 220, 115, 11, 161, 56]], [('', 6), [129, 175, 70, 220, 115, 11]], [('\x8012x5', 1), {'error': 'overflow'}], [(' €ÿ\x80', 5), {'error': 'unencodable'}], [('', 11), [129, 175, 70, 220, 115, 11, 161, 56, 206, 101, 251]], [('0xÿ', 8), [49, 121, 235, 128, 129, 11, 161, 56]], [('99', 3), [229, 129, 70]]], [[('é99\x805', 9), [235, 106, 229, 235, 1, 54, 129, 56, 206]], [('12\x80', 6), [142, 235, 1, 129, 115, 11]], [('5', 2), [54, 129]], [('990', 1), {'error': 'overflow'}], [('599AB€', 8), {'error': 'unencodable'}], [('', 7), [129, 175, 70, 220, 115, 11, 161]], [('xÿ ', 8), [121, 235, 128, 33, 129, 11, 161, 56]], [('995', 11), [229, 54, 129, 220, 115, 11, 161, 56, 206, 101, 251]]]]
labels = ["regression: digit pair codeword", "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 fixtureActualExpectedOutcome
regression: digit pair codeword 0[227, 121, 129, 220, 115][229, 121, 129, 220, 115]Failed
repair trap 1[235, 128, 235, 128, 235, 1, 140][235, 128, 235, 128, 235, 1, 142]Failed
combined fault 2[129, 175, 70, 220, 115, 11][129, 175, 70, 220, 115, 11]Passed
control 3[129, 175, 70, 220, 115, 11, 161, 56, 206, 101, 251][129, 175, 70, 220, 115, 11, 161, 56, 206, 101, 251]Passed
control 4[235, 1, 129, 220][235, 1, 129, 220]Passed
boundary 5{'error': 'overflow'}{'error': 'overflow'}Passed
boundary 6{'error': 'overflow'}{'error': 'overflow'}Passed
control 7[235, 106, 227, 66, 67, 49, 129, 56, 206, 101][235, 106, 229, 66, 67, 49, 129, 56, 206, 101]Failed

SHA-256 / f6d9a2b05f57677c0c5f778b38ea8be2ec576222630ac1a53092e709cc55e87a

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(int(text[i:i + 2]) + 1)
            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 = [[[('99x', 5), [229, 121, 129, 220, 115]], [('ÿÿ\x8012', 7), [235, 128, 235, 128, 235, 1, 142]], [('', 6), [129, 175, 70, 220, 115, 11]], [('', 11), [129, 175, 70, 220, 115, 11, 161, 56, 206, 101, 251]], [('\x80', 4), [235, 1, 129, 220]], [('0AB12', 3), {'error': 'overflow'}], [('ABé', 1), {'error': 'overflow'}], [('é99AB0', 10), [235, 106, 229, 66, 67, 49, 129, 56, 206, 101]]], [[(' x99x', 10), [33, 121, 229, 121, 129, 11, 161, 56, 206, 101]], [('55xé', 9), [185, 121, 235, 106, 129, 11, 161, 56, 206]], [('ABxx', 2), {'error': 'overflow'}], [(' AB', 4), [33, 66, 67, 129]], [('0', 9), [49, 129, 70, 220, 115, 11, 161, 56, 206]], [('', 2), [129, 175]], [('0', 4), [49, 129, 70, 220]], [('AB\x8012', 10), [66, 67, 235, 1, 142, 129, 161, 56, 206, 101]]], [[('99ÿé', 7), [229, 235, 128, 235, 106, 129, 161]], [('12', 3), [142, 129, 70]], [('é€5', 6), {'error': 'unencodable'}], [('éé', 3), {'error': 'overflow'}], [('é\x80\x80', 3), {'error': 'overflow'}], [('', 4), [129, 175, 70, 220]], [('', 5), [129, 175, 70, 220, 115]], [('ÿé12', 9), [235, 128, 235, 106, 142, 129, 161, 56, 206]]], [[('120ÿ', 6), [142, 49, 235, 128, 129, 11]], [('55', 8), [185, 129, 70, 220, 115, 11, 161, 56]], [('', 6), [129, 175, 70, 220, 115, 11]], [('\x8012x5', 1), {'error': 'overflow'}], [(' €ÿ\x80', 5), {'error': 'unencodable'}], [('', 11), [129, 175, 70, 220, 115, 11, 161, 56, 206, 101, 251]], [('0xÿ', 8), [49, 121, 235, 128, 129, 11, 161, 56]], [('99', 3), [229, 129, 70]]], [[('é99\x805', 9), [235, 106, 229, 235, 1, 54, 129, 56, 206]], [('12\x80', 6), [142, 235, 1, 129, 115, 11]], [('5', 2), [54, 129]], [('990', 1), {'error': 'overflow'}], [('599AB€', 8), {'error': 'unencodable'}], [('', 7), [129, 175, 70, 220, 115, 11, 161]], [('xÿ ', 8), [121, 235, 128, 33, 129, 11, 161, 56]], [('995', 11), [229, 54, 129, 220, 115, 11, 161, 56, 206, 101, 251]]]]
labels = ["regression: digit pair codeword", "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 fixtureActualExpectedOutcome
regression: digit pair codeword 0[100, 121, 129, 220, 115][229, 121, 129, 220, 115]Failed
repair trap 1[235, 128, 235, 128, 235, 1, 13][235, 128, 235, 128, 235, 1, 142]Failed
combined fault 2[129, 175, 70, 220, 115, 11][129, 175, 70, 220, 115, 11]Passed
control 3[129, 175, 70, 220, 115, 11, 161, 56, 206, 101, 251][129, 175, 70, 220, 115, 11, 161, 56, 206, 101, 251]Passed
control 4[235, 1, 129, 220][235, 1, 129, 220]Passed
boundary 5{'error': 'overflow'}{'error': 'overflow'}Passed
boundary 6{'error': 'overflow'}{'error': 'overflow'}Passed
control 7[235, 106, 100, 66, 67, 49, 129, 56, 206, 101][235, 106, 229, 66, 67, 49, 129, 56, 206, 101]Failed

SHA-256 / 5024caaba8d55071cb192ffa85ef9dad4b0c5c93688d8336a33fe11191d52814

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 = [[[('99x', 5), [229, 121, 129, 220, 115]], [('ÿÿ\x8012', 7), [235, 128, 235, 128, 235, 1, 142]], [('', 6), [129, 175, 70, 220, 115, 11]], [('', 11), [129, 175, 70, 220, 115, 11, 161, 56, 206, 101, 251]], [('\x80', 4), [235, 1, 129, 220]], [('0AB12', 3), {'error': 'overflow'}], [('ABé', 1), {'error': 'overflow'}], [('é99AB0', 10), [235, 106, 229, 66, 67, 49, 129, 56, 206, 101]]], [[(' x99x', 10), [33, 121, 229, 121, 129, 11, 161, 56, 206, 101]], [('55xé', 9), [185, 121, 235, 106, 129, 11, 161, 56, 206]], [('ABxx', 2), {'error': 'overflow'}], [(' AB', 4), [33, 66, 67, 129]], [('0', 9), [49, 129, 70, 220, 115, 11, 161, 56, 206]], [('', 2), [129, 175]], [('0', 4), [49, 129, 70, 220]], [('AB\x8012', 10), [66, 67, 235, 1, 142, 129, 161, 56, 206, 101]]], [[('99ÿé', 7), [229, 235, 128, 235, 106, 129, 161]], [('12', 3), [142, 129, 70]], [('é€5', 6), {'error': 'unencodable'}], [('éé', 3), {'error': 'overflow'}], [('é\x80\x80', 3), {'error': 'overflow'}], [('', 4), [129, 175, 70, 220]], [('', 5), [129, 175, 70, 220, 115]], [('ÿé12', 9), [235, 128, 235, 106, 142, 129, 161, 56, 206]]], [[('120ÿ', 6), [142, 49, 235, 128, 129, 11]], [('55', 8), [185, 129, 70, 220, 115, 11, 161, 56]], [('', 6), [129, 175, 70, 220, 115, 11]], [('\x8012x5', 1), {'error': 'overflow'}], [(' €ÿ\x80', 5), {'error': 'unencodable'}], [('', 11), [129, 175, 70, 220, 115, 11, 161, 56, 206, 101, 251]], [('0xÿ', 8), [49, 121, 235, 128, 129, 11, 161, 56]], [('99', 3), [229, 129, 70]]], [[('é99\x805', 9), [235, 106, 229, 235, 1, 54, 129, 56, 206]], [('12\x80', 6), [142, 235, 1, 129, 115, 11]], [('5', 2), [54, 129]], [('990', 1), {'error': 'overflow'}], [('599AB€', 8), {'error': 'unencodable'}], [('', 7), [129, 175, 70, 220, 115, 11, 161]], [('xÿ ', 8), [121, 235, 128, 33, 129, 11, 161, 56]], [('995', 11), [229, 54, 129, 220, 115, 11, 161, 56, 206, 101, 251]]]]
labels = ["regression: digit pair codeword", "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 fixtureActualExpectedOutcome
regression: digit pair codeword 0[229, 121, 129, 220, 115][229, 121, 129, 220, 115]Passed
repair trap 1[235, 128, 235, 128, 235, 1, 142][235, 128, 235, 128, 235, 1, 142]Passed
combined fault 2[129, 175, 70, 220, 115, 11][129, 175, 70, 220, 115, 11]Passed
control 3[129, 175, 70, 220, 115, 11, 161, 56, 206, 101, 251][129, 175, 70, 220, 115, 11, 161, 56, 206, 101, 251]Passed
control 4[235, 1, 129, 220][235, 1, 129, 220]Passed
boundary 5{'error': 'overflow'}{'error': 'overflow'}Passed
boundary 6{'error': 'overflow'}{'error': 'overflow'}Passed
control 7[235, 106, 229, 66, 67, 49, 129, 56, 206, 101][235, 106, 229, 66, 67, 49, 129, 56, 206, 101]Passed

SHA-256 / 4fe8830102ab2af1c92d2dba1d2866e3e4332f1183dbfc5555ec23b4518a751e

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 2026-09-29T14:49:47.649672+00:00.

Case digest / 5cc373b6979954bbd04e611cf080bcefffd0fbbca22399d4de3f55badded450d